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Wind Driven Circulation
Surface/Wind Driven Circulation RX Huang, Woods Hole Oceanographic Institution, Woods Hole, MA, USA Ó 2015 Elsevier Ltd. All rights reserved. This article is a revision of the previous edition article by P Bogden and C A Edwards, volume 4, pp 1540–1549, Ó 2003, Elsevier Ltd.
Synopsis Surface motions in the upper ocean include surface waves and wind-driven currents. These motions are driven by surface winds. There is a wave boundary layer in the upper ocean where surface waves dominate. Below this surface boundary layer, the ocean can be conceptually separated into several layers, including the Ekman layer, the mixed layer and the main thermocline, and the thick layer below. These layers are characterized by different dynamics, but they may overlap. The most outstanding feature is the main thermocline, and it can be treated as the base of the wind-driven circulation in the upper ocean.
Introduction Winds on the sea surface provide the major source of energy responsible for motions in the upper ocean over broad spatial and temporal scales, from surface waves and small-scale turbulent motions to large-scale oceanic currents. Although people walking on the beach or on board of ships can easily observe surface waves and small-scale turbulence and currents, the large-scale currents can be studied through well-planned scientific observations only. Wind-driven circulation is a key player in regulating the sea surface temperature and the air– sea heat flux; thus, wind-driven circulation is an important component of the climate system. This article is focused on the dynamic structure of the wind-driven circulation; hence, the feedback to the atmosphere is not discussed here.
Wind Stress Pattern Wind stress on the sea surface is one of the most important driving forces for the oceanic circulation. Wind stress generates small-scale surface waves first; through wave–wave interaction, energy is transferred in phase space, leading to surface waves of long wavelength and large amplitude. However, in comparison with the larger-scale currents, surface waves are considered as small-scale problems and they are not considered as parts of wind-driven circulation discussed in this article. Winds on the sea surface represent the velocity structure at the base of the atmospheric boundary layer. As such, they are directly linked to the circulation above the atmospheric boundary layer, and their pattern reflects the overall structure of the atmospheric general circulation; thus, they have remarkable global-scale structure, Figure 1, where the annual mean winds stress is displayed. The most outstanding feature of the wind stress over the global oceans is the strong westerlies at midlatitudes of both hemispheres, which is the surface expression of the jet stream of the atmospheric circulation. At low latitudes, the trade wind dominates; at the equator, easterlies dominate in the Pacific and Atlantic Oceans, but in the Indian Ocean relatively weak westerlies dominate. For a long time, winds were measured through ship-board instruments over the global oceans. Since the advance of satellite technology, wind speed and direction over the global ocean can be directly inferred from microwave measurements
Encyclopedia of Atmospheric Sciences 2nd Edition, Volume 4
over the sea surface (such as the QuikSCAT data). The common practice in oceanography is to calculate wind stress using the u atm ! u oce jð! u atm ! u oce Þ, bulk formulae sw ¼ rair Cd j! 3 where rair is the air density, Cd z 10 is the empirical drag u oce is the velocity difference between the coefficient, ! u atm ! air and water within the boundary layers. Note that Cd is not a constant, and it varies with the wind speed. The bulk formulae are based on many in-situ measurements; however, the accuracy of the bulk formulae remains to be improved, especially for the case with strong wind. In addition, although in many previous applications the effect of oceanic current were not included in the calculation of wind stress, recent studies indicated that the correction due to the ocean current should be taken into consideration. Wind stress changes with time, and it has a noticeable seasonal cycle over most parts of the world ocean. In particular, seasonal cycle of wind stress in the Indian Ocean and adjacent oceanic regions is quite strong. For example, wind over the Somali and Vietnamese coasts blows in opposite directions during different seasons, Figure 2. The seasonal cycle of wind stress in these areas strongly affects the local upwelling and the strength and direction of coastal currents. Furthermore, wind energy input into surface waves is a strong nonlinear function of wind stress, so that the high frequency components of wind stress make a critical part of contribution to the wind energy input into the ocean. Although monthly mean wind stress can be used to calculate the winddriven circulation with reasonable results, mixed layer property calculation requires wind stress products with high temporal resolution up to 6-hourly wind.
Surface Circulation in the World Ocean Apart from the surface wave boundary, the upmost part of the ocean is occupied by the Ekman layer where the frictional force is balanced by the Coriolis force. Below this relatively thin upper layer, currents in most parts of the world oceans are organized in the form of gigantic gyres, as shown in Figure 3. There are strong subtropical gyres in the North Pacific, North Atlantic, South Pacific, South Atlantic, and the South Indian Oceans. At high latitudes, there are subpolar gyres in the North Pacific and North Atlantic Oceans, and Weddell Sea Gyre and Ross Sea Gyre at the southern edge of the South Ocean.
http://dx.doi.org/10.1016/B978-0-12-382225-3.00280-2
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Figure 2 Seasonal cycle of wind stress in the (a) Somali coast (at 50.125 E, 5.125 N) and (b) South of Vietnam (at 108.125 E, 10.125 N), based on WOA09 data.
These gyres are directly driven by surface winds. Many oceanic currents observed in the oceans are part of the organized winddriven circulation discussed in this article, including the Gulf Stream in the North Atlantic Ocean, the Kuroshio in the North Pacific Ocean, the Brazil Current in the South Atlantic Ocean, the East Australian Current in the South Pacific Ocean, and the Agulhas in the Southwest Indian Ocean. One of the most important features of these winddriven gyres is the western intensification of the currents,
as schematically shown in Figure 3. Although most currents in the ocean interior move relatively slowly, these western boundary currents can reach the speed in excess of 1 m s1. Most importantly, they can carry a huge amount of water. For example, the Gulf Stream transports can reach to 150 Sv (1 Sv ¼ 106 m3 s1). In addition, they carry a large amount of heat and thus play a critically important role in setting up the poleward heat transport in the Earth’s climate machinery.
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The fast-moving western boundary currents were discovered long time ago by marine navigators. Benjamin Franklin and Timothy Folger in 1769–70 created the first chart of the Gulf Stream, which was widely used by navigators going on cruises between European countries and North America. Even at the present day, their chart of the Gulf Stream seems quite accurate in prescribing the large-scale feature of this fast-moving current system. The dynamical explanation of such fast-moving currents or the so-called western intensification had to wait for more than 170 years following this chart. At low latitudes, there are strong equatorial current systems in the Pacific, Atlantic, and Indian Oceans, and they play critical roles in the oceanic circulation and climate system. There is also a strong Antarctic Circumpolar Current (ACC), which is the only circum-earth current system under the present continental setting. In addition, there are many other surface currents, which connect surface circulation in different parts of the world oceans, such as the Indonesian Throughflow and the North Atlantic Current. The shape of subtropical gyres is somewhat similar to the pattern of wind stress in the subtropical basins. The similarity between the circulation patterns in the atmosphere and oceans is deeply rooted in the dynamics. In fact, as will be explained shortly, the formulation of the gyration is the consequence of potential vorticity balance in a closed basin; thus, the wind stress curl is the essential ingredient of wind-driven gyres.
Thermal Structure in the Upper Ocean The circulation in the upper ocean is closely related to the density structure. Seawater density is controlled by temperature and salinity; however, over much of the warm near-surface waters, temperature dominates. Therefore, density structure
can also be inferred from temperature structure in the oceans. There is a mixed layer on the top of the ocean, where the temperature, salinity, and density is vertically nearly homogenized. Water properties and depth of the mixed layer have a profound annual cycle. The mechanical energy required to sustain the turbulent motions in the mixed layer is provided by the wind stress applied to the sea surface. In particular, wind stress inputs about 60 TW (1 TW ¼ 1012 W) of mechanical energy into the surface waves. The exact amount of this energy remains a topic of intensive research, and its pathway in the ocean remains unclear. However, it is believed that most part of this energy is dissipated within the mixed layer, leaving only a quite small portion of it to be transformed into the deeper part of the ocean, probably in forms of near-inertial oscillations. In addition, convection due to surface cooling or salt rejection during sea ice formation can also provide kinetic energy sustaining turbulent motions in the mixed layer. It is to emphasize that, however, the kinetic energy associated with turbulent motions due to convection is converted from the gravitational potential energy originally stored in the system. In fact, convection in the ocean cannot create mechanical energy. Another outstanding feature in the thermal structure in the upper kilometer of the world ocean is the main thermocline. The thermocline is defined as a layer within the water column where the vertical gradient of temperature is a local maximum. There are four major types of thermoclines in the ocean: diurnal, seasonal, main, and abyssal thermoclines. The diurnal thermocline is associated with the diurnal cycle of the mixed layer and it exists in the upper few tens of meters in the ocean; the seasonal thermocline is associated with the seasonal cycle of the mixed layer, and it extends from the base of the diurnal thermocline to the depth of a couple of hundred meters except
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in some special locations where wintertime convection can reach to great depths. The main thermocline is below the seasonal thermocline at depths of 200–800 m. As a result, it is not greatly affected by the seasonal cycle of the mixed layer; hence, it is also called the permanent thermocline. In addition, in part of the world oceans there is abyssal thermocline associated with abyssal circulation. Wind-driven circulation can exist in either a homogeneous ocean or a stratified ocean. Wind-driven circulation in a homogeneous ocean is very weak because the volumetric flux of the circulation is uniformly distributed over the entire depth of the ocean. On the other hand, due to the existence of strong stratification associated with the main thermocline, winddriven circulation is mostly confined to an upper moving layer above the main thermocline. As a result, currents associated with wind-driven circulation in a stratified ocean can be greatly enhanced. In most parts of the world oceans, seawater density is primarily controlled by temperature, with salinity playing a secondary role. Therefore, the main thermocline is also closely linked to the main pycnocline. Note that dynamically the main pycnocline is more directly relevant to the dynamics of the oceanic circulation; however, the main thermocline itself is closely linked to temperature changes in the atmosphere, hence thermocline is a term often used in scientific study of the oceanic circulation and climate changes. The typical structure of the main thermocline can be seen through an east–west temperature section. As shown in Figure 4, the main thermocline is located around the depth of 200 m at the eastern boundary, and gradually slopes down to the depth of 600 m in the North Pacific Ocean and 800 m in the North Atlantic Ocean. As shown in Figure 4, warm water in the upper ocean is separated from the cold water in the deep ocean by a layer of relative shape temperature gradient associated with the main thermocline. In the interior part of the ocean, large-scale currents obey geostrophy. Using geostrophy and thermal wind relation, the
direction of large-scale current can be inferred from temperature or density sections as follows. Since strong wind-driven current is confined in the upper kilometer of the ocean, one can assume that water at great depth is motionless. For example, one can assume that horizontal velocity at the depth of 2.5 km is negligible, and the corresponding horizontal pressure gradient is nearly zero at this depth. As shown in Figure 4, water on the right-hand side of the ocean basins is colder and thus denser than that on the left-hand side. Using the thermal wind relation and the hydrostatic approximation, one comes to the conclusion that at depth shallower than 2.5 km pressure gradient force in the oceanic interior is pointed eastward. According to geostrophy, to balance the pressure gradient force the Coriolis force must point westward; thus, current in the ocean interior should move equatorward. On the other hand, near the western boundary the slope of isopycnal flips sign and becomes quite steep, indicating strong and poleward narrow western boundary currents. Thus, temperature and the corresponding density structure shown in Figure 4 can be interpreted as the sign of the western intensification. Density structure along the meridional section reveals another important dynamic feature, Figure 5. The center of the wind-driven circulation on each isopycnal surface is roughly the deepest part of the isopycnal surface. As shown in Figure 5, the center of the circulation moves northward with increasing density. This is called the poleward intensification of the wind-driven subtropical circulation. This is also linked to the recirculation of the subtropical gyre, as will be discussed shortly. In general, near the equator thermocline is much shallower. Since the Coriolis force vanishes near the equator, the equatorial thermocline is directly linked to the equatorial zonal wind stress. In a steady state, at the sea level the zonal wind stress on surface is balanced by the pressure gradient force associated with the zonal sloping sea surface. In both the Pacific and Atlantic Oceans, easterlies prevail near the equator.
