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Water and Fine-Sediment Circulation
2.01
Water and Fine-Sediment Circulation
RJ Uncles, Plymouth Marine Laboratory, Plymouth, UK SG Monismith, Stanford University, Stanford, CA, USA © 2011 Elsevier Inc. All rights reserved.
2.01.1 2.01.2 2.01.2.1 2.01.3 2.01.3.1 2.01.4 2.01.4.1 2.01.5 2.01.5.1 2.01.6 2.01.6.1 2.01.7 References
Introduction Buoyancy and Its Consequences Stratification, Turbulence, Estuarine Circulation and Mixing Barotropic and Wind-Driven Motions Tides, Winds, and Waves Coastal and Estuarine Interactions River Plumes on the Shelf and Coastal Oceanography Biological Interactions and Sediments Hydrodynamic Interactions with Biota and Sediments Measurements and Modeling Measurement and Modeling Techniques for Estuarine and Coastal Waters Final Remarks
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Abstract This chapter provides an introduction to Volume 2 of the Treatise, which deals with water and fine-sediment circulation in estuaries and the coastal zone. Chapters 2.02, 2.03, 2.04, and 2.05 are concerned primarily with buoyancy and its consequences for circulation and include topics such as stratification, turbulence, estuarine circulation, surface fronts, plumes, and mixing. Chapters 2.06, 2.07, 2.08, 2.09, and 2.10 consider barotropic and wind-driven motions, especially tides, winds, and waves. Coastal and estuarine interactions, incorporating river plumes on the shelf and coastal oceanogra phy, are dealt with in Chapters 2.11 and 2.12. Chapters 2.13, 2.14, and 2.15 describe biological interactions and sediments and particularly hydrodynamic interactions with biota and sediments. Finally, Chapters 2.16 and 2.17 deal with measure ment and modeling techniques for estuarine and coastal waters.
2.01.1 Introduction It is interesting to note that, within the treatise, only approximately 10% of the chapters relate to water circulation and fine-sediment transport. This small percentage hides the fact that at the system level almost all nonphysical processes within estuaries and coastal waters are, actually, strongly dependent on these physical processes – the currents that transport watercolumn biology and chemistry, the mixing that brings both aspects closer to the surface and to light, and the suspension and accretion of mud, or the movements of sand and the tidal drag on the bed that influences to such an extent the biology of the benthic system, or the salt that is mixing with freshwater to influence, along with turbidity, the behavior of chemical components of the system. The list could be much longer, more specific, and better focused of course, but the point has been made: to understand the whole system, it is necessary to understand the physics. To understand why the linkages between disciplines are not as strong as they could be, we perhaps need to quote the great Hungarian-American mathematician, John von Neumann (cited in Deleersnijder and Delhez, 2007):
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena…
But, of course, with the noteworthy exception of the large hydrodynamic–ecosystem collaborations (e.g., Allen et al., 2001), models are usually simplified in order to focus on those processes of immediate concern to the modeler and the modeling team. This volume of the treatise is devoted to water and fine-sediment circulation and is largely physical, although two of its chapters have the biological systems as their focus – the effects of biota on muddy sediments and the effects of plants on water flow. The physical system of concern here is the estuarine–coastal waters–shelf continuum, with emphasis on estuaries and coastal waters. This is a system of great importance to humanity; according to Huntley et al. (2001), most of the world’s population and most populous cities are located near the coast and most of the world’s fish catch comes from coastal regions. These regions are often subjected to environmental pressures from sewage and industrial and agricultural pollution that are also assimilated within them. The wastes and effluents arrive at the coast from industries and cities and river catch ments, having been transported by rivers and estuaries, where nutrients and contaminants are sequestered, degraded, and recycled. The transport by waters and suspended sediments and the sequestering by deposited sediments are the key issues here. Land-to–sea interactions are complex. River flows, tides, waves, and buoyancy, derived from the juxtaposition and mix ing of freshwater and seawater, combine to produce this
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complexity and variability of water movements. Sediment movement through the estuaries to the coastal zone has addi tional complications, especially for fine sediment (which sequesters pollutants), which are caused by flocculation, settling, suspension, and accretion processes. The biogeochem istry and ecology are sensitive to these factors.
2.01.2 Buoyancy and Its Consequences Starting with the estuary and its circulation of water, the funda mental non-tidal processes are due to freshwater flows and the buoyancy they supply to the estuary. The early classification systems for estuaries, comprising fjord, salt wedge, partially mixed, and well mixed, were essentially based on buoyancy distributions (Pritchard, 1955; Cameron and Pritchard, 1963). Pritchard (1952, 1954, 1956) investigated the tidally averaged momentum balance of the James River Estuary and identified the importance of gravitational current (or estuarine circula tion), which is driven by buoyancy. Later, theoretical models were developed that predicted the subtidal estuarine circula tion as a function of the longitudinal (that is, along-axis) density gradients and classified estuaries in terms of their subtidal (or residual) dynamic behavior (Hansen and Rattray, 1965, 1966). However, bathymetry and salinity distributions are rarely laterally (cross-estuary) uniform and the conse quences of this nonuniformity on the transverse distribution of longitudinal subtidal currents were pointed out by Fischer (1972) – especially their important effects on estuarine mass transport. The developing work was not restricted to subtidal phe nomena and a growing body of research focused on intratidal influences, topographic control (Armi and Farmer, 1986), transverse (lateral) variations and cross-estuary circulations (Nunes and Simpson, 1985), the impacts of spatially varying density gradients and fronts (Garvine and Monk, 1974) and turbulence on estuarine dynamics. In many estuaries, per iodicity in the strength of tidal mixing, winds, and waves can lead to an alternation between periods of strong stratification and strong mixing (Simpson et al., 1990). The stratification– destratification cycle acts, in turn, as an important physical control on the local environment and its productivity.
2.01.2.1 Stratification, Turbulence, Estuarine Circulation and Mixing The essential fluid dynamic concepts, their quantitative defini tions, and the underlying physics of estuarine buoyancy, with its crucial consequences for turbulent mixing exchanges, are described in Chapter 2.02. It starts with the basics of sheared, stratified turbulence and then applies that knowledge to estu aries, river plumes, and the coastal ocean. Here, we find definitions for turbulent flow and the Reynolds’ decomposi tion, in which the total kinetic energy (KE) is separated into the mean KE and the turbulent kinetic energy (TKE). Stratification is defined using an inverse timescale, the Brunt Vaisala (or buoyancy) frequency, and the mean shear is expressed in terms of the vertical shears in horizontal flow, from which the gradient Richardson number follows. The fundamental three-way interaction is: turbulence acts to reduce shear and stratification, while shear acts to increase turbulent mixing, and
stratification acts to decrease turbulent mixing. The Kolmogorov and Ozmidov length scales are introduced and the TKE equation is derived. The vertical buoyancy flux is introduced, together with topics concerned with dissipation rate, shear production of TKE and the conversion of TKE to potential energy. Wave–current interactions in the bottom boundary layer are discussed, as is the influence of internal waves; a diagram is presented that distinguishes high-frequency fluctuations due to waves from turbulence. Stratification in estuaries is discussed in terms of tidal and baroclinic straining and turbulent mixing and various examples of unstratified, partially stratified, and persistently stratified estuaries are discussed. The effects of wind and turbulence within plumes and definitions of near-field and far-field effects with respect to the plume mouth and supercritical flow are discussed. The chapter ends with a discussion of turbulence in coastal seas and annual cycles of seasonal stratification. The definitions and concepts described in Chapter 2.02 are put to practical use at the whole-estuary scale by Geyer and Ralston in Chapter 2.03, which deals with highly stratified estuaries and starts by explaining that these are of just two kinds – salt wedges and fjords. Although salt wedges are often thought of as associated with weak tidal mixing, in fact they can also occur in the presence of strong tidal mixing, provided the buoyancy inputs from freshwater inflows are sufficiently great to reestablish stratification every tidal cycle. It is interesting that fjords do not always exhibit large vertical salinity differences but, as is explained, their great depths and associated large potential energy implies weak mixing and therefore dynamical behavior that is similar to that for salt wedges. Chapter 2.03 begins with a discussion of the dimensionless numbers that are used to describe stratified systems at the large, whole-estuary scale; for example, the surface to bed density difference divided by reference density; the flow ratio of fresh water inflow per unit cross-sectional area divided by the root mean-square (or a similar statistic) tidal current; the freshwater Froude number and so on. The two-layer equations form a starting point for a discussion of the dynamics in which an idealized buoyant upper layer and a denser lower layer are separated by a sharp pycnocline. The application of continuity and momentum equations for the two layers clearly illustrates the importance of the composite Froude number in these systems (Armi and Farmer, 1986): Fu2 þ Fl2 ¼ G2 where Fu and Fl are Froude numbers for the upper and lower layers, and determines whether the flow is subcritical or supercritical with respect to internal waves. Salt-wedge dynamics are then described and the point is made that salt wedges are not distinguished by the dominance of any one forcing mechanism, but rather by the intensity of all of them – tidal, fluvial, and estuarine response to buoyancy forcing. The effects of bottom friction are described, using as an illustration the flooding tide in a flat-bottomed estuary, which is shown to lead to a parabolic interface height between advan cing salt wedge and stationary, overlying buoyant waters. It is interesting that a steady two-layer regime cannot be maintained within a salt-wedge estuary with supercritical flow; currents may increase to critical during the ebb, which may lead
