Three-dimensional numerical modeling of thermohaline and wind-driven circulations in the Persian Gulf

Applied Mathematical Modelling 35 (2011) 5884–5902

Contents lists available at ScienceDirect

Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm

Three-dimensional numerical modeling of thermohaline and wind-driven circulations in the Persian Gulf F. Hosseinibalam, S. Hassanzadeh ⇑, A. Rezaei-Latifi Physics Department, Faculty of Sciences, University of Isfahan, Isfahan 81746, Iran

a r t i c l e

i n f o

Article history: Received 15 November 2010 Received in revised form 24 April 2011 Accepted 16 May 2011 Available online 27 May 2011 Keywords: Thermohaline fluxes Wind stress Baroclinic Mesoscale eddy Numerical modeling Persian Gulf

a b s t r a c t The Persian Gulf circulation is investigated with respect to the relevant forcing mechanism including wind stress and thermohaline surface fluxes by using a three-dimensional numerical hydrodynamic model. The model results show a correlation between the strength of the bottom layer outflow of the Persian Gulf and that of the Indian Ocean Surface Water (IOSW) inflow into the Gulf. The inflow of IOSW into the Gulf attain maximum values in May–June in conjunction with peak bottom outflow through the Hormuz Strait. The results of sensitivity experiment indicate that circulation is dominated by thermohaline flows at almost all parts of the Gulf. The heat fluxes play an essential role on the general circulation of the Persian Gulf. In spring and summer, the wind stress generates southeast-flowing surface currents of magnitude about 5 cm/s along the Saudi Arabia and Iranian coasts on the northern Gulf. In winter and autumn, due to weak static stability, the wind produces mesoscale eddies in most parts of the Gulf. In winter and spring the wind stress acts to reinforce the thermohaline circulation of deep outflow. Conversely, in summer and autumn the wind forcing acts in opposition to the thermohaline forcing and causes a bottom inflow from Oman Sea into the Gulf. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction 1.1. The study area The Persian Gulf is a semi-enclosed marginal sea with a mean depth of about 36 m and is connected to the deep Gulf of Oman through the narrow Strait of Hormuz. The Persian Gulf is surrounded by Iran, Iraq, Kuwait, Saudi Arabia, Bahrain, Qatar and United Arab Emirates (Fig. 1). It covers a surface area of approximately 239,000 km2 [1] and has a length of 990 km and a maximum width of 370 km [2]. Due to the vast excess of evaporation over the precipitation plus river runoff, one of the most saline water masses in the world ocean is formed in the Persian Gulf. These features lead to an inverse estuarine circulation with a fresh surface inflow from Gulf of Oman and a highly saline waters leaving the Gulf through the deep part of the Hormuz Strait. The winds in the Gulf are predominantly northwesterly throughout the year [2,3]. In winter, the wind has intermittent nature associated with the passage of synoptic weather systems, but it seldom exceeds a speed of 10 m/s [2]. In contrast, the summer winds are mild and continuous. The major river source in the Persian Gulf is the Arvand Rood, being located at the northern end of the Gulf. Previous estimates of the annual-mean discharge of the Arvand Rood vary from 35 km3/yr [4,5] to 45 km3/yr [6,7]. These values has been reduced to an unknown extent by dam constructions, such as the Ataturk dam built by Turkey in 1990 and other dams and reservoirs built by Iran, Iraq and Syria [2]. ⇑ Corresponding author. E-mail address: [email protected] (S. Hassanzadeh). 0307-904X/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.apm.2011.05.040

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

5885

Fig. 1. Bathymetry and map of the Persian Gulf.

1.2. Thermohaline and wind-driven circulations The thermohaline circulation is the density-driven current of oceans, which is named so because it involves both heat, namely ‘‘thermo’’, and salt, namely ‘‘haline’’. The two attributes, temperature and salinity, together determine the density of seawater, and the differences in density between the water masses in the oceans cause the water to flow. The buoyancy fluxes at the ocean surface give rise to gradients in temperature and salinity, which produce, in turn, density gradient [8]. In the sigma (r) coordinate, the surface flux of temperature is given by

q0 cp J

kT

@T ¼ Q S; @z

ð1:1Þ

where QS is the downwards directed heat flux at the surface, cp the specific heat of seawater at constant pressure, q0 the sea density, kT the vertical eddy coefficient, J the Jacobian of the transformation and T the temperature.Assuming the solar radiation is absorbed at the sea surface, then:

Q S ¼ Q nsol þ Q rad ;