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As a result, equatorial thermocline in these two basins slopes downward from east to west. On the other hand, the main thermocline in the Indian Ocean slopes down eastward because wind in the Indian Ocean is primarily westerly. This combination of equatorial winds leads to a condition favorable for the formation of a large warm pool with the main thermocline sits at the depth of 200 m in the western equatorial Pacific. In the east side, there is a cold tongue in both the equatorial Pacific and Atlantic Oceans, upper panel of Figure 6. In the meridional section, the main thermocline appears in the form of a dumbbell, lower panels of Figure 6. The bowlshaped main thermocline at midlatitudes in these three basins is outstanding. It is clear that the main thermocline is deepest in the South Indian Ocean. The main thermocline in the North Atlantic Ocean is deeper than that in the North Pacific Ocean. The depth of the main thermocline in the world oceans is closely linked to the wind-driven circulation in the upper ocean. In the world oceans, there are five subtropical gyres and they can be clearly identified from the basin-scale bowl-shaped main thermocline, as shown in Figure 7. Note that the main thermocline is a conceptual layer only; thus, such a subsurface vertical temperature gradient maximum may not exist at any specific location. As will be shown shortly, the simple reduced gravity model predicts that the depth of the main thermocline is proportional to the zonal integration of the Ekman pumping rate and inversely proportional to the stratification in the upper ocean. For example, in the Pacific Ocean relatively low salinity in the upper ocean leads to a relatively strong stratification in the upper ocean and thus a shallow main thermocline. On the other hand, high salinity water in the Atlantic and Indian Ocean leads to relatively weak stratification and relatively deep main thermocline.
Theory of the Wind-Driven Circulation Ekman Layer There is an Ekman layer in the upper ocean. The Ekman layer is defined as the surface boundary layer in which the frictional force is balanced by Coriolis force. Ekman in 1905 first formed the idea of such a boundary layer in the ocean. Winds input a large amount of mechanical energy, on the order of 3 TW, which is used to maintain motions in the Ekman layer against friction. Within the Ekman layer, the wind stress is transformed downward through eddy-induced horizontal momentum flux. A major uncertain part of the Ekman layer theory is the vertical eddy viscosity Av. The classical theory of Ekman layer assumes that Av is isotropic and has a constant value over the whole depth of the layer. Under such an assumption, the horizontal velocity for the Ekman layer in a steady state appears in the form of a spiral, quite similar to that in the atmospheric boundary layer. Observing the Ekman layer in the ocean was a great challenge due to the stance of strong surface waves and turbulence in the upper ocean. Ekman layer predicted by the classical theory was confirmed through observation only in the 1980s. Observations indicated that vertical eddy viscosity Av is not constant. In fact, in-situ observations indicated that vertical eddy viscosity decays with increasing depth following some negative power laws or exponentially decaying laws. If Av is not constant or isotropic, the shape of the Ekman spiral can be different from that predicted by the classical theory. The horizontal volume transport integrated over the depth of the Ekman layer is independent of the vertical eddy viscosity; this volume transport is perpendicular to the wind stress and pointing to the right-hand side (in the Northern Hemisphere); ! ¼ ! z ! s =f r , where it can be written in the form of V Ekman
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density. The zonally integrated Ekman transport in the three basins is on the order of 10–20 Sv (Figure 8(a)). As it is inversely proportional to the Coriolis parameter, it becomes unbounded near the equator, indicating that the theory of Ekman layer does not apply to the equatorial band. Thus, there are large horizontal mass transports in the upper ocean, which can play key roles in transporting heat, freshwater, and other tracers. Since it is directly proportional to the wind stress, such transports can change in response to variability in the atmospheric circulation and climate. Due to variation of both wind stress and Coriolis parameter f, Ekman transport varies with geographic location. The convergence (divergence) of Ekman transport leads to the Ekman pumping, wEkman ¼ curl(s/fr0). In general, Ekman pumping velocity is quite small, on the order of 106 m s1, which is equivalent to 0.08 m per day or 30 m per year. However, in subtropical basin interiors this seemingly small vertical velocity leads to an equatorward geostrophic flow in the subsurface layer, and thus dynamically sets up the gigantic wind-driven circulation in the subtropical basins; while in the subpolar basin, Ekman pumping is upward, and it leads to a poleward geostrophic flow in the subsurface layer and thus the cyclonic subpolar gyres. Coastal upwelling/downwelling is induced by long-shore wind. If wind blows along the coast, off-shore (or on-shore) Ekman transport must be compensated by upwelling (downwelling) along the coast. Coastal upwelling can bring nutrientrich water from depth to the surface; thus, high productivity and good fishing grounds along some of the coastlines are closely linked to strong along-shore wind. Since along-shore wind often changes with the season, the strength of coast upwelling also has strong seasonal cycle, and hence the biological productivity. Some of the sites of strongest seasonal cycle of the coastal upwelling are shown in Figure 2. The seasonal cycle of wind stress is strong in the Indian Ocean. In particular, the seasonal cycle of wind stress east of Somalia is very strong, so that coastal upwelling there has a very strong seasonal cycle. In fact, the seasonal cycle of wind is so strong that the direction of the Somali current reverses during the seasonal cycle.
Sverdrup Transport of the Wind-Driven Circulation The simplest way to describe the wind-driven circulation is to treat the circulation in the upper ocean in terms of a single layer; thus, the wind stress is to be treated as a body force uniformly distributed within this layer. The layer integrated volume flux satisfies the Sverdrup relation: bhv ¼ ðvsy =vx vsx =vyÞ=r0 :
[1]
where b ¼ df/dy, h is the layer thickness, v is the meridional velocity, (sx, sy) are the wind stress components, and r0 is the constant reference density. The Sverdrup relation is essentially a potential vorticity equation. According to this equation, negative wind stress curl in the subtropical basin drives an equatorward flow in the basin interior. A zonal integration of this relation leads to the Sverdrup streamfunction (or Sverdrup transport). The Sverdrup transport includes contributions due to surface Ekman transport and the geostrophic transport above the thermocline layer. As an example, Figure 9 shows the Sverdrup transport in the Pacific Ocean. There are clearly the subtropical gyres in both the North and South Pacific Oceans, with the maximum streamfunction on the order of 40 Sv. In addition, there is a subpolar gyre at the northern high latitudes and the equatorial circulation system at low latitudes. Note that the Sverdrup relation is valid for the steady state circulation only.
Theories of the Wind-Driven Gyres The energetics of wind-driven circulation Wind-driven gyres are the direct result of surface wind forcing. These gigantic circulation systems are sustained by mechanical energy input from the surface winds. Wind energy input to the ocean can be separated into several categories. First and most importantly, the total amount of mechanical energy input to the large-scale surface currents is estimated as 1 TW, and most of such energy is put into the South Ocean and other regions of fast currents, such as the Gulf Stream and Kuroshio. Second, the wind energy input to the Ekman layer is about 3 TW; however,
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Sverdrup transport in Pacific (Sv) 50
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Sverdrup transport in the Pacific Ocean, based on QuikSCAT data.
most of this energy is used to overcome the friction in the Ekman layer. Third, surface waves receive approximately 60 TW from the surface wind; however, this huge amount of mechanical energy is mostly dissipated within the surface wave boundary layer. There is the Langmuir circulation in the upper ocean, which is closely linked to surfaced waves. Surface waves and Langmuir circulation play key roles in regulating the surface layer dynamics and the air–sea interaction. In addition, a small amount of mechanical energy received by surface waves can penetrate through the base of the mixed layer and thus contribute to mixing in the subsurface layer; but, the pathway and this energy remains unclear at this time. Fourth, the sea level atmospheric pressure varies with time; combining with the vertical motions of the sea surface, this leads to a mechanical energy input to the ocean. The exact amount of this energy input remains unclear, and current estimate puts it on the order of 0.01–0.04 TW. However, the effect of sea level pressure change is mostly projected into the barotropic mode in the oceans; thus, its effect on the surface motions is small and may be negligible.