Water and Fine-Sediment Circulation
to intense mixing, although most of the mixing and stratification–breakdown occur in the pycnocline, as a result of shear instability; subsequently it appears to be driven by boundary-layer turbulence at the bottom. Fjord dynamics are described, in which the two-layer density-driven flow is more important than tidal exchange and the Knudsen relation and the notion of hydraulic control are introduced to explain the flow at the mouth. The concept of overmixing is described, in which the maximum amount of mixing that can occur depends on the geometry of the mouth and the freshwater inflow – a paradoxical result that is resolved by the transient response of the fjord’s salinity distribution. Hydraulic flow over sills is described and an echo sounder image that records the hydraulic response to a sill at Knight Inlet is shown (e.g., Farmer and Armi, 1999). The response of upper-layer thickness and mixing to wind is described, showing that the dependence is strong, irrespective of freshwater inflow. The chapter ends with a description of unresolved questions and ideas and prospects for future research – not only from the viewpoint of physics, but also those relating to ecology and water quality in strongly stratified systems. The theme of stratification is continued in Chapter 2.04, which discusses, largely from a qualitative perspective but with some theoretical analysis, the behavior of several kinds of sur face frontal systems that form in estuaries. Attention is restricted to small-scale, buoyancy-driven fronts in which the Earth’s rotation plays an insignificant role. The discussion starts with plume fronts, which are possibly the longest- and best-studied frontal type, in which fresh or intermediate sali nity waters spread as a thin, buoyant, surface layer into the ambient estuarine waters and intense surface convergences occur at the boundaries between the two. This is followed by an analysis of the axial convergence front, which occurs within estuaries that are mixed vertically during the flooding tide. It is shown that the role of buoyancy is to generate a longitudinal density gradient that may be acted upon by tidal straining in the horizontal direction, across the width. These fronts tend to form in the deepest part of the main channel and comprise a circulation that consists of two cells, both of which extend over the channel depth and possess a zero transverse velocity near mid-depth. They form in many strongly tidal estuaries at loca tions where the longitudinal salinity and density gradients are large. A theoretical analysis is given that follows the model of Nunes and Simpson (1985). The highly stratified, V-shaped tidal intrusion front also only appears on the flood and, following Simpson and Nunes (1981), an analysis is given in terms of an ebb-directed buoy ancy current that is pushed back up-estuary by the flooding tidal flow. Another example is described in which the tidal intrusion front forms in the neck of an estuary’s inlet, around mid-flood, such that its behavior appears to be governed by an inflow Froude-number criterion. The final type of front that is dealt with separately is the shear front, in which transverse shear in the longitudinal tidal currents, caused by bathymetry and enhanced drag in shallower waters, acts on a longitudinal density gradient in order to produce a lateral density gradient that may, in turn, drive con vergent circulations. They are therefore related to the axial convergence fronts, which may be considered a special case, although they can occur at various stages of the tide and often in the presence of stratification.
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The central role of buoyancy in generating the estuarine circulation and its associated exchange flow through the estu ary mouth, an important driver of the tidally averaged salt transport in estuaries, is illustrated by MacCready and Banas in Chapter 2.05. It starts by illustrating the similarity of the longitudinal and vertical salinity distributions for estuaries of several different size scales and points out the common feature of estuarine circulation as an up-estuary flow near the bottom and an outward, down-estuary flow near the surface, showing that this exchange flow may be many times greater than the freshwater inflow whose buoyancy forcing is responsible for the exchange. The discussion is centered on the volume-integrated estuarine salt budget as a convenient way of summarizing important physical processes on a tidally aver aged basis. The tidally averaged salt flux through a seaward section is theoretically divided into parts associated with the inflowing freshwater from the river, the estuarine circulation, and the tidally-induced dispersion. The salt flux due to the inflowing freshwater from the river is straightforward and is simply the product of the flow and the section-averaged, tidally averaged salinity. A simple model for the gravitational circulation is then considered that is a cubic function of depth beneath the surface and defines residual-velocity scales and salt-intrusion length scales, as well as leading to a prediction for the vertical salinity structure and the salt-intrusion length scale. This helps make the point that the estuarine circulation and the salinity distribution are very closely coupled. An interesting aspect of this analysis is that it predicts a weak power-law dependency between intrusion length and inflow, whereas, in a highly stratified system, the relationship is very strong, as is pointed out in Chapter 2.03. The final part of the salt flux is due to the tidal average of various tidally-driven mechanisms. This is described in terms of dispersion of the mean salt field by tidal residual eddies, such as occur off headlands and off sharp changes in bathymetry (Zimmerman, 1976; Uncles, 1982). Also considered are corre lations between velocity and salinity caused by tidal trapping mechanisms, in which parts of the tracer (salt in this case) are shunted into embayments and subestuaries and then rejoin the main channel at some later time. The chapters described so far all deal with positive buoy ancy. In Chapter 2.08, Winant describes a hypersaline, inverse estuary in which salinity increases toward the head because of high evaporation and low precipitation. It is shown for this estuary that buoyancy forcing is dominant during neap tides when winds are weak; because tidal currents and tidallyinduced residual currents and mixing also are weaker at neap tides, this leads to relatively lower salinity waters flowing into the basin near the surface and relatively higher salinity waters returning to the coastal sea near the bottom.
2.01.3 Barotropic and Wind-Driven Motions The tidal rise and fall of water level and the associated oscilla tory flood and ebb currents are the most obvious features of water movements in many coastal regions and estuaries. The observed tides within an estuary are usually forced by the tidal rise and fall of water level in the adjacent coastal sea. Because tidal wavelength is so long compared with water depths, the flow is mainly horizontal and vertical variations in horizontal
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velocity are greatest close to the bottom boundary layer. As the tide propagates into an estuary, it causes changes in water level, circulations, and mixing. The shallowness of most estuaries also leads to important nonlinear effects, such as the develop ment of overtides and tidally-induced residual currents. Tidal flows can have a profound influence on the water quality and ecology of an estuary. Frictional stresses at the seabed largely determine sediment bed types and associated benthic macrofaunal communities. These stresses also generate vertical turbulence, which, in turn, affects the vertical profiles of temperature, suspended sediment, salt, and other variables. Knowledge of tides also is important in problems of marine transport, coastal erosion, and the design of coastal defenses against flooding. Although estuaries are often thought of as stratified systems that are dominated by tides and buoyancy, some aspects of their dynamics are influenced by wind forcing. Wind stress at the surface results in wind-generated waves that transfer momentum to the water column. The shallowness of many estuaries means that probably there are times when the wave-effected surface layers will overlap the bottom boundary layer.