ð1:2Þ

where Qnssol and Qrad are the non-solar heat flux and the radiative, respectively.The non-solar heat flux has three components as below

Q nsol ¼ Q la þ Q se þ Q lw ;

ð1:3Þ

where Qla is the latent heat flux released by evaporation, Qse the sensible heat flux due to the turbulence of the temperature across the air/sea interface and Qlw the long-wave flux at the sea surface.The surface salinity flux is determined using the formula given by Steinhorn [9]:

q0

kT @S Ss ðEv ap  Rpr Þ ; ¼ J @z 1  0:0001Sa

ð1:4Þ

where Ev ap ¼ QLvla and Rr are the evaporation and precipitation rates in kg m2 s1 and Ss the surface salinity in psu. Lv is the latent heat of vaporization. The wind-driven currents are currents that are created by the force of the wind exerting stress on the sea surface. The horizontal force of the wind (per unit area) on the sea surface is called the wind stress. In another word, it is the vertical transfer of horizontal momentum. The momentum is transferred from atmosphere to the ocean by wind stress. Wind stress s is calculated from:

5886

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

 12 ðss1 ; ss2 Þ ¼ qa C SD U 210 þ V 210 ðU 10 ; V 10 Þ;

ð1:5Þ

where qa is the density of air, (U10, V10) are the components of the wind vector at a reference height of 10 m, and C SD is a dimensionless drag coefficient which is determined as a function of the wind speed by using an empirical relation. 1.3. Objective Due its shallow nature the Persian Gulf appears to be influenced by both wind driven and thermohaline forces [5]. Residual flow in the Gulf has been attributed to two principal factors: wind-forcing, which coupled with Coriolis factors, generate a net anticlockwise circulation; and the effect of density gradients, which are generated and sustained by evaporative losses and radiative heat transfer and, to a lesser extent, by freshwater inflow at the head of the Gulf [10]. The relative importance of these two mechanisms has been a main subject for physical oceanography researches in this area. Hughs and Hunter [11] argued that wind-driven currents made the major component, but Hunter [12] subsequently concluded that the circulation was probably dominated by density-driven flow, geostrophically balanced across the Gulf and frictionally balanced in the direction of flow. Galt et al. [13] obtained the same results in the southern Gulf but they concluded that wind-driven circulation plus the effect of freshwater inflow are major component of flow in the northern Gulf. Lardner et al. [14] estimated the density-driven currents using a simple two-layer model. It was found that as one moves from the Hormuz Strait toward the head of the Gulf the density-driven currents decrease rapidly, and after about 100 km they become appreciably smaller than the wind-driven currents. At the northern end of the Gulf the density-driven effects are highly localized near the Arvand Rood, where substantial freshwater inflow occurs, but over most of this part of the region, wind forcing is the dominant factor. Lardner and Das [15] by using a numerical algorithm based on splitting method concluded that the dominant factor in generating residual flow in most parts of the Gulf, with the exception of Hormuz Strait, is wind forcing rather than density gradient. For simplicity, they applied many approximations in the numerical solution. For example, the advective terms in the horizontal momentum equations are ignored. This could be the cause of the wrong or the weak results. Chao et al. [16] studied the circulation of the Persian Gulf with a three-dimensional hydrodynamic model. They suggested that the northwesterly strong winds in the winter and spring create southeast-flowing surface currents along both coasts in the northern Gulf, confine cyclonic circulation to the southern Gulf, and shift the surface current through the Strait to the south side of the channel. But due to too coarse grid (20 km), this simulation could not describe mesoscale instabilities adequately. Furthermore, the total simulation is limited to 2 years, which is not sufficiently long for the model to reach the steady seasonal cycle. Kumpf and Sadrinasab [2] using a three-dimensional hydrodynamic model studied overall circulation in the Persian Gulf. This work showed that the circulation becomes unstable in winter and autumn and then break up into mesoscale eddies. In this paper, the effect of thermohaline fluxes and wind stress on circulation in the Persian Gulf are studied. Also, this study provides answers for some important scientific questions posed by researchers and oceanographers about circulation in the Persian Gulf, such as: Do winds control the horizontal circulation in the Gulf or does thermohaline circulation drive it? Where are the dense waters formed in the Persian Gulf and how do they flow out of the Gulf? What is the origin of mesoscale eddies observed in the Persian Gulf. This paper is organized as follows. First, the model and design of experiments will be described. Then, general circulation is simulated and compared with limited observations in the Persian Gulf. Finally, the effects of wind stress and thermohaline fluxes on the circulation, which has not been comprehensively investigated before, will be analyzed.