The reduced gravity model The structure of the wind-driven circulation can be explored in terms of the simple reduced gravity model. The basic idea is to treat the main pycnocline as a step function in density coordinate. Assume that the upper and lower layers have constant density r1 and r2, and the lower layer is infinitely deep and motionless. A commonly used parameter in such a model is the reduced gravity, defined as g0 ¼ g(r2 r1)/r0. The simple formulation of the reduced gravity model allows either analytical or straightforward numerical solutions. For simplicity, solutions shown here are obtained through
numerical integration. The model is started from initial states with a fixed amount of warm water in the upper layer and it is forced by a cosine wind stress. The first case is for a model on the f-plane, i.e., f ¼ const. is assumed. As shown in upper panels of Figure 10, both the layer thickness and transport of this solution are symmetric with respect to the E–W and N–S directions. The second case is for a model on a beta-plane (i.e., f ¼ f0 þ b(y y0)), and the corresponding solution is asymmetric with respect to the E–W direction, lower panels in Figure 10. In fact, the current near the western boundary is much stronger than in the interior, and this phenomenon is called the western intensification. The dramatic contrast between a model on the f-plane and a model on the beta-plane was first discovered by Stommel in 1948, who recognized the important meaning of such a difference and made a link between this phenomenon and the Gulf Stream and other strong currents observed in the world oceans. The reason of the western intensification can be explained in terms of the simple reduced gravity model. For the steady flow in the oceanic interior, the lowest order balance of the circulation can be examined in a beta-plane model as follows. Assuming a steady state and omitting the inertial terms and friction terms, the vorticity equation is reduced to Sverdrup relation eqn [1]. Thus, the streamfunction satisfies the Sverdrup relation j ¼ ðvsx =vy vsy =vxÞðxe xÞ=br0 ; and the layer thickness satisfies the following equation " y # 2f 2 sx s 2 2 h ¼ he þ 0 ðxe xÞ; g r0 b f y f x
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where he is the layer thickness along the eastern boundary, b ¼ df/dy is the meridional gradient of the Coriolis parameter.
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The advantage of the reduced gravity model is that it provides a clear description for both the volumetric transport and the depth of the main thermocline. Note that although the quasigeostrophic theory has been widely used for the description of wind-driven gyres in many previous published textbooks and papers, such a description is inaccurate because the winddriven circulation involves large deviation of stratification, so that the wind-driven gyration is beyond the validity of the basic assumptions made in the quasi-geostrophic theory. In a single-moving-layer model for a subtropical basin, the equatorward transport in the basin interior must be closed through the addition of either a western/eastern boundary layer, which can transport the mass poleward. Furthermore, in the Northern hemisphere there is a large amount of negative vorticity input from wind stress over the subtropical basin. In a steady state, the basin-integrated vorticity budget must be balanced; thus, there should be a large source of positive vorticity along the lateral boundaries of the basin. A simple dynamical analysis indicates that only the western boundary can play the role of generating the positive vorticity and thus balancing the vorticity budget for the wind-driven circulation. The existence of western boundary layer manifests in the form of the so-called western intensification. Stommel first postulated a boundary layer for a reduced gravity model in terms of bottom friction. He assumed that friction is linearly proportional to the horizontal velocity in the moving layer. In more accurate terminology, his bottom friction can be generalized as the interfacial friction, which is assumed to be linearly proportional to the velocity difference
between the upper and lower layers. Such an interfacial friction can be interpreted as a crude parameterization of baroclinic instability. Another possible type of boundary current is the lateral friction model postulated by Munk. In addition, Charney and Morgan postulated the inertial boundary layer theory. The structure of western boundary currents postulated in these theories can be examined analytically. Since the western boundary current is rather narrow in the cross-stream direction, the corresponding control equations can be simplified by the standard boundary layer technique. In fact, the cross-stream momentum equation can be simplified in terms of the semigeostrophic approximation, and simple analytical solutions can be obtained, which can be used to illustrate the essential dynamics of the western boundary current. All these boundary layer theories can be used to close the wind-driven gyres. A close reexamination reveals that western boundary currents observed in the ocean are primarily controlled by the inertial terms, i.e., these boundary currents are essentially inertial western boundary layer in nature. The frictional force is of importance only within a relatively thin sublayer. The advantage of the reduced gravity model is that it can predict the basin-wide distribution of the main thermocline depth. The structure of the wind-driven circulation in a closed basin on a beta-plane is shown in the lower panels of Figure 10, where the wind-driven circulation in the subtropical gyre consists of the interior part and the Stommel frictional western boundary current. In this example, the horizontal distribution of the thermocline depth can be seen clearly in
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a reduced gravity model, as shown in Figure 10(c). For most part of the basin away from the western boundary the solution is described by the interior dynamics discussed above. On the other hand, the strong northward current appears along the western boundary, i.e., the western intensification.
strong western boundary currents after separation, such as the Gulf Stream and Kuroshio. Simulating the case with isopycnal outcropping is a critically important step forward in simulating the wind-driven circulation and the associated density structure in the ocean.
Layer model with outcropping
The ventilated thermocline
An advantage of the reduced gravity model is its capability of capturing the strong nonlinearity associated with horizontal variability of stratification, in particular for the case with isopycnal outcropping. Due to the strong wind forcing, surface heat and freshwater fluxes, isopycnals outcrop at high latitudes. A fundamental assumption made in the quasi-geostrophic theory is that variation of the stratification in the horizontal direction is very small; thus, such theory is not suitable for describing the large-scale dynamics associated with layer outcropping. For a model with finite amount of warm water in the upper layer, in part of the basin the layer thickness becomes thinner and thinner as the wind forcing is enhanced. However, when the continuity equation for the layer thickness is transformed into finite difference forms, using the commonly used central difference scheme, the layer thickness may become negative. In order to avoid such situation, the so-called positive-definite scheme should be used. A typical solution with outcropping is shown in the upper panels of Figure 11, where the upper layer vanishes along the outcrop line near the northwest corner of the basin. North of the outcrop line the lower layer outcrop; within the framework of the single-moving-layer model, there is no motion within the outcrop window. A strong internal boundary current is formed along the edge of the outcrop line, which mimics the
Although simple reduced gravity models can provide essential information about the wind-driven circulation, such singlemoving layer models give no information about the vertical structure of the circulation in the upper ocean. In pursuing the structure of the wind-driven circulation, the theory of thermocline gradually formed, which is aimed at explaining the three-dimensional structure of the wind-driven circulation. From the beginning of thermocline theory, two paradigms developed independently: the diffusive thermocline by Stommel and Robinson and ideal-fluid thermocline by Welander. The diffusive thermocline theory interprets the main thermocline as an internal thermal boundary layer, and thus emphasizes the critical role of diffusion in forming the main thermocline. On the other hand, the ideal-fluid thermocline theory interprets the main thermocline in terms of ideal-fluid theory, and emphasizes the critical role of adiabatic deformation of the stratification set up by a background thermohaline circulation. Welander actually produced some simple and elegant solutions based on the ideal-fluid thermocline theory. In the beginning, the theory of diffusive thermocline was pursued by many researchers, apparently due to the seemingly more complete dynamical framework by incorporating the diffusion term. Due to the complicated dynamics involved, exact analytical solutions for the diffusive thermocline were
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Oceanographic Topics j Surface/Wind Driven Circulation hard to find. Instead, most studies were aimed at finding different kinds of similarity solutions. The searching for similarity solutions was summed up by Veronis in 1970s. On the other hand, the ideal-fluid thermocline theory was unpopular because it seemed rather incomplete for not including the diffusion terms. The major deficit of similarity solutions is that they cannot satisfy the essential dynamical constraints, such as the Sverdrup relation; thus, searching for nonsimilarity solutions was a main research frontier. In addition, recent in-situ measurements indicate that diffusion in the main thermocline is rather weak; thus, the theory of ideal-fluid thermocline regains its momentum. One of the conceptual difficulties in pursuing an ideal-fluid theory for the thermocline is as follows. In an ideal-fluid ocean, the interfacial friction must be small and negligible; in such a framework, how are the subsurface layers set in motion? The major breakthroughs took place in early 1980s. Rhines and Young postulated the potential vorticity homogenization theory. They argued that under strong wind forcing, potential vorticity in the subsurface layers is homogenized. As a result, closed potential vorticity contours appear in the subsurface layer, along which water parcels can move freely according to the ideal-fluid thermocline theory. Furthermore, under the assumption of infinitesimal dissipation of potential vorticity, potential vorticity within the close contours are homogenized toward the value along poleward boundary of the circulation. Therefore, a unique solution, which is stable to small perturbations, exists. Another major breakthrough is the theory of ventilated thermocline. In the stratified ocean, most isopycnals outcrop at high latitudes in winter. The outcropping phenomenon can be clearly seen even in annual mean meridional section of temperature and density, as shown in Figures 5 and 6. Iselin in 1939 first postulated the idea that water masses are formed at
the sea surface in late winter, and subsequently pushed downward through Ekman pumping. His physical insightful idea and Welander’s framework of ideal-fluid thermocline were not pursued for a long time. Apparently inspired by the success of the potential vorticity homogenization theory, these two ideas were combined and extended into a beautiful theory of the ventilated thermocline by Luyten, Pedlosky, and Stommel. They formulated the model in terms of three-moving layers plus a deep stagnant layer in the abyss. At lower latitudes, the uppermost layer is exposed to Ekman pumping; however, with the increase of latitudes, upper layers outcrop and lower layers are directly exposed to Ekman pumping. At higher latitudes, Ekman pumping drives the outcropping lower layers in motions, and ventilation and subduction take place. Ventilation and subduction are the basic elements of the wind-driven circulation in a stratified ocean (Figure 12). The ocean is conceptually separated into four layers; an Ekman layer of the top (not drawn in this sketch), the upper and lower layer below the Ekman layer, and a thick and stagnant layer at the bottom. Wind stress induces the Ekman pumping at the base of the Ekman layer. The upper/lower layer is directly forced when it is exposed to Ekman pumping, as indicated by vertical arrows on the top of the layer. The upper layer outcrops along the zonal outcrop line; thus, north of the outcrop line the lower layer is directly driven by the Ekman pumping. Since the lower layer is exposed to the surface force, we also call this as the ventilation of the lower layer. As a result, there is an anticyclonic circulation in this layer, indicated by the blue curved arrows. Poleward of the outcrop line the meridional volume transport in this layer satisfies the Sverdrup constraint. Equatorward of the outcrop line, the lower layer moves underneath the upper layer, and this is called subduction. Since there is motion in the lower layer north of the outcrop line, there is no reason why it should stop movement after it is subducted; thus, it should continue its anticyclonic movement Ekman pumping leads to the wind-driven gyres