2.01.3.1
Tides, Winds, and Waves
The three-dimensional (3D) equations of motion with density terms ignored in order to focus on free-surface barotropic motions, such as seiches and other oscillations at tidal or subtidal frequencies, are presented by Li in Chapter 2.06. The discussion starts with the case of a tidal channel that is narrow (much narrower than the Rossby deformation radius) and where friction is linearized and nonlinear terms are neglected. Analytic solutions are then found that express the tidal (or seiche) oscillations along the estuary as a superposition of damped, oppositely traveling incident and reflected waves. As the estuary’s length increases, tidal velocity amplitude at the mouth increases until the channel length is close to a quarter of a tidal wavelength, at which point the amplitude reaches its maximum due to near-resonance conditions. The effects of further increases in length are also explored, as is the effect of the Earth’s rotation. It is shown that, in the presence of lateral (cross-channel) depth variations, there is a cross-channel variation in the phase of the longitudinal tidal velocity for different drag coefficient values and, particularly, a phase difference between shallow and deep water over a given cross section – the along-channel velo city in shallow water experiences flood and ebb earlier than that in deep water. Also, the amplitude of the longitudinal velocity is faster in deeper water and slower in shallower water and large lateral bottom slopes can cause large lateral flows. Results are given for tidally-induced residual flows that show that the residual flow for short channels is up-estuary in the deep water, whereas it is down-estuary over the shoals. When the estuary length is further increased, the residual exchange flow at the seaward end eventually reverses direction, so that residual flow in the deep channel is down-estuary, whereas flow on the shoals is up-estuary. These results apply only to estuaries with relatively straight channels and a discus sion is given of the effects of channel curvature. The effects of the Earth’s rotation and the influence of bathymetry on the tidally-driven, wind-driven, and
density-driven residual flows are described by Valle-Levinson in Chapter 2.07. The predicted flows without rotation are first discussed and then the effects of rotation on each of the tidally-, wind- or density-driven flows are described in order to high light the major influences of the Earth’s rotation. The two-dimensional (2D), depth-averaged equations of motion without the Earth’s rotation are subjected to a perturbation expansion and solved to zero order to yield the tidal behavior and to first order to yield the residual flow, which is shown to be the sum of a Stokes’ transport velocity, a flow due to the tidal stress associated with spatial gradients in the tidal flow and a flow due to the residual surface slope (or residual pressure gradient) along the estuary. For long estuaries, a down-estuary residual flow occurs in the deep channel near the mouth and an up-estuary flow on the shoals, whereas this is reversed close to the head (as in Chapter 2.06). These results are essentially unaltered by rotation in a long and wide estuary where friction is large. However, the lateral flows change substantially with rotation and describe a gyre in the vertical plane. For weak friction, the along-estuary tidal residual flow depicts a horizon tal, estuary-wide counterclockwise gyre with residual inflow on the right (looking into the estuary in the northern hemisphere) and residual outflow on the left. An important effect of the Earth’s rotation is to increase lateral circulations. The generation of wind-driven flows without baroclinic effects is then described, first without rotation and then with rotation. In estuaries with strong lateral variations in bathyme try, the flow is downwind over the shoals and upwind in the channel. The flow becomes vertically sheared as lateral variations in bathymetry become less pronounced. Downwind flow is confined to a near-surface layer and upwind flow occurs near the bottom. The main influence of the Earth’s rotation on the wind-driven flows is the production of asymmetries in the long itudinal flows and the generation of important lateral flows. The generation of density-driven flows is then described, first without rotation and then with rotation. The solution represents the classical estuarine circulation, comprising a resi dual outflow at the surface and an inflow near the bottom. This pattern may be modified if lateral variations in bathymetry are introduced. For low Ekman number or deep waters, the exchange flow is nearly geostrophic and vertically sheared. Also, the along-basin flow is asymmetrically distributed because of Coriolis accelerations. By contrast, for high Ekman number or shallow waters, the along-basin flow is frictionally dominated and laterally sheared. In Chapter 2.08, Winant shows that wind stress has a strong influence in the upper reaches of his study area and is highly correlated with subtidal fluctuations in the longitudinal, baro tropic pressure gradient. The sign of the correlation and the amplitude of the regression coefficient are consistent with wind-driven models. Where the bathymetry is reasonably sim ple, the wind-driven flow in the deeper sections is upwind, forced by a setup of water level that ensures that there is no integrated residual flow over any cross section of the estuary. Where the bathymetry of channels is complicated, observations show that the flow direction varies with depth and is not simply related to either local orientation of the bathymetry or the direction of the wind. The effects of wind stress on estuaries are reviewed by O’Callaghan and Stevens in Chapter 2.09. This review considers how the stress transfer to the waters is represented analytically
Water and Fine-Sediment Circulation
and how the stress transfer is incorporated into circulation mod els. It starts by considering the quadratic stress relationship and its associated surface drag coefficient, but expresses concern about the amount of scatter that is observed for this coefficient at low and high wind speeds. They describe how atmospheric forcing of circulation within an estuary occurs through local and remote effects. Locally, wind stress acts on an estuary’s surface and drives surface currents, waves, and turbulence, whereas remote forcing is generated by along-shelf winds that induce Ekman setup across the shelf, which, in turn, causes water-level fluctuations at the estuary mouth that then propagate into the estuary. Lag correlations of <1 day exist between high wind stresses and subsequent destratification of the water column, which demonstrates the importance of the turbulent mixing that results from local wind stress. They discuss a published regime diagram that summarizes several numerical simulations of wind influences on estuaries and observational data from several authors. It shows that up-estuary winds tend to decrease stratification, whereas down-estuary winds can cause either an increase or a decrease. Waves in coastal and estuarine waters are discussed by Wolf et al. in Chapter 2.10. The topics covered include air–sea inter actions, including the transfer of momentum from wind to sea; bottom stress due to winds and the resuspension of sediment caused by enhanced bottom shear stresses; wave breaking at the shore and its consequences for coastal erosion and the forma tion of sandy beaches; wave setup at the coast, thereby contributing to flooding; wave-generated longshore drift and the associated transport of sediments; and mixing processes due to wave-induced turbulence and Langmuir circulations. Detailed theory is not provided, although references are cited where needed. Nevertheless, the chapter starts with a mathe matical description of linear wave theory and wave groups and describes waves in shallow waters before discussing the obser vation of waves, including extreme wave events, using both in situ methods and remote sensing. Wave modeling is dealt with next, including third-generation (3G) spectral models (WAve prediction Model (WAM), Simulating WAves Nearshore (SWAN), and others), together with related aspects, such as wind inputs, dissipation, bottom friction, nonlinear interactions, and propagation. Applications of wave models are described for the UK coast, including the use of WAM and several examples of stationary SWAN applications, together with a discussion of nonstationary SWAN. Examples are then given of parametric wave modeling. The Proudman Oceanographic Laboratory Coastal Ocean Model System (POLCOMS)-WAM model is described, as are new develop ments in shallow-water wave modeling. Finally, wave–current interactions are discussed together with aspects of the utility of wave modeling to coastal engineer ing, including modeling the surf zone, coastal defense (along with several case studies), and marine renewable energy and climate-change studies.
2.01.4 Coastal and Estuarine Interactions The importance of coastal regions to humanity has already been mentioned – it is beyond dispute – and yet, as human pressures on coastal zones steadily increase, so too do natural pressures. Understanding and managing the coastal zone is one
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of the most important challenges facing us. In the context of this volume, river discharge is buoyant in seawater and may contain large concentrations of land-derived nutrients, con taminants, and pollutants that may greatly modify the estuarine and coastal environments and their ecosystems and, subsequently, large areas of the shelf seas. The river-derived buoyancy inputs tend to induce water-column stratification and may drive significant density currents along the coast. These coastal and shelf–sea regions of freshwater influence are often referred to as ROFIs and are such that times of haline stratification, due to large estuarine buoy ancy inputs to the coastal waters, alternate with times of strong vertical mixing by tides and winds. The extent of stratification tends to vary with spring–neap periodicity and with wind strength. Haline stratification also may be reinforced by seaso nal thermal stratification on the shelf.
2.01.4.1 River Plumes on the Shelf and Coastal Oceanography River plumes and their formation, transport, and dispersal into coastal waters are described in Chapter 2.11 by Chant. The chapter starts by presenting the basic scaling relationships in terms of the nondimensional numbers that are associated with an outflow of buoyancy to the coastal zone. Next, the region within one tidal excursion of the buoyancy outflow (referred to as the ‘near field’) is discussed, focusing on the effects of the tides in driving exchanges of water, momentum, and materials between estuaries and their coastal waters, which is followed by an exploration of the effects of shear-induced mixing on the stratified and spreading buoyant outflow. Details of the coastal currents arising from this outflow, which are characterized as bottom attached or surface advected, are then described, as are the effects of upwelling and downwelling winds and the con sequences of freshwater bulge formation. The chapter ends with illustrations of example outflows from the Columbia, Delaware, Hudson, Chesapeake, and Rhine systems. Coastal circulations are dealt with by Lane et al. in Chapter 2.12; attention is focused on strongly tidal shelf regions where tidal circulations generally dominate, but where wind and buoyancy effects are nevertheless important. The discussion starts with tidally-driven behavior, including tidal elevations, tidal currents, and the effects of the Earth’s rotation, from which follows a description of the generation of higher harmo nics and residual currents by nonlinear tidal interactions. Long-term changes in mean sea level are also described, includ ing the seasonal variation of mean sea level as approximated by the sum of an annual and semiannual tide. Density-driven circulation patterns are discussed, incorporating the influences of salinity and temperature distributions and the annual tem perature cycle, along with the consequences of stratification and tidal straining on the vertical structure of residual currents. Wind-driven circulations are considered from both theoretical and observational viewpoints, considering the local responses to wind forcing and the generation and propagation of storm surges. A case study of Liverpool Bay is presented that deals with its circulation due to M2 tides and the generation of higher harmonics and tidal residual currents, as well as the effects of drying beaches on tidal circulation patterns. The chapter ends with a discussion on the prediction of important management issues, such as coastal flooding and
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erosion in the coastal zone and possible ways forward, includ ing the provision of whole-system models that comprise integrated, well-validated, robust, portable, and reliable mod ules. In this approach, ideally, coastal managers should have access to a range of modeling capabilities that are routinely assessed by a wide range of continuously monitored data.
2.01.5 Biological Interactions and Sediments Water velocities and roughness lengths are affected by the pre sence of plants on the bottom, for example seagrass meadows, beds of kelp and other macrophytes. These modify the flow at several spatial scales from, for example, individual blades to the reef, meadow, and forest (canopy) scale. Different scales are relevant to different processes. At the large scale, penetration of turbulence into the canopy is limited by the canopy drag, which determines the displacement of the logarithmic velocity profile above the canopy and the decay of stress-driven flow within it. The interaction between flow and sediments and biology is a growing area of research interest. Benthic diatoms and other organisms that inhabit intertidal mudflats in estuaries pro duce polysaccharide polymers (extracellular polymeric substances, EPSs) and influence the local stability of the muddy sediment by increasing its threshold for erosion. EPS may also act as a source of organic material that coats the surfaces of suspended fine sediment and enhances their abil ity to aggregate and produce large flocs. The surface diatom layer (biofilm) on intertidal mudflats modifies the initial erosion of the surface mud layer, although bio-stabilization of sediments may result from several mechanisms, including microphytobenthos, algal mats, higher plants, polychaetes, and mussel beds; bio-destabilization mainly results from the bioturbation caused by burrowing and deposit-feeding ani mals (Widdows, 2001). The transport and behavior of sediment, and fine sediment in particular, are important topics because they affect practical issues, such as coastal and estuarine erosion, accretion within ports, harbors and canals, diversion of tributary river waters for societal use, and the need for maintaining navigational chan nels. Also, because of the high adsorptive capacity of fine sediments for dissolved pollutants, their behavior needs to be understood in water-quality problems. The accurate modeling of fine sediment phenomena is therefore a prerequisite for the prediction of these and other issues. In the past, this has largely been the remit of the engineer and has involved the derivation and solution of physically based relationships between the sediment and its physical and chemical environment, but the growing awareness of biological effects will invariably lead to the inclusion of these in future models.