2. Numerical model and configuration 2.1. Governing equations We have employed the hydrodynamic part of the Coupled Hydrodynamic-Ecological Model for Regional and shelf seas (COHERENS) with realistic bottom topography and coastal geometry. The hydrodynamic part of the model, in Cartesian coordinates, uses the following basic equations: The momentum equations based on the Boussinesq approximation and hydrostatic equilibrium:

@u @u @u @u 1 @p @ þu þv þw  fv ¼  þ @t @x @y @z q0 @x @z @v @v @v @v 1 @p @ þ þu þv þw þ fu ¼  @t @x @y @z q0 @y @z 

1 @p

q @z

¼ qg:



vT



vT

 @u @ sxx @ syx þ þ ; @z @x @y @v @z

 þ

@ sxy @ syy þ ; @x @y

ð2:1Þ

ð2:2Þ

ð2:3Þ

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

5887

The continuity equation:

@u @ v @w þ ¼ 0: þ @x @y @z

ð2:4Þ

The equations of temperature and salinity:

      @T @T @T @T 1 @I @ @T @ @T @ @T þu þv þw ¼ þ kT þ kH þ kH ; @t @x @y @z q0 cp @z @z @z @x @x @y @y

ð2:5Þ

      @S @S @S @S @ @S @ @S @ @S þu þv þw ¼ kT þ kH þ kH ; @t @x @y @z @z @z @x @x @y @y

ð2:6Þ

where (u, v, w) are the components of the current, t is time, T denotes the temperature, S the salinity, f the Coriolis parameter, p the pressure, vT, kT the vertical eddy viscosity and diffusion coefficients, kH the horizontal diffusion coefficient for salinity and temperature, q the density, q0 a reference density, cp the specific heat of sea water at constant pressure and I is solar irradiance.The horizontal components of the stress tensor are expressed as follows:

sxx ¼ 2mH

@u ; @x

sxy ¼ syx ¼ mH syy ¼ 2mH

ð2:7Þ   @u @ v þ ; @x @y

ð2:8Þ

@v ; @y

ð2:9Þ

where mH is the horizontal diffusion coefficient.The 2-D continuity equation for the surface elevation f and the depth-integrated momentum equations for U and V are obtained by integrating the equations of continuity and horizontal momentum over the vertical coordinate.International equation of state of sea water released by Joint Panel Oceanographic and Standards on oceanographic tables and standard [17] has been used, wherein pressure effects on density are ignored. 2.2. Numerical resolution Conservative finite differences are used to discretize the mathematical model in space. The grid chosen for horizontal discretization is the well known Arakawa ‘‘C’’ grid which staggers the currents and pressure/elevation nodes to give a good representation of the crucial gravity waves and provides simple representation of open and coastal boundaries. In the vertical, the equations are discretized over the bottom topography using sigma coordinate. This coordinate system tries to solve the problems from the combined influences of steep topography and string stratification. The r-coordinate varies between 0 at the bottom and 1 at the surface, according to the formula below:

r¼

zþh

gþh

¼

zþh ; H

ð2:10Þ

where H is the total water depth, h is the mean water depth and g is the sea surface elevation. In analogy with the wellknown POM model the equations are integrated in time using the mode-splitting technique with separate time steps for the 2-D external barotropic equations and the 3-D internal baroclinic equations. The 2-D time step has to be small enough to satisfy the Courant–Friedrichs–Lewy (CFL) criterion. Time step for the 3-D baroclinic mode is larger. The sea surface elevation and the depth-integrated velocities are calculated by mode external, while the three-dimension currents, temperature and salinity are determined by the internal mode. All horizontal derivatives are evaluated explicitly while vertical diffusion is computed fully implicitly and vertical advection quasi-implicitly. In order to solve the horizontal momentum equations predictor–corrector method is used. This satisfies the requirement that, when using a mode-splitting technique of solution, the currents in the 3-D equations should have the same depth integral as the ones obtained from the 2-D depth-integrated equations. For the advection of momentum and scalars, the total variation diminishing (TVD) scheme is applied whereby the advective flux is evaluated as a weighted average between the upwind flux and either the Lax–Wendroff in the horizontal or the central flux in the vertical. 2.3. Turbulence formulation In the present simulations the vertical eddy coefficients were determined with the ‘‘K  e’’ turbulence closure scheme, developed by Luyten et al. [18]. This scheme defines the vertical eddy coefficients mT for momentum and kT for temperature and salinity in term of the turbulence energy K and its dissipation rate e using 2

mT ¼ Su

k

e

þ mb ;

kT ¼ Sb

k

2

e

þ kb ;