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after subduction, as indicated by the dashed lines with arrow. South of the outcrop line, the upper layer is directly forced by Ekman pumping. Because both layers are in motion, in this regime the Sverdrup constraint should apply to the meridional volume transport integrated over the total depth of these two layers. In order to determine the solution in this regime, one more dynamical constraint is required. For ideal-fluid motion, the potential vorticity in the second layer should be conserved when it is not directly forced by Ekman pumping. A simple and elegant solution of this problem is postulated in the ventilated thermocline theory. In the ocean interior, relative vorticity is negligible for large-scale motions; thus, potential vorticity for a two-moving layer model is q1 ¼ f/h1 and q2 ¼ f/h2. In fact, keeping the potential vorticity of the second layer at its value when it is subducted along the outcrop line gives the additional dynamical constraint for solving the problem. The theories of potential vorticity homogenization and ventilated thermocline represent major breakthroughs in understanding the three-dimensional structure of wind-driven circulation. In particular, the discovery of shadow zone, the ventilated zone, and the pool zone bought about completely new physical insight for the wind-driven circulation in the upper ocean. As an example, a two-layer ventilated thermocline model is shown in the lower panels of Figure 11 for a northern hemisphere model ocean, in which the zonal dashed lines indicate the outcropping line of the upper layer. The model is forced by a simple sinusoidal Ekman pumping field, which works on the layer exposed to the upper surface forcing, i.e., the lower layer north of the outcrop line and the upper layer south of the outcrop line. North of the outcrop line, the lower layer is exposed to the Ekman pumping, and an anticyclonic circulation can be clearly seen north of the outcrop line. South of the outcrop line, the lower layer is subducted; however, it continues its south-westward movement as shown in Figure 11(d). The upper layer has zero thickness north of the outcrop line; but, south of the outcrop line it is directly exposed to Ekman pumping. As shown in Figure 11(d), geostrophic flow in the lower layer after subduction can be separated into three dynamical zones: the pool zone near the western boundary, the shadow zone near the eastern boundary, and the ventilated zone in the middle. An important conceptual breakthrough in the ventilated thermocline theory is the existence of a shadow zone within the subsurface layer near the eastern boundary. A strong kinematic condition along the eastern boundary is the no-flow-penetration condition along the eastern boundary. Thus, the subsurface layer should have a constant thickness h2 along the eastern boundary. If the eastern boundary were a streamline, then the corresponding potential vorticity f/h2 should be constant along the eastern boundary. Because the Coriolis parameter declines equatorward, f/h2 cannot be constant. Therefore, the eastern boundary cannot be a streamline for the subsurface layer; instead, there should be a shadow zone near the eastern boundary where the subsurface layers are stagnant. From hydrographic data, the existence of shadow zone can be inferred from the appearance of extremely low oxygen levels at the depth of 1000 m and near the eastern boundary at low latitudes. There are two other dynamical zones in Figure 11(d). Potential vorticity in the ventilated zone is sent up along the
outcrop line when the lower layer is subducted. Pool zone is defined by streamlines emerging from the western boundary. As such, potential vorticity in the pool zone is not set up by wind-driven forcing within the basin. Instead, it is set up by either potential vorticity homogenization or other dynamics. The original Sverdrup relation applies for a single-movinglayer model only. For a model with multiple moving layers, it is extended to an integral constraint for the meridional volume flux for all the moving layers. The ventilated thermocline theory was generalized to a theory for the continuously stratified ocean by Huang. Such a model provides density and current structure in the ocean, which are comparable with observations. Note that the Sverdrup relation applies for the steady circulation only. There are two important issues related to the application of this relation. First, the steady solution of winddriven circulation in a basin is established after the wave adjustment. The volume flux over the whole depth of the ocean is established after the barotropic Rossby waves passing through. Since barotropic Rossby waves move quite fast, the timescale for the barotropic circulation to be established is in the order of 7–10 days for a tropical basin. However, the baroclinic Rossby waves move relatively slowly, with the speed in the order of 0.1 m s1. Thus, for the midlatitudes of the North Atlantic or the North Pacific Ocean, the steady circulation of the first baroclinic mode takes about 10–20 years to be established. In general, the time-dependent solution of the wind-driven circulation can be calculated by the integrating the time delayed Ekman pumping rate. Furthermore, the contribution due to eddies is not included in the Sverdrup relation. In the ocean, eddies give rise to nonlinear contribution to the meridional volume flux. As a result, meridional volume flux across the zonal section can deviate from the Sverdrup relation.
Combination of Surface and Deep Currents Currents in the North Atlantic Ocean Although surface currents are mostly controlled by wind stress, the thermohaline circulation, which occupies the whole depth of the ocean also manifests in the upper ocean. The circulation in the North Atlantic Ocean is a good example. As shown in Figure 13, there is a warm current crossing the equator. This current moves northward and joins the warm water in the Gulf Stream, which exists as an internal boundary current separating the subtropical gyre to the south and the subpolar gyre to the north. It is important to note that the wind-driven gyre in the North Atlantic Ocean consists of the linear Sverdrup interior and the recirculations. The recirculation regimes are located roughly where the surface expression of the western boundary current emerges from the western boundary region by separation from the coast, where the nonlinearity of the circulation is not negligible. As a result, the Sverdrup dynamics does not apply and eddy activity associated with the nonlinear inertial terms become large and dominating. Instead of the laminar fluid like current, at any given time the Gulf Stream encompasses many large-amplitude eddies. Furthermore, the total volumetric flux in the Gulf Stream recirculation regime is in the order of 150 Sv, much larger than
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the value predicted from the linear Sverdrup theory. This large volume transport includes contribution of 30–35 Sv due to the linear wind-driven circulation, about 15–20 Sv from the returning flow of the deep thermohaline circulation, and approximately 90–100 Sv due to the nonlinear dynamics (in forms of the southern recirculation and the north recirculation), Figure 13. The return flow of the thermohaline circulation continues its poleward movement and appears in the form of the North Atlantic Current, which moves to the high latitude part of the North Atlantic basin and eventually feeds the deepwater formation.
The Antarctic Circumpolar Current There is a strong circum-earth current system in the South Ocean, and it is called the ACC. There is no meridional boundary in the Southern Ocean. As a result, there is no zonal pressure gradient force to maintain any meridional geostrophic flow; thus, the classical Sverdrup dynamics does not apply to ACC. The formation of ACC depends on many dynamical factors, including wind stress, wind stress curl, the shape of coastline and bottom topography, the surface thermohaline forcing, and, most importantly, the contribution of mesoscale eddies. In particular, mesoscale eddies play capital roles in setting the structure of ACC. ACC plays an important role in regulating the global oceanic circulation and climate. However, the complete description of the ACC dynamics requires an indepth discussion and it is beyond the scope of this article.
past decade. In fact, physical oceanography is now entering the eddy resolving era. By definition, two kinds of eddies are now the focus of research. The mesoscale eddies have horizontal scales from 10 to 500 km and vertical scales from tens to hundreds of meters, and the submesoscale eddies have horizontal dimensions on the order of 1–10 km and vertical scales on the order of tens of meters or smaller. The ocean is a turbulent environment, and eddy motions are one of the fundamental aspects of oceanic circulation. In fact, it is estimated that the total amount of eddy kinetic energy is about 100 times larger than that of the mean flow. The roles of mesoscale and submesoscale eddies in the oceanic circulation and climate remain to be explored. It is expected that with the great technical advances in satellite observation and global observation program like ARGO, eddy study is pushed forward with a great speed. Studies of these eddies, including observations, theory, laboratory experiments, and parameterization in numerical models, will be the most productive research frontiers for the next 10–20 years.
See also: Air Sea Interactions: Surface Waves. Boundary Layer (Atmospheric) and Air Pollution: Ocean Mixed Layer. Oceanographic Topics: Thermohaline Circulation. Satellites and Satellite Remote Sensing: Surface Wind and Stress.
Further Reading Mesoscale Eddies Most classical theories of wind-driven circulation treat the circulation in terms of laminar fluids, with the roles of eddies neglected. The framework of three-dimensional structure of gyre-scale wind-driven circulation was completed in 1980s, represented by the multilayer ventilated thermocline theory and its extension to the case of continuously stratified ocean. These theories provided the lowest order structure of the winddriven circulation and laid down the foundation for the further development of oceanic circulation. With the advance in technology in observation, theory, and numerical models, the situation has changed rapidly over the
Chelton, D.B., Schlax, M.G., Samelson, R.M., 2011. Global observations of nonlinear mesoscale eddies. Progress in Oceanography 91, 167–216. Ekman, V.W., 1905. On the influence of the earth’s rotation on ocean currents. Arkiv för Matematik, Astronomi och fysik 2, 1–52. Gill, A.E., Green, J.S.A., Simmons, A.J., 1974. Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies. Deep Sea Research 21, 499–528. Huang, R.X., 2010. Ocean Circulation, Wind-Driven and Thermohaline Processes. Cambridge Press. Luyten, J., Pedlosky, J., Stommel, H.M., 1983. The ventilated thermocline. Journal of Physical Oceanography 13, 292–309. Olbers, D., Borowski, D., Völker, C., et al., 2004. The dynamical balance, transport and circulation of the Antarctic Circumpolar Current. Antarctic Science 16 (4), 439–470. Pedlosky, J., 1996. Ocean Circulation Theory. Springer-Verlag, Heidelberg.
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Pedlosky, J., 2006. A history of thermocline theory. In: Jochum, M., Murtugudde, R. (Eds.), Physical Oceanography Developments since 1950. Springer, New York, pp. 139–152. Price, J., Weller, R.A., Schudlich, R.R., 1987. Wind-driven ocean currents and Ekman transport. Science 238, 1534–1538. Qiu, B., 2001. Kuroshio and Oyashio currents. In: Encyclopedia of Ocean Sciences. Academic Press, pp. 1413–1425. Rhines, P.B., Young, W.R., 1982. A theory of the wind-driven circulation. I. Mid-ocean gyres. Journal of Marine Research 40 (Suppl.), 559–596. Richardson, P., 1980. Benjamin Franklin and Timothy Folger’s first printed chart of the Gulf Stream. Science 207 (4431), 643–645. http://dx.doi.org/10.1126/science.207. 4431.643.
Stommel, H., 1948. The western intensification of wind-driven ocean currents. Transactions of the American Geophysical Union 29, 202–206. Veronis, G., 1969. On theoretical models of the thermocline circulation. Deep Sea Research 16 (Suppl), 301–323. Weller, R.A., Bigorre, S.P., Lord, J., Ware, J.D., Edson, J.B., 2012. A surface mooring for air–sea interaction research in the Gulf Stream. Part I: Mooring design and instrumentation. Journal of Atmospheric and Oceanic Technology 29, 1363–1376. http://dx.doi.org/10.1175/JTECH-D-12-00060.1.