2.01.5.1 Hydrodynamic Interactions with Biota and Sediments Flow over and through biota due to waves and unidirectional currents is discussed by Nepf in Chapter 2.13. It describes the mean and turbulent flow near aquatic plants and corals. It starts with a description of the flow at the scale of individual blades and branches and then goes on to describe the flow at the canopy scale.
The biological influences that affect sediment transport and behavior are described by Andersen and Pejrup in Chapter 2.14. They show that biology and biological processes affect sediments and sediment transport processes. Vegetation pro tects the bed from erosion and can increase sedimentation. On intertidal mudflats, benthic microphytobenthos and bacteria stabilize the surface of fine-grained sediments, whereas macrofauna generally increase erodibility. They point out that whereas the biological influence on sediment flocculation in the water column has received significant research attention, the influence on settling behavior largely has been ignored. The physical analyses of muddy sedimentation processes are dealt with in Chapter 2.15 by Winterwerp, who summarizes the considerable amount of physical-based work on sedimentation processes that has been undertaken in estuaries and in coastal seas. The chapter focuses on fine, cohesive sediment processes through the water column and over tidal cycles. A description is given of floc formation induced by turbulent mixing and stres ses. It is pointed out that whereas flocs may settle as individual aggregated particles, they may also be subject to ‘hindered’ set tling when suspended sediment concentrations are large. When a network of flocs is formed (a gel), the water–sediment mixture is referred to as fluid mud and, in general, fluid mud is in a transient state, consolidating in areas of slow currents and erod ing when bottom shear-stresses become large.
2.01.6 Measurements and Modeling Advances in instrumentation, such as the acoustic Doppler current profiler (ADCP), the high-frequency (HF) oceansurface-current radar (OSCR), and airborne and space-borne technology, have greatly facilitated the observation of spatial variations in estuaries and coastal seas. Detailed maps of sur face currents in the coastal zone have been derived from OSCR and, provided only near-surface data are required, satellite and airborne remote sensing gives new insights into spatial varia bility that is of great value to studies of estuarine and coastal water quality. Because airborne remote sensing operates from low-flying light aircraft, it can provide very high spatial resolution – of the order of several meters or less. Advances in the development and application of numerical modeling techniques to estuarine and coastal waters over the past 20 years have led to great advances in our understanding of complex 3D processes. The huge increase in computer power over this period has been a major driver in the application of 3D models and they are now routinely used for understanding processes within estuaries and adjacent coastal seas.
2.01.6.1 Measurement and Modeling Techniques for Estuarine and Coastal Waters Measurement technologies for applications to estuarine and coastal waters are described by Souza et al. in Chapter 2.16. They begin by pointing out that systematic marine monitoring programs, hand-in-hand with computer modeling studies, are vital for addressing both the threat to our estuaries and coastal zones from climate-change impacts and their sustainable envir onmental management. Such monitoring programs require a combination of remote sensing, moorings, and coastal stations and all of these topics are dealt with in some depth in this
Water and Fine-Sediment Circulation
chapter, the aim of which is to provide a framework for the design of physically based measurement programs and an assessment of the capabilities and limitations of their essential measurement technologies. In situ measurements are considered for sea-level monitoring using stilling well and float, pressure, acoustic, and radar sys tems. Wave measurements using staffs, buoys, bottom-mounted pressure and velocity sensors and ADCPs are described, together with the deployment of networks of these sensors in multisensor arrays. Instruments for measuring salinity (via conductivity) and temperature are mentioned, as is the measurement of currents using acoustic Doppler current meters of various types (the acoustic Doppler velocimeter (ADV) and the ADCP). The esti mation of turbulence using ADCPs and microstructure shear probes is described. For suspended sediment phenomena, the optical backscatter point sensor (OBS) and the acoustic back scatter profiling sensors (ABS and ADCP) are described for concentration measurements and the laser in situ scattering trans missometer (LISST) for both concentration and suspended sediment particle-size distributions. Remote sensing is discussed at length: first the use of satel lites and aircraft to measure sea-surface elevations and waves, meteorology, surface currents, temperature and salinity, and ocean color; then, the use of land-based radar (HF and X-band) to measure surface currents, including those due to waves. Another coastal application for radar is the derivation of depth data and the production of bathymetric maps that cover large areas of complex sand banks without the need for boat surveys. Finally, real-time monitoring is covered from the view point of operational oceanography (e.g., to provide real-time and near real-time wind fields, wave height spectra, tempera ture and salinity, floating sea ice, chlorophyll, tides, currents, and storm surges) and the use of coastal observatories. As mentioned, modeling is an important component of the effort to address both the threat to our estuaries and coastal zones from climate-change impacts and for their sustainable environmental management. In Chapter 2.17, Torres and Uncles cover a range of hydrodynamic modeling methods and their applications to estuarine and coastal waters. The 3D governing equations are presented first in their Cartesian and spherical coordinate forms, together with boundary conditions and the specification of eddy viscosities and diffusivities, along with the transformation to sigma coordinates in the vertical. The 2D depth-averaged and width-averaged equations for water levels, currents, salinity, and temperature and the one-dimensional (1D) cross-sectional averaged equations are then described. The assimilation of data into numerical models is discussed in broad terms next, paying special attention to the Kalman Filter family. The topics of parallelism and of structured and unstructured grid choice are covered, together with examples of both grid types in the application of current 3D models. Results from simulations of POLCOMS for the western English Channel are given as an example of a structured grid model and the Finite Volume Coastal Ocean Model (FVCOM) is applied to the Plymouth coastal zone and estuaries as an example of an unstructured grid model. Depth-averaged 2D hydrodynamic models and their applications to the calculation of shelf and estuary tides and overtides and to the calculation of wind effects and other phenomena are then described. Finally, some simpli fied, long timescale models are presented and applied to the
7
simulation of salinity during droughts and during rising sea levels, and to the simulations of oxygen isotope ratios, seasonal temperature cycles, and intratidal variations in turbidity.
2.01.7 Final Remarks We believe that the chapters in this volume represent the current state of the art with regard to both our understanding of the physical processes operating in estuaries and the coastal ocean and current technologies for measuring and modeling those processes. Nonetheless, we recognize that technologies will con tinue to evolve. Indeed, during the span of our own careers, circulation models have advanced dramatically in step with remarkable advances in computing technology, reaching the point where they can be routinely used to help make difficult management decisions as well as be deployed as experimental tools for enhancing our understanding of the fundamental phy sics of estuarine and coastal systems. In the same way, observing techniques have also evolved, most notably through the intro duction and widespread use of ADCPs, instruments that have given us a remarkable ability to measure spatial structure and temporal variations of currents, waves, and turbulence. However, we remain convinced that physical insight as exempli fied by the conceptual and analytical models of coastal and estuarine flows described in this volume will always play a central role in advancing our understanding, and thus in enabling society to make the best decisions possible in protect ing, restoring, and managing valuable coastal ecosystems.
Acknowledgments For one of us (RJU), this work is a contribution to the UK’s Natural Environment Research Council (NERC) Oceans 2025 program. The second editor (SGM) would like to acknowledge the exceptional efforts of the first editor. Both editors also wish to thank all of the contributing authors for having provided us with such exceptional material for this volume.
References Allen, J.I., Blackford, J.C., Holt, J., Proctor, R., Ashworth, M., Siddorn, J., 2001. A highly spatially resolved ecosystem model for the North West European Continental Shelf. Sarsia 86, 423–440. Armi, L., Farmer, D.M., 1986. Maximal two-layer exchange through a contraction with barotropic net flow. Journal of Fluid Mechanics 164, 27–51. Cameron, W.M., Pritchard, D.W., 1963. Estuaries. In: Hill, M.N. (Ed.), The Sea: Ideas and Observations on Progress in the Study of the Seas, Vol. 2. Interscience, London, pp. 306–325. Deleersnijder, E., Delhez, E.J.M., 2007. Timescale- and tracer-based methods for understanding the results of complex marine models. Estuarine, Coastal and Shelf Science 74, v–vii. Farmer, D.F., Armi, L., 1999. Stratified flow over topography: the role of small scale entrainment and mixing in flow establishment. Proceedings of the Royal Society of London 455A, 3221–3258. Fischer, H.B., 1972. Mass transport mechanisms in partially stratified estuaries. Journal of Fluid Mechanics 53, 671–687. Garvine, R.W., Monk, J.D., 1974. Frontal structure of a river plume. Journal of Geophysical Research 79, 2251–2259. Hansen, D.V., Rattray, M., Jr., 1965. Gravitational circulation in straits and estuaries. Journal of Marine Research 23, 104–122.