ð2:11Þ

5888

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

where Su and Sb are usually referred as the stability functions and mb and kb are prescribed background coefficients. su and Sb are functions of the stability parameter aN = k2N2/e2, where N2 is squared buoyancy frequency. Their explicit forms, derived from an algebraic stress model, are given by

Su ¼

0:108 þ 0:0229aN ; 1 þ 0:471aN þ 0:027a2N

ð2:12Þ

Sb ¼

0:177 : 1 þ 0:403aN

ð2:13Þ

The turbulence energy k is obtained by solving a transport equation. The dissipation rate is computed from

e ¼ e0 k3=2 =l;

ð2:14Þ

where e0 is a constant coefficient and the mixing length, l is obtained algebraically using ‘‘quasi-parabolic’’ law. Horizontal diffusion coefficients are taken proportional to the horizontal grid spacing and the magnitude of the velocity deformation tensor. 2.4. Initial and boundary conditions Seawater is well mixed in winter, and therefore the model is initialized in December using uniform temperature and salinity fields with values of 19 °C and 38 psu. Three components of velocity and the sea surface elevation were initially set equal to zero. The model is forced by the climatologic monthly mean wind stress and heat/salt fluxes. The surface and bottom boundary conditions used for currents, temperature and salinity are Neumann type conditions. The surface boundary condition for horizontal current is obtained by specifying the surface stress as function of the wind component (relation 1.5). The surface boundary conditions for temperature and salinity are determined by (1.1) and (1.4), respectively. A slip boundary condition is applied for the horizontal current at the bottom which takes the form



q0 v T @u @ v J

;

@z @z



¼ ðsb1 ; sb2 Þ:

ð2:15Þ

The bottom stress components are determined by quadratic friction law:

 1 ðsb1 ; sb2 Þ ¼ q0 C bD u2b þ v 2b 2 ðub þ v b Þ:

ð2:16Þ

The quadratic bottom drag coefficient be expressed as a function of the roughness length z0 and the vertical grid spacing.The bottom boundary conditions for temperature and salinity are obtained by considering a zero flux normal to seabed.The open boundary values for the depth-integrated current are determined with the aid of the method of Riemann characteristics:

U¼

 1 U Rþ þ RU ; 2

ð2:17Þ

where RUþ ; RU are Riemann variables as incoming and outgoing, respectively. The characteristic equation gives the outgoing Riemann variable RU but RUþ is obtained by an harmonic expansion of the input of residual and tidal forcing data. RUþ is determined by applying the sea surface elevation fin in harmonic form,

fin ¼ F har ; RUþ ¼ RU þ 2cF har ;

ð2:18Þ

where c is the wave speed of the barotropic mode and

F har ¼ f0 ðx1 ; x2 Þ þ

NT X

An cos ðxn þ /n0  /n ðx1 ; x2 ÞÞ;

ð2:19Þ

n¼1

where f0 represents the residual input in m, An are the tidal amplitudes in meter, xn the tidal frequencies in rad/s, /n0 the initial value of the phase xn þ /n0 in radians, /n the tidal phases in radians at open boundary, t the time in seconds elapsed since the start of the program and NT the number of tidal. The Persian Gulf is encountered with major semi-diurnal and diurnal tidal constituents, M2, S2, K1 and O1. Along the eastern open-ocean boundary, amplitudes and phases of the major tidal constituents are prescribed as constant values. The tidal influence on river discharge is ignored.In order to prevent spurious vertical velocities at open sea boundaries, the 3D horizontal current is computed assuming a zero normal gradient for the velocity deviation. Temperature and salinity values at the eastern boundary have been prescribed by using a two-layer profiles. Similarly, at the river mouth, the boundary conditions are determined by specifying a two-layer stratification, whereby a fresh water value is prescribed within surface layer with a zero gradient condition in the bottom layer.