Synopsis Surface motions in the upper ocean include surface waves and wind-driven currents. These motions are driven by surface winds. There is a wave boundary layer in the upper ocean where surface waves dominate. Below this surface boundary layer, the ocean can be conceptually separated into several layers, including the Ekman layer, the mixed layer and the main thermocline, and the thick layer below. These layers are characterized by different dynamics, but they may overlap. The most outstanding feature is the main thermocline, and it can be treated as the base of the wind-driven circulation in the upper ocean.
Introduction Winds on the sea surface provide the major source of energy responsible for motions in the upper ocean over broad spatial and temporal scales, from surface waves and small-scale turbulent motions to large-scale oceanic currents. Although people walking on the beach or on board of ships can easily observe surface waves and small-scale turbulence and currents, the large-scale currents can be studied through well-planned scientific observations only. Wind-driven circulation is a key player in regulating the sea surface temperature and the air– sea heat flux; thus, wind-driven circulation is an important component of the climate system. This article is focused on the dynamic structure of the wind-driven circulation; hence, the feedback to the atmosphere is not discussed here.
Wind Stress Pattern Wind stress on the sea surface is one of the most important driving forces for the oceanic circulation. Wind stress generates small-scale surface waves first; through wave–wave interaction, energy is transferred in phase space, leading to surface waves of long wavelength and large amplitude. However, in comparison with the larger-scale currents, surface waves are considered as small-scale problems and they are not considered as parts of wind-driven circulation discussed in this article. Winds on the sea surface represent the velocity structure at the base of the atmospheric boundary layer. As such, they are directly linked to the circulation above the atmospheric boundary layer, and their pattern reflects the overall structure of the atmospheric general circulation; thus, they have remarkable global-scale structure, Figure 1, where the annual mean winds stress is displayed. The most outstanding feature of the wind stress over the global oceans is the strong westerlies at midlatitudes of both hemispheres, which is the surface expression of the jet stream of the atmospheric circulation. At low latitudes, the trade wind dominates; at the equator, easterlies dominate in the Pacific and Atlantic Oceans, but in the Indian Ocean relatively weak westerlies dominate. For a long time, winds were measured through ship-board instruments over the global oceans. Since the advance of satellite technology, wind speed and direction over the global ocean can be directly inferred from microwave measurements
Encyclopedia of Atmospheric Sciences 2nd Edition, Volume 4
over the sea surface (such as the QuikSCAT data). The common practice in oceanography is to calculate wind stress using the u atm ! u oce jð! u atm ! u oce Þ, bulk formulae sw ¼ rair Cd j! 3 where rair is the air density, Cd z 10 is the empirical drag u oce is the velocity difference between the coefficient, ! u atm ! air and water within the boundary layers. Note that Cd is not a constant, and it varies with the wind speed. The bulk formulae are based on many in-situ measurements; however, the accuracy of the bulk formulae remains to be improved, especially for the case with strong wind. In addition, although in many previous applications the effect of oceanic current were not included in the calculation of wind stress, recent studies indicated that the correction due to the ocean current should be taken into consideration. Wind stress changes with time, and it has a noticeable seasonal cycle over most parts of the world ocean. In particular, seasonal cycle of wind stress in the Indian Ocean and adjacent oceanic regions is quite strong. For example, wind over the Somali and Vietnamese coasts blows in opposite directions during different seasons, Figure 2. The seasonal cycle of wind stress in these areas strongly affects the local upwelling and the strength and direction of coastal currents. Furthermore, wind energy input into surface waves is a strong nonlinear function of wind stress, so that the high frequency components of wind stress make a critical part of contribution to the wind energy input into the ocean. Although monthly mean wind stress can be used to calculate the winddriven circulation with reasonable results, mixed layer property calculation requires wind stress products with high temporal resolution up to 6-hourly wind.
Surface Circulation in the World Ocean Apart from the surface wave boundary, the upmost part of the ocean is occupied by the Ekman layer where the frictional force is balanced by the Coriolis force. Below this relatively thin upper layer, currents in most parts of the world oceans are organized in the form of gigantic gyres, as shown in Figure 3. There are strong subtropical gyres in the North Pacific, North Atlantic, South Pacific, South Atlantic, and the South Indian Oceans. At high latitudes, there are subpolar gyres in the North Pacific and North Atlantic Oceans, and Weddell Sea Gyre and Ross Sea Gyre at the southern edge of the South Ocean.
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These gyres are directly driven by surface winds. Many oceanic currents observed in the oceans are part of the organized winddriven circulation discussed in this article, including the Gulf Stream in the North Atlantic Ocean, the Kuroshio in the North Pacific Ocean, the Brazil Current in the South Atlantic Ocean, the East Australian Current in the South Pacific Ocean, and the Agulhas in the Southwest Indian Ocean. One of the most important features of these winddriven gyres is the western intensification of the currents,
as schematically shown in Figure 3. Although most currents in the ocean interior move relatively slowly, these western boundary currents can reach the speed in excess of 1 m s1. Most importantly, they can carry a huge amount of water. For example, the Gulf Stream transports can reach to 150 Sv (1 Sv ¼ 106 m3 s1). In addition, they carry a large amount of heat and thus play a critically important role in setting up the poleward heat transport in the Earth’s climate machinery.
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The fast-moving western boundary currents were discovered long time ago by marine navigators. Benjamin Franklin and Timothy Folger in 1769–70 created the first chart of the Gulf Stream, which was widely used by navigators going on cruises between European countries and North America. Even at the present day, their chart of the Gulf Stream seems quite accurate in prescribing the large-scale feature of this fast-moving current system. The dynamical explanation of such fast-moving currents or the so-called western intensification had to wait for more than 170 years following this chart. At low latitudes, there are strong equatorial current systems in the Pacific, Atlantic, and Indian Oceans, and they play critical roles in the oceanic circulation and climate system. There is also a strong Antarctic Circumpolar Current (ACC), which is the only circum-earth current system under the present continental setting. In addition, there are many other surface currents, which connect surface circulation in different parts of the world oceans, such as the Indonesian Throughflow and the North Atlantic Current. The shape of subtropical gyres is somewhat similar to the pattern of wind stress in the subtropical basins. The similarity between the circulation patterns in the atmosphere and oceans is deeply rooted in the dynamics. In fact, as will be explained shortly, the formulation of the gyration is the consequence of potential vorticity balance in a closed basin; thus, the wind stress curl is the essential ingredient of wind-driven gyres.
Thermal Structure in the Upper Ocean The circulation in the upper ocean is closely related to the density structure. Seawater density is controlled by temperature and salinity; however, over much of the warm near-surface waters, temperature dominates. Therefore, density structure
can also be inferred from temperature structure in the oceans. There is a mixed layer on the top of the ocean, where the temperature, salinity, and density is vertically nearly homogenized. Water properties and depth of the mixed layer have a profound annual cycle. The mechanical energy required to sustain the turbulent motions in the mixed layer is provided by the wind stress applied to the sea surface. In particular, wind stress inputs about 60 TW (1 TW ¼ 1012 W) of mechanical energy into the surface waves. The exact amount of this energy remains a topic of intensive research, and its pathway in the ocean remains unclear. However, it is believed that most part of this energy is dissipated within the mixed layer, leaving only a quite small portion of it to be transformed into the deeper part of the ocean, probably in forms of near-inertial oscillations. In addition, convection due to surface cooling or salt rejection during sea ice formation can also provide kinetic energy sustaining turbulent motions in the mixed layer. It is to emphasize that, however, the kinetic energy associated with turbulent motions due to convection is converted from the gravitational potential energy originally stored in the system. In fact, convection in the ocean cannot create mechanical energy. Another outstanding feature in the thermal structure in the upper kilometer of the world ocean is the main thermocline. The thermocline is defined as a layer within the water column where the vertical gradient of temperature is a local maximum. There are four major types of thermoclines in the ocean: diurnal, seasonal, main, and abyssal thermoclines. The diurnal thermocline is associated with the diurnal cycle of the mixed layer and it exists in the upper few tens of meters in the ocean; the seasonal thermocline is associated with the seasonal cycle of the mixed layer, and it extends from the base of the diurnal thermocline to the depth of a couple of hundred meters except
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in some special locations where wintertime convection can reach to great depths. The main thermocline is below the seasonal thermocline at depths of 200–800 m. As a result, it is not greatly affected by the seasonal cycle of the mixed layer; hence, it is also called the permanent thermocline. In addition, in part of the world oceans there is abyssal thermocline associated with abyssal circulation. Wind-driven circulation can exist in either a homogeneous ocean or a stratified ocean. Wind-driven circulation in a homogeneous ocean is very weak because the volumetric flux of the circulation is uniformly distributed over the entire depth of the ocean. On the other hand, due to the existence of strong stratification associated with the main thermocline, winddriven circulation is mostly confined to an upper moving layer above the main thermocline. As a result, currents associated with wind-driven circulation in a stratified ocean can be greatly enhanced. In most parts of the world oceans, seawater density is primarily controlled by temperature, with salinity playing a secondary role. Therefore, the main thermocline is also closely linked to the main pycnocline. Note that dynamically the main pycnocline is more directly relevant to the dynamics of the oceanic circulation; however, the main thermocline itself is closely linked to temperature changes in the atmosphere, hence thermocline is a term often used in scientific study of the oceanic circulation and climate changes. The typical structure of the main thermocline can be seen through an east–west temperature section. As shown in Figure 4, the main thermocline is located around the depth of 200 m at the eastern boundary, and gradually slopes down to the depth of 600 m in the North Pacific Ocean and 800 m in the North Atlantic Ocean. As shown in Figure 4, warm water in the upper ocean is separated from the cold water in the deep ocean by a layer of relative shape temperature gradient associated with the main thermocline. In the interior part of the ocean, large-scale currents obey geostrophy. Using geostrophy and thermal wind relation, the
direction of large-scale current can be inferred from temperature or density sections as follows. Since strong wind-driven current is confined in the upper kilometer of the ocean, one can assume that water at great depth is motionless. For example, one can assume that horizontal velocity at the depth of 2.5 km is negligible, and the corresponding horizontal pressure gradient is nearly zero at this depth. As shown in Figure 4, water on the right-hand side of the ocean basins is colder and thus denser than that on the left-hand side. Using the thermal wind relation and the hydrostatic approximation, one comes to the conclusion that at depth shallower than 2.5 km pressure gradient force in the oceanic interior is pointed eastward. According to geostrophy, to balance the pressure gradient force the Coriolis force must point westward; thus, current in the ocean interior should move equatorward. On the other hand, near the western boundary the slope of isopycnal flips sign and becomes quite steep, indicating strong and poleward narrow western boundary currents. Thus, temperature and the corresponding density structure shown in Figure 4 can be interpreted as the sign of the western intensification. Density structure along the meridional section reveals another important dynamic feature, Figure 5. The center of the wind-driven circulation on each isopycnal surface is roughly the deepest part of the isopycnal surface. As shown in Figure 5, the center of the circulation moves northward with increasing density. This is called the poleward intensification of the wind-driven subtropical circulation. This is also linked to the recirculation of the subtropical gyre, as will be discussed shortly. In general, near the equator thermocline is much shallower. Since the Coriolis force vanishes near the equator, the equatorial thermocline is directly linked to the equatorial zonal wind stress. In a steady state, at the sea level the zonal wind stress on surface is balanced by the pressure gradient force associated with the zonal sloping sea surface. In both the Pacific and Atlantic Oceans, easterlies prevail near the equator.