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Hansen, D.V., Rattray, M., Jr., 1966. New dimensions in estuary classification. Limnology and Oceanography 11, 319–326. Huntley, D., Leeks, G., Walling, D., 2001. From rivers to coastal seas: the background and context of the land–ocean interaction study. In: Huntley, D., Leeks, G., Walling, D. (Eds.), Land Ocean Interaction – Measuring and Modelling Fluxes from River Basins to Coastal Seas, 286 pp. IWA Publishing, London, pp. 1–7. Nunes, R.A., Simpson, J.H., 1985. Axial Convergence in a Well-Mixed Estuary. Estuarine, Coastal and Shelf Science 20, 637–649. Pritchard, D.W., 1952. Salinity distribution and circulation in the Chesapeake Bay estuarine system. Journal of Marine Research 11, 106–123. Pritchard, D.W., 1954. A study of the salt balance in a coastal plain estuary. Journal of Marine Research 13, 133–144. Pritchard, D.W., 1955. Estuarine circulation patterns. Proceedings of the American Society of Civil Engineers 81 (717), 1–11.
Pritchard, D.W., 1956. The dynamic structure of a coastal plain estuary. Journal of Marine Research 15, 33–42. Simpson, J.H., Brown, J., Matthews, J., Allen, G., 1990. Tidal straining, density currents, and stirring in the control of estuarine stratification. Estuaries 13, 125–132. Simpson, J.H., Nunes, R.A., 1981. The tidal intrusion front: an estuarine convergence zone. Estuarine, Coastal and Shelf Science 13, 257–266. Uncles, R.J., 1982. Residual currents in the Severn Estuary and their effects on dispersion. Oceanol. Acta 5, 403–410. Widdows, J., 2001. The intertidal zone. In: Huntley, D.A., Leeks, G.J.L., Walling, D.E. (Eds.), Land–ocean interaction: measuring and modelling fluxes from river basins to coastal seas. IWA Publishing, London, pp. 184–208. Zimmerman, J.T.F., 1976. Mixing and flushing of tidal embayments in the western Dutch Wadden Sea, Part II. Netherlands Journal of Sea Research 10, 397–439.
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RJ Uncles, Plymouth Marine Laboratory, Plymouth, UK SG Monismith, Stanford University, Stanford, CA, USA © 2011 Elsevier Inc. All rights reserved.
2.01.1 2.01.2 2.01.2.1 2.01.3 2.01.3.1 2.01.4 2.01.4.1 2.01.5 2.01.5.1 2.01.6 2.01.6.1 2.01.7 References
Introduction Buoyancy and Its Consequences Stratification, Turbulence, Estuarine Circulation and Mixing Barotropic and Wind-Driven Motions Tides, Winds, and Waves Coastal and Estuarine Interactions River Plumes on the Shelf and Coastal Oceanography Biological Interactions and Sediments Hydrodynamic Interactions with Biota and Sediments Measurements and Modeling Measurement and Modeling Techniques for Estuarine and Coastal Waters Final Remarks
1 2 2 3 4 5 5 6 6 6 6 7 7
Abstract This chapter provides an introduction to Volume 2 of the Treatise, which deals with water and fine-sediment circulation in estuaries and the coastal zone. Chapters 2.02, 2.03, 2.04, and 2.05 are concerned primarily with buoyancy and its consequences for circulation and include topics such as stratification, turbulence, estuarine circulation, surface fronts, plumes, and mixing. Chapters 2.06, 2.07, 2.08, 2.09, and 2.10 consider barotropic and wind-driven motions, especially tides, winds, and waves. Coastal and estuarine interactions, incorporating river plumes on the shelf and coastal oceanogra phy, are dealt with in Chapters 2.11 and 2.12. Chapters 2.13, 2.14, and 2.15 describe biological interactions and sediments and particularly hydrodynamic interactions with biota and sediments. Finally, Chapters 2.16 and 2.17 deal with measure ment and modeling techniques for estuarine and coastal waters.
2.01.1 Introduction It is interesting to note that, within the treatise, only approximately 10% of the chapters relate to water circulation and fine-sediment transport. This small percentage hides the fact that at the system level almost all nonphysical processes within estuaries and coastal waters are, actually, strongly dependent on these physical processes – the currents that transport watercolumn biology and chemistry, the mixing that brings both aspects closer to the surface and to light, and the suspension and accretion of mud, or the movements of sand and the tidal drag on the bed that influences to such an extent the biology of the benthic system, or the salt that is mixing with freshwater to influence, along with turbidity, the behavior of chemical components of the system. The list could be much longer, more specific, and better focused of course, but the point has been made: to understand the whole system, it is necessary to understand the physics. To understand why the linkages between disciplines are not as strong as they could be, we perhaps need to quote the great Hungarian-American mathematician, John von Neumann (cited in Deleersnijder and Delhez, 2007):
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena…
But, of course, with the noteworthy exception of the large hydrodynamic–ecosystem collaborations (e.g., Allen et al., 2001), models are usually simplified in order to focus on those processes of immediate concern to the modeler and the modeling team. This volume of the treatise is devoted to water and fine-sediment circulation and is largely physical, although two of its chapters have the biological systems as their focus – the effects of biota on muddy sediments and the effects of plants on water flow. The physical system of concern here is the estuarine–coastal waters–shelf continuum, with emphasis on estuaries and coastal waters. This is a system of great importance to humanity; according to Huntley et al. (2001), most of the world’s population and most populous cities are located near the coast and most of the world’s fish catch comes from coastal regions. These regions are often subjected to environmental pressures from sewage and industrial and agricultural pollution that are also assimilated within them. The wastes and effluents arrive at the coast from industries and cities and river catch ments, having been transported by rivers and estuaries, where nutrients and contaminants are sequestered, degraded, and recycled. The transport by waters and suspended sediments and the sequestering by deposited sediments are the key issues here. Land-to–sea interactions are complex. River flows, tides, waves, and buoyancy, derived from the juxtaposition and mix ing of freshwater and seawater, combine to produce this
1
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complexity and variability of water movements. Sediment movement through the estuaries to the coastal zone has addi tional complications, especially for fine sediment (which sequesters pollutants), which are caused by flocculation, settling, suspension, and accretion processes. The biogeochem istry and ecology are sensitive to these factors.
2.01.2 Buoyancy and Its Consequences Starting with the estuary and its circulation of water, the funda mental non-tidal processes are due to freshwater flows and the buoyancy they supply to the estuary. The early classification systems for estuaries, comprising fjord, salt wedge, partially mixed, and well mixed, were essentially based on buoyancy distributions (Pritchard, 1955; Cameron and Pritchard, 1963). Pritchard (1952, 1954, 1956) investigated the tidally averaged momentum balance of the James River Estuary and identified the importance of gravitational current (or estuarine circula tion), which is driven by buoyancy. Later, theoretical models were developed that predicted the subtidal estuarine circula tion as a function of the longitudinal (that is, along-axis) density gradients and classified estuaries in terms of their subtidal (or residual) dynamic behavior (Hansen and Rattray, 1965, 1966). However, bathymetry and salinity distributions are rarely laterally (cross-estuary) uniform and the conse quences of this nonuniformity on the transverse distribution of longitudinal subtidal currents were pointed out by Fischer (1972) – especially their important effects on estuarine mass transport. The developing work was not restricted to subtidal phe nomena and a growing body of research focused on intratidal influences, topographic control (Armi and Farmer, 1986), transverse (lateral) variations and cross-estuary circulations (Nunes and Simpson, 1985), the impacts of spatially varying density gradients and fronts (Garvine and Monk, 1974) and turbulence on estuarine dynamics. In many estuaries, per iodicity in the strength of tidal mixing, winds, and waves can lead to an alternation between periods of strong stratification and strong mixing (Simpson et al., 1990). The stratification– destratification cycle acts, in turn, as an important physical control on the local environment and its productivity.