5889

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902 Table 1 Tidal amplitudes and phases prescribed at the eastern boundary. Tidal constituent

Amplitude (cm)

Phase angle (°)

M2 S2 K1 O1

76 29 29 29

299 335 57 55

2.5. Input data The meteorological parameters and simulated SST by the model were used to calculate the fluxes of momentums, heat and salinity. The meteorological parameters are wind speed components at 10 m above ground, air temperature, relative humidity, cloud cover and precipitation. All these data were derived from the National Oceanic and Atmospheric Administration (NOAA). The Persian Gulf coastline and depth are determined based on ETOPO-2 dataset, which was generated from digital data base of seafloor and land elevation on a 4-min latitude/longitude grid. At the eastern boundary the temperature and salinity values within the upper layer were employed from hydrographic observations on a monthly basis, while the water column underneath is kept at a temperature 22 °C and salinity of 36.5 psu [2]. Amplitudes and phases of the four major tidal constituents M2, S2, O1, K1, prescribed at the open eastern boundary, were extracted from Elhakeem et al. [19] (Table 1). The present simulation are taken in a Cartesian coordinate system with x-axis increasing eastward and y-axis northwards, respectively. The domain of the model is from 47.6° E to 58.2° E and from 23.1° N to 30.5° N. The model was run with an external mode time step 20 s and an internal mode time step 5 min, which satisfies the Courant–Friedrichs–Lewy (CFL) criterion.

2.6. Experimental design To analyse the salinity variation in the Persian Gulf three numerical experiments have been set up. The control run (Run 1) used the lateral open boundary condition, complete meteorological data, k–e turbulence scheme, tidal forcing and river run off. Sensitive analyses are performed to determine the influence of the wind stress and surface fluxes. The ‘‘no fluxes’’ run (Run 2) did not account for surface heat and salt fluxes. In the ‘‘no wind’’ run (Run 3) the only difference noted from the control run is that the wind stress was not taken into account. It should be noted that in this model run the wind speed is considered to calculate the latent and sensible fluxes. The difference between Run 1 minus Run 2 or Run 3 indicates the wind stress or surface flux effect on salinity.

3. Results 3.1. Simulated circulation versus observations Direct observations of the circulation within the Persian Gulf are scarce [20]. The limited current meter and drifter observations indicate northwest flow with speeds of 10–20 cm/s along the Iranian coast from the Hormuz Strait to the change in trend of the coast near 51.5° E and a southeastward-flowing current in the southern portion of the Gulf [7,21]. The seasonalmean surface currents simulated by the model in the control run is shown in fig. 2. In summer and spring northwest flow along the Iranian coast reaches head of the Gulf and joins the river plume fed by the Arvand Rood and flows back southeastward along the coasts of Kuwait and Saudi Arabia. In agreement with Renolds [7] and Hassanzadeh et al. [22], the center of the northern Gulf shows fairly a stagnant region. This region is spread over a wide area in spring. The results of the model indicate a southeastward flow along the Kuwait and Saudi Arabia which is stronger in summer than other seasons. This flow is significantly weakened in winter due to the thermohaline and wind-driven currents which are in the opposite direction of the river plume (see next sections). Furthermore, the output model in the control run shows a southward-flowing surface current from the central Gulf toward Bahrain-Qatar shelf and the shallow bank off UAE(hereafter referred to as southern shallows) (Fig. 2). This current is strongest during the spring and summer (about 12 cm/s) and weakest in winter (about 6 cm/s). No field measurements are available to compare our finding with it in these regions. High variability of the surface current in winter and autumn suggests the presence of the mesoscale eddies with diameters of about 30–120 km over the Gulf (Fig. 2a and d). The examination of a historical database of hydrographic observations made by Swift and Bower [20] revealed that the seasonally-variable incursion of IOSW into the Gulf peaks in late spring. They attributed the timing of this peak to the seasonal changes in sea surface slope caused by varying rates of evaporation in the Gulf. The model results, in agreement with Swift and Bower [20], indicate that the inflow of IOSW into the Persian Gulf peaks in May–Jun (Fig. 3b), however, contrary to

5890

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

Fig. 2. Averaged-season horizontal velocity field at the surface over (a) winter, (b) spring, (c) summer and (d) autumn.

Fig. 3. Time series of (a) bottom outflow and (b) surface inflow of IOSW, through the Hormuz Strait.

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

5891

Fig. 4. Time series of the surface-averaged latent heat flux.

the claim made by them, the evaporation rate over the Gulf increases in summer, i.e. June–August (Fig. 4). Hence, the evaporative lowering of sea surface height does not appear to be the major reason for inflow increase into Gulf in late spring. The model shows that the densest waters are formed in southern shallows and around Bahrain (not shown), and the bottom water is driven from these regions toward the Hormuz Strait during the year (Fig. 5). Also, the bottom outflow through the Hormuz Strait attains maximum value in late spring in conjunction with peak inflow IOSW into the Gulf (Fig. 3). Thus, it appears to be a coupling between the strength of the bottom outflow and that of the IOSW inflow into the Persian Gulf, so that the intensified bottom outflow magnifies the influx of IOSW into the Gulf. It is clear that the density difference between

Fig. 5. Averaged-seasonal horizontal velocity field at the bottom over (a) winter, (b) spring, (c) summer and (d) autumn.