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As a result, equatorial thermocline in these two basins slopes downward from east to west. On the other hand, the main thermocline in the Indian Ocean slopes down eastward because wind in the Indian Ocean is primarily westerly. This combination of equatorial winds leads to a condition favorable for the formation of a large warm pool with the main thermocline sits at the depth of 200 m in the western equatorial Pacific. In the east side, there is a cold tongue in both the equatorial Pacific and Atlantic Oceans, upper panel of Figure 6. In the meridional section, the main thermocline appears in the form of a dumbbell, lower panels of Figure 6. The bowlshaped main thermocline at midlatitudes in these three basins is outstanding. It is clear that the main thermocline is deepest in the South Indian Ocean. The main thermocline in the North Atlantic Ocean is deeper than that in the North Pacific Ocean. The depth of the main thermocline in the world oceans is closely linked to the wind-driven circulation in the upper ocean. In the world oceans, there are five subtropical gyres and they can be clearly identified from the basin-scale bowl-shaped main thermocline, as shown in Figure 7. Note that the main thermocline is a conceptual layer only; thus, such a subsurface vertical temperature gradient maximum may not exist at any specific location. As will be shown shortly, the simple reduced gravity model predicts that the depth of the main thermocline is proportional to the zonal integration of the Ekman pumping rate and inversely proportional to the stratification in the upper ocean. For example, in the Pacific Ocean relatively low salinity in the upper ocean leads to a relatively strong stratification in the upper ocean and thus a shallow main thermocline. On the other hand, high salinity water in the Atlantic and Indian Ocean leads to relatively weak stratification and relatively deep main thermocline.
Theory of the Wind-Driven Circulation Ekman Layer There is an Ekman layer in the upper ocean. The Ekman layer is defined as the surface boundary layer in which the frictional force is balanced by Coriolis force. Ekman in 1905 first formed the idea of such a boundary layer in the ocean. Winds input a large amount of mechanical energy, on the order of 3 TW, which is used to maintain motions in the Ekman layer against friction. Within the Ekman layer, the wind stress is transformed downward through eddy-induced horizontal momentum flux. A major uncertain part of the Ekman layer theory is the vertical eddy viscosity Av. The classical theory of Ekman layer assumes that Av is isotropic and has a constant value over the whole depth of the layer. Under such an assumption, the horizontal velocity for the Ekman layer in a steady state appears in the form of a spiral, quite similar to that in the atmospheric boundary layer. Observing the Ekman layer in the ocean was a great challenge due to the stance of strong surface waves and turbulence in the upper ocean. Ekman layer predicted by the classical theory was confirmed through observation only in the 1980s. Observations indicated that vertical eddy viscosity Av is not constant. In fact, in-situ observations indicated that vertical eddy viscosity decays with increasing depth following some negative power laws or exponentially decaying laws. If Av is not constant or isotropic, the shape of the Ekman spiral can be different from that predicted by the classical theory. The horizontal volume transport integrated over the depth of the Ekman layer is independent of the vertical eddy viscosity; this volume transport is perpendicular to the wind stress and pointing to the right-hand side (in the Northern Hemisphere); ! ¼ ! z ! s =f r , where it can be written in the form of V Ekman
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density. The zonally integrated Ekman transport in the three basins is on the order of 10–20 Sv (Figure 8(a)). As it is inversely proportional to the Coriolis parameter, it becomes unbounded near the equator, indicating that the theory of Ekman layer does not apply to the equatorial band. Thus, there are large horizontal mass transports in the upper ocean, which can play key roles in transporting heat, freshwater, and other tracers. Since it is directly proportional to the wind stress, such transports can change in response to variability in the atmospheric circulation and climate. Due to variation of both wind stress and Coriolis parameter f, Ekman transport varies with geographic location. The convergence (divergence) of Ekman transport leads to the Ekman pumping, wEkman ¼ curl(s/fr0). In general, Ekman pumping velocity is quite small, on the order of 106 m s1, which is equivalent to 0.08 m per day or 30 m per year. However, in subtropical basin interiors this seemingly small vertical velocity leads to an equatorward geostrophic flow in the subsurface layer, and thus dynamically sets up the gigantic wind-driven circulation in the subtropical basins; while in the subpolar basin, Ekman pumping is upward, and it leads to a poleward geostrophic flow in the subsurface layer and thus the cyclonic subpolar gyres. Coastal upwelling/downwelling is induced by long-shore wind. If wind blows along the coast, off-shore (or on-shore) Ekman transport must be compensated by upwelling (downwelling) along the coast. Coastal upwelling can bring nutrientrich water from depth to the surface; thus, high productivity and good fishing grounds along some of the coastlines are closely linked to strong along-shore wind. Since along-shore wind often changes with the season, the strength of coast upwelling also has strong seasonal cycle, and hence the biological productivity. Some of the sites of strongest seasonal cycle of the coastal upwelling are shown in Figure 2. The seasonal cycle of wind stress is strong in the Indian Ocean. In particular, the seasonal cycle of wind stress east of Somalia is very strong, so that coastal upwelling there has a very strong seasonal cycle. In fact, the seasonal cycle of wind is so strong that the direction of the Somali current reverses during the seasonal cycle.
Sverdrup Transport of the Wind-Driven Circulation The simplest way to describe the wind-driven circulation is to treat the circulation in the upper ocean in terms of a single layer; thus, the wind stress is to be treated as a body force uniformly distributed within this layer. The layer integrated volume flux satisfies the Sverdrup relation: bhv ¼ ðvsy =vx vsx =vyÞ=r0 :
[1]
where b ¼ df/dy, h is the layer thickness, v is the meridional velocity, (sx, sy) are the wind stress components, and r0 is the constant reference density. The Sverdrup relation is essentially a potential vorticity equation. According to this equation, negative wind stress curl in the subtropical basin drives an equatorward flow in the basin interior. A zonal integration of this relation leads to the Sverdrup streamfunction (or Sverdrup transport). The Sverdrup transport includes contributions due to surface Ekman transport and the geostrophic transport above the thermocline layer. As an example, Figure 9 shows the Sverdrup transport in the Pacific Ocean. There are clearly the subtropical gyres in both the North and South Pacific Oceans, with the maximum streamfunction on the order of 40 Sv. In addition, there is a subpolar gyre at the northern high latitudes and the equatorial circulation system at low latitudes. Note that the Sverdrup relation is valid for the steady state circulation only.
Theories of the Wind-Driven Gyres The energetics of wind-driven circulation Wind-driven gyres are the direct result of surface wind forcing. These gigantic circulation systems are sustained by mechanical energy input from the surface winds. Wind energy input to the ocean can be separated into several categories. First and most importantly, the total amount of mechanical energy input to the large-scale surface currents is estimated as 1 TW, and most of such energy is put into the South Ocean and other regions of fast currents, such as the Gulf Stream and Kuroshio. Second, the wind energy input to the Ekman layer is about 3 TW; however,
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most of this energy is used to overcome the friction in the Ekman layer. Third, surface waves receive approximately 60 TW from the surface wind; however, this huge amount of mechanical energy is mostly dissipated within the surface wave boundary layer. There is the Langmuir circulation in the upper ocean, which is closely linked to surfaced waves. Surface waves and Langmuir circulation play key roles in regulating the surface layer dynamics and the air–sea interaction. In addition, a small amount of mechanical energy received by surface waves can penetrate through the base of the mixed layer and thus contribute to mixing in the subsurface layer; but, the pathway and this energy remains unclear at this time. Fourth, the sea level atmospheric pressure varies with time; combining with the vertical motions of the sea surface, this leads to a mechanical energy input to the ocean. The exact amount of this energy input remains unclear, and current estimate puts it on the order of 0.01–0.04 TW. However, the effect of sea level pressure change is mostly projected into the barotropic mode in the oceans; thus, its effect on the surface motions is small and may be negligible.
The reduced gravity model The structure of the wind-driven circulation can be explored in terms of the simple reduced gravity model. The basic idea is to treat the main pycnocline as a step function in density coordinate. Assume that the upper and lower layers have constant density r1 and r2, and the lower layer is infinitely deep and motionless. A commonly used parameter in such a model is the reduced gravity, defined as g0 ¼ g(r2 r1)/r0. The simple formulation of the reduced gravity model allows either analytical or straightforward numerical solutions. For simplicity, solutions shown here are obtained through
numerical integration. The model is started from initial states with a fixed amount of warm water in the upper layer and it is forced by a cosine wind stress. The first case is for a model on the f-plane, i.e., f ¼ const. is assumed. As shown in upper panels of Figure 10, both the layer thickness and transport of this solution are symmetric with respect to the E–W and N–S directions. The second case is for a model on a beta-plane (i.e., f ¼ f0 þ b(y y0)), and the corresponding solution is asymmetric with respect to the E–W direction, lower panels in Figure 10. In fact, the current near the western boundary is much stronger than in the interior, and this phenomenon is called the western intensification. The dramatic contrast between a model on the f-plane and a model on the beta-plane was first discovered by Stommel in 1948, who recognized the important meaning of such a difference and made a link between this phenomenon and the Gulf Stream and other strong currents observed in the world oceans. The reason of the western intensification can be explained in terms of the simple reduced gravity model. For the steady flow in the oceanic interior, the lowest order balance of the circulation can be examined in a beta-plane model as follows. Assuming a steady state and omitting the inertial terms and friction terms, the vorticity equation is reduced to Sverdrup relation eqn [1]. Thus, the streamfunction satisfies the Sverdrup relation j ¼ ðvsx =vy vsy =vxÞðxe xÞ=br0 ; and the layer thickness satisfies the following equation " y # 2f 2 sx s 2 2 h ¼ he þ 0 ðxe xÞ; g r0 b f y f x
[2]
[3]
where he is the layer thickness along the eastern boundary, b ¼ df/dy is the meridional gradient of the Coriolis parameter.