2.01.2.1 Stratification, Turbulence, Estuarine Circulation and Mixing The essential fluid dynamic concepts, their quantitative defini tions, and the underlying physics of estuarine buoyancy, with its crucial consequences for turbulent mixing exchanges, are described in Chapter 2.02. It starts with the basics of sheared, stratified turbulence and then applies that knowledge to estu aries, river plumes, and the coastal ocean. Here, we find definitions for turbulent flow and the Reynolds’ decomposi tion, in which the total kinetic energy (KE) is separated into the mean KE and the turbulent kinetic energy (TKE). Stratification is defined using an inverse timescale, the Brunt Vaisala (or buoyancy) frequency, and the mean shear is expressed in terms of the vertical shears in horizontal flow, from which the gradient Richardson number follows. The fundamental three-way interaction is: turbulence acts to reduce shear and stratification, while shear acts to increase turbulent mixing, and
stratification acts to decrease turbulent mixing. The Kolmogorov and Ozmidov length scales are introduced and the TKE equation is derived. The vertical buoyancy flux is introduced, together with topics concerned with dissipation rate, shear production of TKE and the conversion of TKE to potential energy. Wave–current interactions in the bottom boundary layer are discussed, as is the influence of internal waves; a diagram is presented that distinguishes high-frequency fluctuations due to waves from turbulence. Stratification in estuaries is discussed in terms of tidal and baroclinic straining and turbulent mixing and various examples of unstratified, partially stratified, and persistently stratified estuaries are discussed. The effects of wind and turbulence within plumes and definitions of near-field and far-field effects with respect to the plume mouth and supercritical flow are discussed. The chapter ends with a discussion of turbulence in coastal seas and annual cycles of seasonal stratification. The definitions and concepts described in Chapter 2.02 are put to practical use at the whole-estuary scale by Geyer and Ralston in Chapter 2.03, which deals with highly stratified estuaries and starts by explaining that these are of just two kinds – salt wedges and fjords. Although salt wedges are often thought of as associated with weak tidal mixing, in fact they can also occur in the presence of strong tidal mixing, provided the buoyancy inputs from freshwater inflows are sufficiently great to reestablish stratification every tidal cycle. It is interesting that fjords do not always exhibit large vertical salinity differences but, as is explained, their great depths and associated large potential energy implies weak mixing and therefore dynamical behavior that is similar to that for salt wedges. Chapter 2.03 begins with a discussion of the dimensionless numbers that are used to describe stratified systems at the large, whole-estuary scale; for example, the surface to bed density difference divided by reference density; the flow ratio of fresh water inflow per unit cross-sectional area divided by the root mean-square (or a similar statistic) tidal current; the freshwater Froude number and so on. The two-layer equations form a starting point for a discussion of the dynamics in which an idealized buoyant upper layer and a denser lower layer are separated by a sharp pycnocline. The application of continuity and momentum equations for the two layers clearly illustrates the importance of the composite Froude number in these systems (Armi and Farmer, 1986): Fu2 þ Fl2 ¼ G2 where Fu and Fl are Froude numbers for the upper and lower layers, and determines whether the flow is subcritical or supercritical with respect to internal waves. Salt-wedge dynamics are then described and the point is made that salt wedges are not distinguished by the dominance of any one forcing mechanism, but rather by the intensity of all of them – tidal, fluvial, and estuarine response to buoyancy forcing. The effects of bottom friction are described, using as an illustration the flooding tide in a flat-bottomed estuary, which is shown to lead to a parabolic interface height between advan cing salt wedge and stationary, overlying buoyant waters. It is interesting that a steady two-layer regime cannot be maintained within a salt-wedge estuary with supercritical flow; currents may increase to critical during the ebb, which may lead
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to intense mixing, although most of the mixing and stratification–breakdown occur in the pycnocline, as a result of shear instability; subsequently it appears to be driven by boundary-layer turbulence at the bottom. Fjord dynamics are described, in which the two-layer density-driven flow is more important than tidal exchange and the Knudsen relation and the notion of hydraulic control are introduced to explain the flow at the mouth. The concept of overmixing is described, in which the maximum amount of mixing that can occur depends on the geometry of the mouth and the freshwater inflow – a paradoxical result that is resolved by the transient response of the fjord’s salinity distribution. Hydraulic flow over sills is described and an echo sounder image that records the hydraulic response to a sill at Knight Inlet is shown (e.g., Farmer and Armi, 1999). The response of upper-layer thickness and mixing to wind is described, showing that the dependence is strong, irrespective of freshwater inflow. The chapter ends with a description of unresolved questions and ideas and prospects for future research – not only from the viewpoint of physics, but also those relating to ecology and water quality in strongly stratified systems. The theme of stratification is continued in Chapter 2.04, which discusses, largely from a qualitative perspective but with some theoretical analysis, the behavior of several kinds of sur face frontal systems that form in estuaries. Attention is restricted to small-scale, buoyancy-driven fronts in which the Earth’s rotation plays an insignificant role. The discussion starts with plume fronts, which are possibly the longest- and best-studied frontal type, in which fresh or intermediate sali nity waters spread as a thin, buoyant, surface layer into the ambient estuarine waters and intense surface convergences occur at the boundaries between the two. This is followed by an analysis of the axial convergence front, which occurs within estuaries that are mixed vertically during the flooding tide. It is shown that the role of buoyancy is to generate a longitudinal density gradient that may be acted upon by tidal straining in the horizontal direction, across the width. These fronts tend to form in the deepest part of the main channel and comprise a circulation that consists of two cells, both of which extend over the channel depth and possess a zero transverse velocity near mid-depth. They form in many strongly tidal estuaries at loca tions where the longitudinal salinity and density gradients are large. A theoretical analysis is given that follows the model of Nunes and Simpson (1985). The highly stratified, V-shaped tidal intrusion front also only appears on the flood and, following Simpson and Nunes (1981), an analysis is given in terms of an ebb-directed buoy ancy current that is pushed back up-estuary by the flooding tidal flow. Another example is described in which the tidal intrusion front forms in the neck of an estuary’s inlet, around mid-flood, such that its behavior appears to be governed by an inflow Froude-number criterion. The final type of front that is dealt with separately is the shear front, in which transverse shear in the longitudinal tidal currents, caused by bathymetry and enhanced drag in shallower waters, acts on a longitudinal density gradient in order to produce a lateral density gradient that may, in turn, drive con vergent circulations. They are therefore related to the axial convergence fronts, which may be considered a special case, although they can occur at various stages of the tide and often in the presence of stratification.
3
The central role of buoyancy in generating the estuarine circulation and its associated exchange flow through the estu ary mouth, an important driver of the tidally averaged salt transport in estuaries, is illustrated by MacCready and Banas in Chapter 2.05. It starts by illustrating the similarity of the longitudinal and vertical salinity distributions for estuaries of several different size scales and points out the common feature of estuarine circulation as an up-estuary flow near the bottom and an outward, down-estuary flow near the surface, showing that this exchange flow may be many times greater than the freshwater inflow whose buoyancy forcing is responsible for the exchange. The discussion is centered on the volume-integrated estuarine salt budget as a convenient way of summarizing important physical processes on a tidally aver aged basis. The tidally averaged salt flux through a seaward section is theoretically divided into parts associated with the inflowing freshwater from the river, the estuarine circulation, and the tidally-induced dispersion. The salt flux due to the inflowing freshwater from the river is straightforward and is simply the product of the flow and the section-averaged, tidally averaged salinity. A simple model for the gravitational circulation is then considered that is a cubic function of depth beneath the surface and defines residual-velocity scales and salt-intrusion length scales, as well as leading to a prediction for the vertical salinity structure and the salt-intrusion length scale. This helps make the point that the estuarine circulation and the salinity distribution are very closely coupled. An interesting aspect of this analysis is that it predicts a weak power-law dependency between intrusion length and inflow, whereas, in a highly stratified system, the relationship is very strong, as is pointed out in Chapter 2.03. The final part of the salt flux is due to the tidal average of various tidally-driven mechanisms. This is described in terms of dispersion of the mean salt field by tidal residual eddies, such as occur off headlands and off sharp changes in bathymetry (Zimmerman, 1976; Uncles, 1982). Also considered are corre lations between velocity and salinity caused by tidal trapping mechanisms, in which parts of the tracer (salt in this case) are shunted into embayments and subestuaries and then rejoin the main channel at some later time. The chapters described so far all deal with positive buoy ancy. In Chapter 2.08, Winant describes a hypersaline, inverse estuary in which salinity increases toward the head because of high evaporation and low precipitation. It is shown for this estuary that buoyancy forcing is dominant during neap tides when winds are weak; because tidal currents and tidallyinduced residual currents and mixing also are weaker at neap tides, this leads to relatively lower salinity waters flowing into the basin near the surface and relatively higher salinity waters returning to the coastal sea near the bottom.
2.01.3 Barotropic and Wind-Driven Motions The tidal rise and fall of water level and the associated oscilla tory flood and ebb currents are the most obvious features of water movements in many coastal regions and estuaries. The observed tides within an estuary are usually forced by the tidal rise and fall of water level in the adjacent coastal sea. Because tidal wavelength is so long compared with water depths, the flow is mainly horizontal and vertical variations in horizontal
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velocity are greatest close to the bottom boundary layer. As the tide propagates into an estuary, it causes changes in water level, circulations, and mixing. The shallowness of most estuaries also leads to important nonlinear effects, such as the develop ment of overtides and tidally-induced residual currents. Tidal flows can have a profound influence on the water quality and ecology of an estuary. Frictional stresses at the seabed largely determine sediment bed types and associated benthic macrofaunal communities. These stresses also generate vertical turbulence, which, in turn, affects the vertical profiles of temperature, suspended sediment, salt, and other variables. Knowledge of tides also is important in problems of marine transport, coastal erosion, and the design of coastal defenses against flooding. Although estuaries are often thought of as stratified systems that are dominated by tides and buoyancy, some aspects of their dynamics are influenced by wind forcing. Wind stress at the surface results in wind-generated waves that transfer momentum to the water column. The shallowness of many estuaries means that probably there are times when the wave-effected surface layers will overlap the bottom boundary layer.