5892

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

Fig. 6. Time variation of the density difference between (a) southern shallows and (b) Bahrain–Qatar shelf, with comparable depth on the Oman–Iran continental shelf.

Fig. 7. Time changes of height difference between waters in (a) southern shallows and (b) Bahrain–Qatar shelf, with Oman–Iran shelf.

dense water in the southern shallow regions and water at comparable depths in the Oman–Iran continental shelf plays an important role in driving the deep water and in bottom outflow variability through the Hormuz Strait. However, unlike the temporal variability in the strength of the bottom outflow and that of the IOSW inflow, this density contrast peaks in March for Bahrain–Qatar shelf and in December for southern shallows (Fig. 6). Also, contrary to seasonal cycle of the water exchange through the Strait in which inflow/outflow volume transport attains minimum values in autumn, the density contrast between southern shallows and the Oman–Iran shelf reaches minimum value in summer (Fig. 6). As a result, in addition to the density contrast, it should be other reasons for this seasonal cycle of the volume transport. The model results show that variation of barotropic pressure due to change of the sea surface height difference between water in southern

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

5893

Fig. 8. Time variation of the salinity of the deep water outflow.

Fig. 9. Time series of the along-strait deep mean current at southern part of Hormuz strait.

shallows and in around Bahrain. with Oman–Iran Shelf can be an important factor for seasonal variability of the inflow and outflow through the Hormuz Strait (Fig. 7). Johns et al. [5] investigated the water exchange between the Persian Gulf and the Indian Ocean using hydrographic and moored acoustic Doppler current profiler data from the Strait of Hormuz during the period December 1996 to March 1998. They reported that the monthly mean values for the deep outflow transport vary from 0.08 Sv to 0.18 Sv (1Sv = 106 m3/s), with the maximum occurring in March and minimum in December. Since there was not available data for current during the June and July, due to the problems on the instrumentation, they estimated the monthly mean transports in this period by linear interpolation from the value observed in May and August. With this estimates included, they obtained the annual mean deep outflow transport of 0.15 Sv. The model successfully simulated the well known outflow from the Hormuz Strait and volume transports vary from 0.08 Sv to 0.19 Sv in November and June, respectively (Fig. 3a). The annual mean transport

5894

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

Fig. 10. Comparison between the observed salinity (from Swift and Bower [1]) and simulated salinity by the model at the surface layer during the January– August.

is 0.14 Sv, which is very close to value reported by Johns et al. [5]. The maximum value of estimated transport in May instead of June might be biased by linear interpolation of currents measured in May and August. In addition, they reported that the salinity of the deep outflow varies from 39.3 to 40.8 psu with highest outflow salinities occurring in winter months (December–March). These values are similar to those simulated by the model (Fig. 8). The fig. 9 shows time series of the mean along-strait current from 40 m depth to bottom at southern part of Hormuz Strait. The current speed varies from about 15 cm/s to about 28 cm/s during the year with a mean value of about 21 cm/ s. This result is in a relatively good agreement with the measured current of Johns et al. [5], which obtained the mean speed of approximately 20 cm/s with a seasonal variation about ±20%. Fig. 10 shows comparison between surface salinity distribution simulated by the model and observed value published by Swift and Bower [20] during January–August. The surface salinity difference between the model simulation and observations is less than 0.5 psu over most of the Gulf during the January–June. However, in July–August over some shallow regions of the Gulf simulated values are about 0.5–1.5 psu higher than observed value. It should be noted that observational data cover in shallow regions during summer is weak (see Fig. 3 in swift and Bower [20]. Thus, this salinity difference could be partly due to bias introduced by the use of data from a single station to represent a large region of the Gulf. The model simulation

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

5895

Fig. 11. Comparison between the observed salinity published by Swift and Bower [1] and simulated salinity by the model during the January–August at the 47–53 m depth.

suggests that the presence of low-salinity water (<37.5 psu) within the Iranian half of the Gulf increases from January to June and then decreases in July and August. Such a simulated pattern agrees well with field measurement. The observed and simulated deep salinities in the Gulf are compared in Fig. 11. The simulated deep salinity values are close to observation results reported by Swift and Bower [20]. In addition, temporal variability pattern of simulated deep salinity is similar to its observed counterpart and both show comparatively little changes during January–August. Note that bathymetry used in this study (ETOPO-2 data) is slightly different with that of swift and Bower. 3.2. Effects of surface thermohaline fluxes on circulation In order to examine the influence of surface thermohaline on circulation the Run 2 was performed. In this sensitivity study, the surface heat and salinity fluxes terms are removed. Otherwise, the same parameters as the Run 1 are used. The effects of the surface fluxes will be found by subtracting the model output of Runs 1 and 2 (Run 1 minus Run 2).