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The advantage of the reduced gravity model is that it provides a clear description for both the volumetric transport and the depth of the main thermocline. Note that although the quasigeostrophic theory has been widely used for the description of wind-driven gyres in many previous published textbooks and papers, such a description is inaccurate because the winddriven circulation involves large deviation of stratification, so that the wind-driven gyration is beyond the validity of the basic assumptions made in the quasi-geostrophic theory. In a single-moving-layer model for a subtropical basin, the equatorward transport in the basin interior must be closed through the addition of either a western/eastern boundary layer, which can transport the mass poleward. Furthermore, in the Northern hemisphere there is a large amount of negative vorticity input from wind stress over the subtropical basin. In a steady state, the basin-integrated vorticity budget must be balanced; thus, there should be a large source of positive vorticity along the lateral boundaries of the basin. A simple dynamical analysis indicates that only the western boundary can play the role of generating the positive vorticity and thus balancing the vorticity budget for the wind-driven circulation. The existence of western boundary layer manifests in the form of the so-called western intensification. Stommel first postulated a boundary layer for a reduced gravity model in terms of bottom friction. He assumed that friction is linearly proportional to the horizontal velocity in the moving layer. In more accurate terminology, his bottom friction can be generalized as the interfacial friction, which is assumed to be linearly proportional to the velocity difference
between the upper and lower layers. Such an interfacial friction can be interpreted as a crude parameterization of baroclinic instability. Another possible type of boundary current is the lateral friction model postulated by Munk. In addition, Charney and Morgan postulated the inertial boundary layer theory. The structure of western boundary currents postulated in these theories can be examined analytically. Since the western boundary current is rather narrow in the cross-stream direction, the corresponding control equations can be simplified by the standard boundary layer technique. In fact, the cross-stream momentum equation can be simplified in terms of the semigeostrophic approximation, and simple analytical solutions can be obtained, which can be used to illustrate the essential dynamics of the western boundary current. All these boundary layer theories can be used to close the wind-driven gyres. A close reexamination reveals that western boundary currents observed in the ocean are primarily controlled by the inertial terms, i.e., these boundary currents are essentially inertial western boundary layer in nature. The frictional force is of importance only within a relatively thin sublayer. The advantage of the reduced gravity model is that it can predict the basin-wide distribution of the main thermocline depth. The structure of the wind-driven circulation in a closed basin on a beta-plane is shown in the lower panels of Figure 10, where the wind-driven circulation in the subtropical gyre consists of the interior part and the Stommel frictional western boundary current. In this example, the horizontal distribution of the thermocline depth can be seen clearly in
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a reduced gravity model, as shown in Figure 10(c). For most part of the basin away from the western boundary the solution is described by the interior dynamics discussed above. On the other hand, the strong northward current appears along the western boundary, i.e., the western intensification.
strong western boundary currents after separation, such as the Gulf Stream and Kuroshio. Simulating the case with isopycnal outcropping is a critically important step forward in simulating the wind-driven circulation and the associated density structure in the ocean.
Layer model with outcropping
The ventilated thermocline
An advantage of the reduced gravity model is its capability of capturing the strong nonlinearity associated with horizontal variability of stratification, in particular for the case with isopycnal outcropping. Due to the strong wind forcing, surface heat and freshwater fluxes, isopycnals outcrop at high latitudes. A fundamental assumption made in the quasi-geostrophic theory is that variation of the stratification in the horizontal direction is very small; thus, such theory is not suitable for describing the large-scale dynamics associated with layer outcropping. For a model with finite amount of warm water in the upper layer, in part of the basin the layer thickness becomes thinner and thinner as the wind forcing is enhanced. However, when the continuity equation for the layer thickness is transformed into finite difference forms, using the commonly used central difference scheme, the layer thickness may become negative. In order to avoid such situation, the so-called positive-definite scheme should be used. A typical solution with outcropping is shown in the upper panels of Figure 11, where the upper layer vanishes along the outcrop line near the northwest corner of the basin. North of the outcrop line the lower layer outcrop; within the framework of the single-moving-layer model, there is no motion within the outcrop window. A strong internal boundary current is formed along the edge of the outcrop line, which mimics the
Although simple reduced gravity models can provide essential information about the wind-driven circulation, such singlemoving layer models give no information about the vertical structure of the circulation in the upper ocean. In pursuing the structure of the wind-driven circulation, the theory of thermocline gradually formed, which is aimed at explaining the three-dimensional structure of the wind-driven circulation. From the beginning of thermocline theory, two paradigms developed independently: the diffusive thermocline by Stommel and Robinson and ideal-fluid thermocline by Welander. The diffusive thermocline theory interprets the main thermocline as an internal thermal boundary layer, and thus emphasizes the critical role of diffusion in forming the main thermocline. On the other hand, the ideal-fluid thermocline theory interprets the main thermocline in terms of ideal-fluid theory, and emphasizes the critical role of adiabatic deformation of the stratification set up by a background thermohaline circulation. Welander actually produced some simple and elegant solutions based on the ideal-fluid thermocline theory. In the beginning, the theory of diffusive thermocline was pursued by many researchers, apparently due to the seemingly more complete dynamical framework by incorporating the diffusion term. Due to the complicated dynamics involved, exact analytical solutions for the diffusive thermocline were
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Figure 11 Models with outcrop: A. a single moving layer with outcrop: (a) Layer thickness (100 m), (b) Volume transport (Sv); B. a two-movinglayer ventilated model: (c) Upper layer thickness and (d) Lower layer thickness.
Oceanographic Topics j Surface/Wind Driven Circulation hard to find. Instead, most studies were aimed at finding different kinds of similarity solutions. The searching for similarity solutions was summed up by Veronis in 1970s. On the other hand, the ideal-fluid thermocline theory was unpopular because it seemed rather incomplete for not including the diffusion terms. The major deficit of similarity solutions is that they cannot satisfy the essential dynamical constraints, such as the Sverdrup relation; thus, searching for nonsimilarity solutions was a main research frontier. In addition, recent in-situ measurements indicate that diffusion in the main thermocline is rather weak; thus, the theory of ideal-fluid thermocline regains its momentum. One of the conceptual difficulties in pursuing an ideal-fluid theory for the thermocline is as follows. In an ideal-fluid ocean, the interfacial friction must be small and negligible; in such a framework, how are the subsurface layers set in motion? The major breakthroughs took place in early 1980s. Rhines and Young postulated the potential vorticity homogenization theory. They argued that under strong wind forcing, potential vorticity in the subsurface layers is homogenized. As a result, closed potential vorticity contours appear in the subsurface layer, along which water parcels can move freely according to the ideal-fluid thermocline theory. Furthermore, under the assumption of infinitesimal dissipation of potential vorticity, potential vorticity within the close contours are homogenized toward the value along poleward boundary of the circulation. Therefore, a unique solution, which is stable to small perturbations, exists. Another major breakthrough is the theory of ventilated thermocline. In the stratified ocean, most isopycnals outcrop at high latitudes in winter. The outcropping phenomenon can be clearly seen even in annual mean meridional section of temperature and density, as shown in Figures 5 and 6. Iselin in 1939 first postulated the idea that water masses are formed at
the sea surface in late winter, and subsequently pushed downward through Ekman pumping. His physical insightful idea and Welander’s framework of ideal-fluid thermocline were not pursued for a long time. Apparently inspired by the success of the potential vorticity homogenization theory, these two ideas were combined and extended into a beautiful theory of the ventilated thermocline by Luyten, Pedlosky, and Stommel. They formulated the model in terms of three-moving layers plus a deep stagnant layer in the abyss. At lower latitudes, the uppermost layer is exposed to Ekman pumping; however, with the increase of latitudes, upper layers outcrop and lower layers are directly exposed to Ekman pumping. At higher latitudes, Ekman pumping drives the outcropping lower layers in motions, and ventilation and subduction take place. Ventilation and subduction are the basic elements of the wind-driven circulation in a stratified ocean (Figure 12). The ocean is conceptually separated into four layers; an Ekman layer of the top (not drawn in this sketch), the upper and lower layer below the Ekman layer, and a thick and stagnant layer at the bottom. Wind stress induces the Ekman pumping at the base of the Ekman layer. The upper/lower layer is directly forced when it is exposed to Ekman pumping, as indicated by vertical arrows on the top of the layer. The upper layer outcrops along the zonal outcrop line; thus, north of the outcrop line the lower layer is directly driven by the Ekman pumping. Since the lower layer is exposed to the surface force, we also call this as the ventilation of the lower layer. As a result, there is an anticyclonic circulation in this layer, indicated by the blue curved arrows. Poleward of the outcrop line the meridional volume transport in this layer satisfies the Sverdrup constraint. Equatorward of the outcrop line, the lower layer moves underneath the upper layer, and this is called subduction. Since there is motion in the lower layer north of the outcrop line, there is no reason why it should stop movement after it is subducted; thus, it should continue its anticyclonic movement Ekman pumping leads to the wind-driven gyres
Flow in the lower layer
Ventilation through exposure to atmospheric forcing
Flow in the upper layer
Subduction via motion continuous from the outcropping
ρ − Δρ
ρ
ρ + Δρ
Figure 12
Sketch of ventilation and subduction.