2.01.3.1
Tides, Winds, and Waves
The three-dimensional (3D) equations of motion with density terms ignored in order to focus on free-surface barotropic motions, such as seiches and other oscillations at tidal or subtidal frequencies, are presented by Li in Chapter 2.06. The discussion starts with the case of a tidal channel that is narrow (much narrower than the Rossby deformation radius) and where friction is linearized and nonlinear terms are neglected. Analytic solutions are then found that express the tidal (or seiche) oscillations along the estuary as a superposition of damped, oppositely traveling incident and reflected waves. As the estuary’s length increases, tidal velocity amplitude at the mouth increases until the channel length is close to a quarter of a tidal wavelength, at which point the amplitude reaches its maximum due to near-resonance conditions. The effects of further increases in length are also explored, as is the effect of the Earth’s rotation. It is shown that, in the presence of lateral (cross-channel) depth variations, there is a cross-channel variation in the phase of the longitudinal tidal velocity for different drag coefficient values and, particularly, a phase difference between shallow and deep water over a given cross section – the along-channel velo city in shallow water experiences flood and ebb earlier than that in deep water. Also, the amplitude of the longitudinal velocity is faster in deeper water and slower in shallower water and large lateral bottom slopes can cause large lateral flows. Results are given for tidally-induced residual flows that show that the residual flow for short channels is up-estuary in the deep water, whereas it is down-estuary over the shoals. When the estuary length is further increased, the residual exchange flow at the seaward end eventually reverses direction, so that residual flow in the deep channel is down-estuary, whereas flow on the shoals is up-estuary. These results apply only to estuaries with relatively straight channels and a discus sion is given of the effects of channel curvature. The effects of the Earth’s rotation and the influence of bathymetry on the tidally-driven, wind-driven, and
density-driven residual flows are described by Valle-Levinson in Chapter 2.07. The predicted flows without rotation are first discussed and then the effects of rotation on each of the tidally-, wind- or density-driven flows are described in order to high light the major influences of the Earth’s rotation. The two-dimensional (2D), depth-averaged equations of motion without the Earth’s rotation are subjected to a perturbation expansion and solved to zero order to yield the tidal behavior and to first order to yield the residual flow, which is shown to be the sum of a Stokes’ transport velocity, a flow due to the tidal stress associated with spatial gradients in the tidal flow and a flow due to the residual surface slope (or residual pressure gradient) along the estuary. For long estuaries, a down-estuary residual flow occurs in the deep channel near the mouth and an up-estuary flow on the shoals, whereas this is reversed close to the head (as in Chapter 2.06). These results are essentially unaltered by rotation in a long and wide estuary where friction is large. However, the lateral flows change substantially with rotation and describe a gyre in the vertical plane. For weak friction, the along-estuary tidal residual flow depicts a horizon tal, estuary-wide counterclockwise gyre with residual inflow on the right (looking into the estuary in the northern hemisphere) and residual outflow on the left. An important effect of the Earth’s rotation is to increase lateral circulations. The generation of wind-driven flows without baroclinic effects is then described, first without rotation and then with rotation. In estuaries with strong lateral variations in bathyme try, the flow is downwind over the shoals and upwind in the channel. The flow becomes vertically sheared as lateral variations in bathymetry become less pronounced. Downwind flow is confined to a near-surface layer and upwind flow occurs near the bottom. The main influence of the Earth’s rotation on the wind-driven flows is the production of asymmetries in the long itudinal flows and the generation of important lateral flows. The generation of density-driven flows is then described, first without rotation and then with rotation. The solution represents the classical estuarine circulation, comprising a resi dual outflow at the surface and an inflow near the bottom. This pattern may be modified if lateral variations in bathymetry are introduced. For low Ekman number or deep waters, the exchange flow is nearly geostrophic and vertically sheared. Also, the along-basin flow is asymmetrically distributed because of Coriolis accelerations. By contrast, for high Ekman number or shallow waters, the along-basin flow is frictionally dominated and laterally sheared. In Chapter 2.08, Winant shows that wind stress has a strong influence in the upper reaches of his study area and is highly correlated with subtidal fluctuations in the longitudinal, baro tropic pressure gradient. The sign of the correlation and the amplitude of the regression coefficient are consistent with wind-driven models. Where the bathymetry is reasonably sim ple, the wind-driven flow in the deeper sections is upwind, forced by a setup of water level that ensures that there is no integrated residual flow over any cross section of the estuary. Where the bathymetry of channels is complicated, observations show that the flow direction varies with depth and is not simply related to either local orientation of the bathymetry or the direction of the wind. The effects of wind stress on estuaries are reviewed by O’Callaghan and Stevens in Chapter 2.09. This review considers how the stress transfer to the waters is represented analytically
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and how the stress transfer is incorporated into circulation mod els. It starts by considering the quadratic stress relationship and its associated surface drag coefficient, but expresses concern about the amount of scatter that is observed for this coefficient at low and high wind speeds. They describe how atmospheric forcing of circulation within an estuary occurs through local and remote effects. Locally, wind stress acts on an estuary’s surface and drives surface currents, waves, and turbulence, whereas remote forcing is generated by along-shelf winds that induce Ekman setup across the shelf, which, in turn, causes water-level fluctuations at the estuary mouth that then propagate into the estuary. Lag correlations of <1 day exist between high wind stresses and subsequent destratification of the water column, which demonstrates the importance of the turbulent mixing that results from local wind stress. They discuss a published regime diagram that summarizes several numerical simulations of wind influences on estuaries and observational data from several authors. It shows that up-estuary winds tend to decrease stratification, whereas down-estuary winds can cause either an increase or a decrease. Waves in coastal and estuarine waters are discussed by Wolf et al. in Chapter 2.10. The topics covered include air–sea inter actions, including the transfer of momentum from wind to sea; bottom stress due to winds and the resuspension of sediment caused by enhanced bottom shear stresses; wave breaking at the shore and its consequences for coastal erosion and the forma tion of sandy beaches; wave setup at the coast, thereby contributing to flooding; wave-generated longshore drift and the associated transport of sediments; and mixing processes due to wave-induced turbulence and Langmuir circulations. Detailed theory is not provided, although references are cited where needed. Nevertheless, the chapter starts with a mathe matical description of linear wave theory and wave groups and describes waves in shallow waters before discussing the obser vation of waves, including extreme wave events, using both in situ methods and remote sensing. Wave modeling is dealt with next, including third-generation (3G) spectral models (WAve prediction Model (WAM), Simulating WAves Nearshore (SWAN), and others), together with related aspects, such as wind inputs, dissipation, bottom friction, nonlinear interactions, and propagation. Applications of wave models are described for the UK coast, including the use of WAM and several examples of stationary SWAN applications, together with a discussion of nonstationary SWAN. Examples are then given of parametric wave modeling. The Proudman Oceanographic Laboratory Coastal Ocean Model System (POLCOMS)-WAM model is described, as are new develop ments in shallow-water wave modeling. Finally, wave–current interactions are discussed together with aspects of the utility of wave modeling to coastal engineer ing, including modeling the surf zone, coastal defense (along with several case studies), and marine renewable energy and climate-change studies.
2.01.4 Coastal and Estuarine Interactions The importance of coastal regions to humanity has already been mentioned – it is beyond dispute – and yet, as human pressures on coastal zones steadily increase, so too do natural pressures. Understanding and managing the coastal zone is one
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of the most important challenges facing us. In the context of this volume, river discharge is buoyant in seawater and may contain large concentrations of land-derived nutrients, con taminants, and pollutants that may greatly modify the estuarine and coastal environments and their ecosystems and, subsequently, large areas of the shelf seas. The river-derived buoyancy inputs tend to induce water-column stratification and may drive significant density currents along the coast. These coastal and shelf–sea regions of freshwater influence are often referred to as ROFIs and are such that times of haline stratification, due to large estuarine buoy ancy inputs to the coastal waters, alternate with times of strong vertical mixing by tides and winds. The extent of stratification tends to vary with spring–neap periodicity and with wind strength. Haline stratification also may be reinforced by seaso nal thermal stratification on the shelf.
2.01.4.1 River Plumes on the Shelf and Coastal Oceanography River plumes and their formation, transport, and dispersal into coastal waters are described in Chapter 2.11 by Chant. The chapter starts by presenting the basic scaling relationships in terms of the nondimensional numbers that are associated with an outflow of buoyancy to the coastal zone. Next, the region within one tidal excursion of the buoyancy outflow (referred to as the ‘near field’) is discussed, focusing on the effects of the tides in driving exchanges of water, momentum, and materials between estuaries and their coastal waters, which is followed by an exploration of the effects of shear-induced mixing on the stratified and spreading buoyant outflow. Details of the coastal currents arising from this outflow, which are characterized as bottom attached or surface advected, are then described, as are the effects of upwelling and downwelling winds and the con sequences of freshwater bulge formation. The chapter ends with illustrations of example outflows from the Columbia, Delaware, Hudson, Chesapeake, and Rhine systems. Coastal circulations are dealt with by Lane et al. in Chapter 2.12; attention is focused on strongly tidal shelf regions where tidal circulations generally dominate, but where wind and buoyancy effects are nevertheless important. The discussion starts with tidally-driven behavior, including tidal elevations, tidal currents, and the effects of the Earth’s rotation, from which follows a description of the generation of higher harmo nics and residual currents by nonlinear tidal interactions. Long-term changes in mean sea level are also described, includ ing the seasonal variation of mean sea level as approximated by the sum of an annual and semiannual tide. Density-driven circulation patterns are discussed, incorporating the influences of salinity and temperature distributions and the annual tem perature cycle, along with the consequences of stratification and tidal straining on the vertical structure of residual currents. Wind-driven circulations are considered from both theoretical and observational viewpoints, considering the local responses to wind forcing and the generation and propagation of storm surges. A case study of Liverpool Bay is presented that deals with its circulation due to M2 tides and the generation of higher harmonics and tidal residual currents, as well as the effects of drying beaches on tidal circulation patterns. The chapter ends with a discussion on the prediction of important management issues, such as coastal flooding and
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erosion in the coastal zone and possible ways forward, includ ing the provision of whole-system models that comprise integrated, well-validated, robust, portable, and reliable mod ules. In this approach, ideally, coastal managers should have access to a range of modeling capabilities that are routinely assessed by a wide range of continuously monitored data.