5896

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

Fig. 12. Thermohaline circulation (velocity difference between Run 1 and Run 2) at the surface averaged over seasons of (a) winter, (b) spring, (c) summer, and (d) autumn.

Figs. 12 and 13 show the influence of thermohaline fluxes on the Persian Gulf circulation. The simulation results of thermohaline circulation (Figs. 12 and 13) are, to large extent, similar to simulated general circulation (Figs. 2 and 5) over almost all of the basin. Thus, contrary to Larder and Das [15], currents driven by thermohaline fluxes have major contribution on the Persian Gulf circulation. The sensitivity studies (not shown) indicate that the precipitation and river fluxes do not have any noticeable influence on the general circulation in the Gulf. As a result, the heat fluxes play an essential role on the overall circulation pattern in the Persian Gulf. In winter and spring the main stream of surface inflow driven by thermohaline fluxes does not flow along the Iranian shoreline, but rather follows a westerly course from the Hormuz to the Qatar peninsular and then continues close to the Saudi Arabia and Kuwait coasts (Fig. 12a and b). This is consistent with numerical computation of density-driven flows by Larder and Das [15]. This current in the general circulation (Fig. 2a and b), is weak mostly under the action of river plume, which is freshwater input from the north towards south along the Kuwait and Saudi Arabia. In Spring–Autumn, the thermohaline forcing produces a southeastward surface current along the Kuwait and Saudi Arabia coasts, which in summer is stronger compared to Spring and Autumn (Fig. 12b–d). In spring and summer due to increase of evaporation rate at southern shallows, the surface thermohaline flow from the Hormuz Strait toward this region becomes stronger than winter and autumn (Figs. 12b and c). The numerical simulations show that the thermohaline fluxes in spring and summer establish vertically stratified temperature with a decrease and, hence, the density increase, from top to bottom at most parts of Gulf. During winter and autumn, the thermal stratification and density contrast are removed because of the cooling effect of the surface fluxes. As a dq result, in spring and summer the static stability, i.e, E  1 q dz , is significantly more positive than winter and autumn (Fig. 14). In winter and autumn at some parts of the Gulf the water column is baroclinicly unstable. This baroclinic instability generates mesoscale eddies with diameters about 40–70 km and maximum current speeds of about 8–15 cm/s which are observable in some parts of Gulf (Fig. 12a and d). At the bottom, it can be seen that the simulated thermohaline current is qualitatively very similar to the overall simulated flow in the Gulf but slightly stronger than it (Fig. 13). Thus, the deep outflow transport under the influence of the salinity and heat fluxes (Fig. 15a) is stronger than deep outflow transport under the action all the surface forcing functions (Fig. 3a). This

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

5897

Fig. 13. Thermohaline circulation (velocity difference between Run 1 and Run 2) at the bottom averaged over seasons of (a) winter, (b) spring, (c) summer, and (d) autumn.

Fig. 14. Time series of the domain-averaged static stability.

lesser outflow in the control run seems to be more related to the dilution of the waters of Bahrain–Qatar shelf and southern shallows and, hence corresponding decrease in density and baroclinic pressure, which occurs under the impact of injection of the river plume and the wind-driven current from the northern Gulf and central basin toward these regions. Moreover, while general outflow attains maximum values on May–June, as mentioned in previous section, the thermohaline outflow peaks on

5898

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

Fig. 15. Time series of (a) bottom outflow and (b) surface inflow, driven by thermohaline fluxes through the Hormuz strait.