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after subduction, as indicated by the dashed lines with arrow. South of the outcrop line, the upper layer is directly forced by Ekman pumping. Because both layers are in motion, in this regime the Sverdrup constraint should apply to the meridional volume transport integrated over the total depth of these two layers. In order to determine the solution in this regime, one more dynamical constraint is required. For ideal-fluid motion, the potential vorticity in the second layer should be conserved when it is not directly forced by Ekman pumping. A simple and elegant solution of this problem is postulated in the ventilated thermocline theory. In the ocean interior, relative vorticity is negligible for large-scale motions; thus, potential vorticity for a two-moving layer model is q1 ¼ f/h1 and q2 ¼ f/h2. In fact, keeping the potential vorticity of the second layer at its value when it is subducted along the outcrop line gives the additional dynamical constraint for solving the problem. The theories of potential vorticity homogenization and ventilated thermocline represent major breakthroughs in understanding the three-dimensional structure of wind-driven circulation. In particular, the discovery of shadow zone, the ventilated zone, and the pool zone bought about completely new physical insight for the wind-driven circulation in the upper ocean. As an example, a two-layer ventilated thermocline model is shown in the lower panels of Figure 11 for a northern hemisphere model ocean, in which the zonal dashed lines indicate the outcropping line of the upper layer. The model is forced by a simple sinusoidal Ekman pumping field, which works on the layer exposed to the upper surface forcing, i.e., the lower layer north of the outcrop line and the upper layer south of the outcrop line. North of the outcrop line, the lower layer is exposed to the Ekman pumping, and an anticyclonic circulation can be clearly seen north of the outcrop line. South of the outcrop line, the lower layer is subducted; however, it continues its south-westward movement as shown in Figure 11(d). The upper layer has zero thickness north of the outcrop line; but, south of the outcrop line it is directly exposed to Ekman pumping. As shown in Figure 11(d), geostrophic flow in the lower layer after subduction can be separated into three dynamical zones: the pool zone near the western boundary, the shadow zone near the eastern boundary, and the ventilated zone in the middle. An important conceptual breakthrough in the ventilated thermocline theory is the existence of a shadow zone within the subsurface layer near the eastern boundary. A strong kinematic condition along the eastern boundary is the no-flow-penetration condition along the eastern boundary. Thus, the subsurface layer should have a constant thickness h2 along the eastern boundary. If the eastern boundary were a streamline, then the corresponding potential vorticity f/h2 should be constant along the eastern boundary. Because the Coriolis parameter declines equatorward, f/h2 cannot be constant. Therefore, the eastern boundary cannot be a streamline for the subsurface layer; instead, there should be a shadow zone near the eastern boundary where the subsurface layers are stagnant. From hydrographic data, the existence of shadow zone can be inferred from the appearance of extremely low oxygen levels at the depth of 1000 m and near the eastern boundary at low latitudes. There are two other dynamical zones in Figure 11(d). Potential vorticity in the ventilated zone is sent up along the
outcrop line when the lower layer is subducted. Pool zone is defined by streamlines emerging from the western boundary. As such, potential vorticity in the pool zone is not set up by wind-driven forcing within the basin. Instead, it is set up by either potential vorticity homogenization or other dynamics. The original Sverdrup relation applies for a single-movinglayer model only. For a model with multiple moving layers, it is extended to an integral constraint for the meridional volume flux for all the moving layers. The ventilated thermocline theory was generalized to a theory for the continuously stratified ocean by Huang. Such a model provides density and current structure in the ocean, which are comparable with observations. Note that the Sverdrup relation applies for the steady circulation only. There are two important issues related to the application of this relation. First, the steady solution of winddriven circulation in a basin is established after the wave adjustment. The volume flux over the whole depth of the ocean is established after the barotropic Rossby waves passing through. Since barotropic Rossby waves move quite fast, the timescale for the barotropic circulation to be established is in the order of 7–10 days for a tropical basin. However, the baroclinic Rossby waves move relatively slowly, with the speed in the order of 0.1 m s1. Thus, for the midlatitudes of the North Atlantic or the North Pacific Ocean, the steady circulation of the first baroclinic mode takes about 10–20 years to be established. In general, the time-dependent solution of the wind-driven circulation can be calculated by the integrating the time delayed Ekman pumping rate. Furthermore, the contribution due to eddies is not included in the Sverdrup relation. In the ocean, eddies give rise to nonlinear contribution to the meridional volume flux. As a result, meridional volume flux across the zonal section can deviate from the Sverdrup relation.
Combination of Surface and Deep Currents Currents in the North Atlantic Ocean Although surface currents are mostly controlled by wind stress, the thermohaline circulation, which occupies the whole depth of the ocean also manifests in the upper ocean. The circulation in the North Atlantic Ocean is a good example. As shown in Figure 13, there is a warm current crossing the equator. This current moves northward and joins the warm water in the Gulf Stream, which exists as an internal boundary current separating the subtropical gyre to the south and the subpolar gyre to the north. It is important to note that the wind-driven gyre in the North Atlantic Ocean consists of the linear Sverdrup interior and the recirculations. The recirculation regimes are located roughly where the surface expression of the western boundary current emerges from the western boundary region by separation from the coast, where the nonlinearity of the circulation is not negligible. As a result, the Sverdrup dynamics does not apply and eddy activity associated with the nonlinear inertial terms become large and dominating. Instead of the laminar fluid like current, at any given time the Gulf Stream encompasses many large-amplitude eddies. Furthermore, the total volumetric flux in the Gulf Stream recirculation regime is in the order of 150 Sv, much larger than
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70° N Subpolar gyre
Recirculation Surface western boundary current Poleward branch of MOC
35° N
Equator
Deepwater formation
Subtropical gyre
Deep western boundary current Equatorward branch of MOC
Figure 13
Combination of surface wind-driven circulation and deep circulation in the North Atlantic Ocean.
the value predicted from the linear Sverdrup theory. This large volume transport includes contribution of 30–35 Sv due to the linear wind-driven circulation, about 15–20 Sv from the returning flow of the deep thermohaline circulation, and approximately 90–100 Sv due to the nonlinear dynamics (in forms of the southern recirculation and the north recirculation), Figure 13. The return flow of the thermohaline circulation continues its poleward movement and appears in the form of the North Atlantic Current, which moves to the high latitude part of the North Atlantic basin and eventually feeds the deepwater formation.
The Antarctic Circumpolar Current There is a strong circum-earth current system in the South Ocean, and it is called the ACC. There is no meridional boundary in the Southern Ocean. As a result, there is no zonal pressure gradient force to maintain any meridional geostrophic flow; thus, the classical Sverdrup dynamics does not apply to ACC. The formation of ACC depends on many dynamical factors, including wind stress, wind stress curl, the shape of coastline and bottom topography, the surface thermohaline forcing, and, most importantly, the contribution of mesoscale eddies. In particular, mesoscale eddies play capital roles in setting the structure of ACC. ACC plays an important role in regulating the global oceanic circulation and climate. However, the complete description of the ACC dynamics requires an indepth discussion and it is beyond the scope of this article.
past decade. In fact, physical oceanography is now entering the eddy resolving era. By definition, two kinds of eddies are now the focus of research. The mesoscale eddies have horizontal scales from 10 to 500 km and vertical scales from tens to hundreds of meters, and the submesoscale eddies have horizontal dimensions on the order of 1–10 km and vertical scales on the order of tens of meters or smaller. The ocean is a turbulent environment, and eddy motions are one of the fundamental aspects of oceanic circulation. In fact, it is estimated that the total amount of eddy kinetic energy is about 100 times larger than that of the mean flow. The roles of mesoscale and submesoscale eddies in the oceanic circulation and climate remain to be explored. It is expected that with the great technical advances in satellite observation and global observation program like ARGO, eddy study is pushed forward with a great speed. Studies of these eddies, including observations, theory, laboratory experiments, and parameterization in numerical models, will be the most productive research frontiers for the next 10–20 years.
See also: Air Sea Interactions: Surface Waves. Boundary Layer (Atmospheric) and Air Pollution: Ocean Mixed Layer. Oceanographic Topics: Thermohaline Circulation. Satellites and Satellite Remote Sensing: Surface Wind and Stress.
Further Reading Mesoscale Eddies Most classical theories of wind-driven circulation treat the circulation in terms of laminar fluids, with the roles of eddies neglected. The framework of three-dimensional structure of gyre-scale wind-driven circulation was completed in 1980s, represented by the multilayer ventilated thermocline theory and its extension to the case of continuously stratified ocean. These theories provided the lowest order structure of the winddriven circulation and laid down the foundation for the further development of oceanic circulation. With the advance in technology in observation, theory, and numerical models, the situation has changed rapidly over the
Chelton, D.B., Schlax, M.G., Samelson, R.M., 2011. Global observations of nonlinear mesoscale eddies. Progress in Oceanography 91, 167–216. Ekman, V.W., 1905. On the influence of the earth’s rotation on ocean currents. Arkiv för Matematik, Astronomi och fysik 2, 1–52. Gill, A.E., Green, J.S.A., Simmons, A.J., 1974. Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies. Deep Sea Research 21, 499–528. Huang, R.X., 2010. Ocean Circulation, Wind-Driven and Thermohaline Processes. Cambridge Press. Luyten, J., Pedlosky, J., Stommel, H.M., 1983. The ventilated thermocline. Journal of Physical Oceanography 13, 292–309. Olbers, D., Borowski, D., Völker, C., et al., 2004. The dynamical balance, transport and circulation of the Antarctic Circumpolar Current. Antarctic Science 16 (4), 439–470. Pedlosky, J., 1996. Ocean Circulation Theory. Springer-Verlag, Heidelberg.
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Pedlosky, J., 2006. A history of thermocline theory. In: Jochum, M., Murtugudde, R. (Eds.), Physical Oceanography Developments since 1950. Springer, New York, pp. 139–152. Price, J., Weller, R.A., Schudlich, R.R., 1987. Wind-driven ocean currents and Ekman transport. Science 238, 1534–1538. Qiu, B., 2001. Kuroshio and Oyashio currents. In: Encyclopedia of Ocean Sciences. Academic Press, pp. 1413–1425. Rhines, P.B., Young, W.R., 1982. A theory of the wind-driven circulation. I. Mid-ocean gyres. Journal of Marine Research 40 (Suppl.), 559–596. Richardson, P., 1980. Benjamin Franklin and Timothy Folger’s first printed chart of the Gulf Stream. Science 207 (4431), 643–645. http://dx.doi.org/10.1126/science.207. 4431.643.
Stommel, H., 1948. The western intensification of wind-driven ocean currents. Transactions of the American Geophysical Union 29, 202–206. Veronis, G., 1969. On theoretical models of the thermocline circulation. Deep Sea Research 16 (Suppl), 301–323. Weller, R.A., Bigorre, S.P., Lord, J., Ware, J.D., Edson, J.B., 2012. A surface mooring for air–sea interaction research in the Gulf Stream. Part I: Mooring design and instrumentation. Journal of Atmospheric and Oceanic Technology 29, 1363–1376. http://dx.doi.org/10.1175/JTECH-D-12-00060.1.