2.01.5 Biological Interactions and Sediments Water velocities and roughness lengths are affected by the pre sence of plants on the bottom, for example seagrass meadows, beds of kelp and other macrophytes. These modify the flow at several spatial scales from, for example, individual blades to the reef, meadow, and forest (canopy) scale. Different scales are relevant to different processes. At the large scale, penetration of turbulence into the canopy is limited by the canopy drag, which determines the displacement of the logarithmic velocity profile above the canopy and the decay of stress-driven flow within it. The interaction between flow and sediments and biology is a growing area of research interest. Benthic diatoms and other organisms that inhabit intertidal mudflats in estuaries pro duce polysaccharide polymers (extracellular polymeric substances, EPSs) and influence the local stability of the muddy sediment by increasing its threshold for erosion. EPS may also act as a source of organic material that coats the surfaces of suspended fine sediment and enhances their abil ity to aggregate and produce large flocs. The surface diatom layer (biofilm) on intertidal mudflats modifies the initial erosion of the surface mud layer, although bio-stabilization of sediments may result from several mechanisms, including microphytobenthos, algal mats, higher plants, polychaetes, and mussel beds; bio-destabilization mainly results from the bioturbation caused by burrowing and deposit-feeding ani mals (Widdows, 2001). The transport and behavior of sediment, and fine sediment in particular, are important topics because they affect practical issues, such as coastal and estuarine erosion, accretion within ports, harbors and canals, diversion of tributary river waters for societal use, and the need for maintaining navigational chan nels. Also, because of the high adsorptive capacity of fine sediments for dissolved pollutants, their behavior needs to be understood in water-quality problems. The accurate modeling of fine sediment phenomena is therefore a prerequisite for the prediction of these and other issues. In the past, this has largely been the remit of the engineer and has involved the derivation and solution of physically based relationships between the sediment and its physical and chemical environment, but the growing awareness of biological effects will invariably lead to the inclusion of these in future models.
2.01.5.1 Hydrodynamic Interactions with Biota and Sediments Flow over and through biota due to waves and unidirectional currents is discussed by Nepf in Chapter 2.13. It describes the mean and turbulent flow near aquatic plants and corals. It starts with a description of the flow at the scale of individual blades and branches and then goes on to describe the flow at the canopy scale.
The biological influences that affect sediment transport and behavior are described by Andersen and Pejrup in Chapter 2.14. They show that biology and biological processes affect sediments and sediment transport processes. Vegetation pro tects the bed from erosion and can increase sedimentation. On intertidal mudflats, benthic microphytobenthos and bacteria stabilize the surface of fine-grained sediments, whereas macrofauna generally increase erodibility. They point out that whereas the biological influence on sediment flocculation in the water column has received significant research attention, the influence on settling behavior largely has been ignored. The physical analyses of muddy sedimentation processes are dealt with in Chapter 2.15 by Winterwerp, who summarizes the considerable amount of physical-based work on sedimentation processes that has been undertaken in estuaries and in coastal seas. The chapter focuses on fine, cohesive sediment processes through the water column and over tidal cycles. A description is given of floc formation induced by turbulent mixing and stres ses. It is pointed out that whereas flocs may settle as individual aggregated particles, they may also be subject to ‘hindered’ set tling when suspended sediment concentrations are large. When a network of flocs is formed (a gel), the water–sediment mixture is referred to as fluid mud and, in general, fluid mud is in a transient state, consolidating in areas of slow currents and erod ing when bottom shear-stresses become large.
2.01.6 Measurements and Modeling Advances in instrumentation, such as the acoustic Doppler current profiler (ADCP), the high-frequency (HF) oceansurface-current radar (OSCR), and airborne and space-borne technology, have greatly facilitated the observation of spatial variations in estuaries and coastal seas. Detailed maps of sur face currents in the coastal zone have been derived from OSCR and, provided only near-surface data are required, satellite and airborne remote sensing gives new insights into spatial varia bility that is of great value to studies of estuarine and coastal water quality. Because airborne remote sensing operates from low-flying light aircraft, it can provide very high spatial resolution – of the order of several meters or less. Advances in the development and application of numerical modeling techniques to estuarine and coastal waters over the past 20 years have led to great advances in our understanding of complex 3D processes. The huge increase in computer power over this period has been a major driver in the application of 3D models and they are now routinely used for understanding processes within estuaries and adjacent coastal seas.
2.01.6.1 Measurement and Modeling Techniques for Estuarine and Coastal Waters Measurement technologies for applications to estuarine and coastal waters are described by Souza et al. in Chapter 2.16. They begin by pointing out that systematic marine monitoring programs, hand-in-hand with computer modeling studies, are vital for addressing both the threat to our estuaries and coastal zones from climate-change impacts and their sustainable envir onmental management. Such monitoring programs require a combination of remote sensing, moorings, and coastal stations and all of these topics are dealt with in some depth in this
Water and Fine-Sediment Circulation
chapter, the aim of which is to provide a framework for the design of physically based measurement programs and an assessment of the capabilities and limitations of their essential measurement technologies. In situ measurements are considered for sea-level monitoring using stilling well and float, pressure, acoustic, and radar sys tems. Wave measurements using staffs, buoys, bottom-mounted pressure and velocity sensors and ADCPs are described, together with the deployment of networks of these sensors in multisensor arrays. Instruments for measuring salinity (via conductivity) and temperature are mentioned, as is the measurement of currents using acoustic Doppler current meters of various types (the acoustic Doppler velocimeter (ADV) and the ADCP). The esti mation of turbulence using ADCPs and microstructure shear probes is described. For suspended sediment phenomena, the optical backscatter point sensor (OBS) and the acoustic back scatter profiling sensors (ABS and ADCP) are described for concentration measurements and the laser in situ scattering trans missometer (LISST) for both concentration and suspended sediment particle-size distributions. Remote sensing is discussed at length: first the use of satel lites and aircraft to measure sea-surface elevations and waves, meteorology, surface currents, temperature and salinity, and ocean color; then, the use of land-based radar (HF and X-band) to measure surface currents, including those due to waves. Another coastal application for radar is the derivation of depth data and the production of bathymetric maps that cover large areas of complex sand banks without the need for boat surveys. Finally, real-time monitoring is covered from the view point of operational oceanography (e.g., to provide real-time and near real-time wind fields, wave height spectra, tempera ture and salinity, floating sea ice, chlorophyll, tides, currents, and storm surges) and the use of coastal observatories. As mentioned, modeling is an important component of the effort to address both the threat to our estuaries and coastal zones from climate-change impacts and for their sustainable environmental management. In Chapter 2.17, Torres and Uncles cover a range of hydrodynamic modeling methods and their applications to estuarine and coastal waters. The 3D governing equations are presented first in their Cartesian and spherical coordinate forms, together with boundary conditions and the specification of eddy viscosities and diffusivities, along with the transformation to sigma coordinates in the vertical. The 2D depth-averaged and width-averaged equations for water levels, currents, salinity, and temperature and the one-dimensional (1D) cross-sectional averaged equations are then described. The assimilation of data into numerical models is discussed in broad terms next, paying special attention to the Kalman Filter family. The topics of parallelism and of structured and unstructured grid choice are covered, together with examples of both grid types in the application of current 3D models. Results from simulations of POLCOMS for the western English Channel are given as an example of a structured grid model and the Finite Volume Coastal Ocean Model (FVCOM) is applied to the Plymouth coastal zone and estuaries as an example of an unstructured grid model. Depth-averaged 2D hydrodynamic models and their applications to the calculation of shelf and estuary tides and overtides and to the calculation of wind effects and other phenomena are then described. Finally, some simpli fied, long timescale models are presented and applied to the
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simulation of salinity during droughts and during rising sea levels, and to the simulations of oxygen isotope ratios, seasonal temperature cycles, and intratidal variations in turbidity.
2.01.7 Final Remarks We believe that the chapters in this volume represent the current state of the art with regard to both our understanding of the physical processes operating in estuaries and the coastal ocean and current technologies for measuring and modeling those processes. Nonetheless, we recognize that technologies will con tinue to evolve. Indeed, during the span of our own careers, circulation models have advanced dramatically in step with remarkable advances in computing technology, reaching the point where they can be routinely used to help make difficult management decisions as well as be deployed as experimental tools for enhancing our understanding of the fundamental phy sics of estuarine and coastal systems. In the same way, observing techniques have also evolved, most notably through the intro duction and widespread use of ADCPs, instruments that have given us a remarkable ability to measure spatial structure and temporal variations of currents, waves, and turbulence. However, we remain convinced that physical insight as exempli fied by the conceptual and analytical models of coastal and estuarine flows described in this volume will always play a central role in advancing our understanding, and thus in enabling society to make the best decisions possible in protect ing, restoring, and managing valuable coastal ecosystems.
Acknowledgments For one of us (RJU), this work is a contribution to the UK’s Natural Environment Research Council (NERC) Oceans 2025 program. The second editor (SGM) would like to acknowledge the exceptional efforts of the first editor. Both editors also wish to thank all of the contributing authors for having provided us with such exceptional material for this volume.
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