April (Figs, 15a and 3a). Because the bottom outflow driven by wind stress in May–June is significantly stronger than April (not shown), it can be concluded that this timing of thermohaline outflow peak is due to the lack of wind stress. Since the change in bottom outflow, based on conservation of volume, should be compensated by a change in surface inflow, the thermohaline surface inflow peaks on April as well (Fig. 15b). 3.3. Effects of surface wind stress on the circulation In order to examine the influence of surface wind stress on the circulation the simulation 3 was performed. So, the effect of wind stress on the surface was removed. Otherwise, the same parameters as the control run were used. The difference of the model output (Run 1 minus Run 3) indicates the wind effect. The wind-driven currents were considerably weaker than the thermohaline current in most parts of the Persian Gulf (Fig. 16 and 17). As a result, the wind-driven currents do not make the major contribution on circulation in the Persian Gulf. This result is in agreement with earlier work by Hunter [12]. He based on the analysis of ship drift data as well as experimental drift buoy studies concluded that the circulation was probably dominated by density-driven flow rather than wind-driven currents. At the surface and in spring and summer, the wind stress generates southeast-flowing currents of magnitude about 5 cm/ s along both the Saudi Arabia and Iranian coasts on the northern Gulf (Fig. 16b and c). In the central area of the northern Gulf closer to Saudi Arabia coast and across the northern coast of Bahrain and around the Qatar peninsula there is a return flow of magnitude about 4 cm/s toward the northwest. In the southern Gulf, the wind stress produces south-flowing surface currents from main basin of the Gulf toward United Arab Emirates coast and Bahrain-Qatar shelf .Furthermore, the strong, northwest wind in the spring and summer shifts a relatively large portion of the surface inflow from the Hormuz Strait toward the southern shallows. In most seasons, at the northern end of the Gulf, the wind stress generates anticyclonic circulation which in spring is relatively stronger (Fig. 16a–d). In winter and autumn, the wind stress produces a dynamic instability, i.e. wind blowing on the sea creates waves and then the surface becomes dynamically unstable and eventually the waves break. The turbulence mixes fluid in the vertical, leading to a vertical eddy viscosity and eddy diffusivity. The relative importance of static stability and dynamic instability is expressed by Richardson number [23]:

Ri 

gE ð@U=@zÞ2

;

ð3:1Þ

where the numerator is the strength of the static stability, and the denominator is the strength of the velocity shear. When the Reynolds number is large, the small Richardson Number (smaller than 0.25) is criterion for dynamic instability [21]. Fig. 18 shows time series of the domain-averaged Richardson Number estimated by the model for the Persian Gulf. In the

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

5899

Fig. 16. Wind-driven circulation (velocity difference between Run 1 and Run 3) at the surface averaged over seasons of (a) winter, (b) spring, (c) summer, and (d) autumn.

winter and autumn the Richardson Number is much smaller than spring and autumn. Therefore, in winter and autumn, due to dynamic instability the wind generates mesoscale eddies with diameters of about 30–120 km and speed of 4–15 cm/s over most parts of the Gulf (Fig. 16a and 16d). In the bottom, the wind effect on circulation is considerably weaker than the surface. In winter and spring the wind stress acts to reinforce the thermohaline circulation of deep outflow (Fig 17a and b) .Conversely, in summer and autumn the wind forcing acts in opposition to the thermohaline forcing and causes a bottom inflow from Oman Sea into the Gulf (Fig. 17c and d). This may be caused by the influence of wind on the density and sea surface height in the southern shallows. In winter and autumn, mesoscale eddies generated by the wind has maximum speed of 3 cm/s, and shallow regions are stronger (Fig. 17a and d). Fig. 19a and b shows the averaged salinity of surface water with and without of wind stress forcing, respectively. The wind stress freshens the surface water of the Gulf about 0.1–0.5 psu during the year. This is mostly due to surface water exchange between Oman-Iran shelf and Persian Gulf through the Hormuz Strait, which is caused by wind forcing (Fig. 20). Also, The increase of the surface water exchange between the Persian Gulf and Oman Gulf on May by the wind leads to shift in minimum surface salinity from February to May (Fig. 19). It should be noted that without the wind stress the surface water of the Persian Gulf in winter is saltier than spring but fresher than summer (Fig. 19). The wind forcing, to some extent, modifies this seasonal cycle of surface salinity and causes the surface water to become saltier in winter than spring and summer. Chao et al. [16] claimed that influx increase of IOSW due to relaxation of surface wind stress causes the surface water of the Gulf fresher in summer than winter. The Run 3 results do not show this. The model indicates that the inflow of IOSW under the influence of the wind force in summer is not stronger than winter (Fig. 20b). In addition, although inflow and

5900

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

Fig. 17. Wind-driven circulatin (velocity difference between Run 1 and Run 3) at the bottom averaged over seasons of (a) winter, (b) spring, (c) summer, and (d) autumn.

Fig. 18. The domain-averaged Richardson number time series.

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

5901

Fig. 19. Averaged salinity of surface water in case of (a) without the wind stress (b) with the wind stress.

Fig. 20. (a) Surface outflow and (b) surface inflow of IOSW driven by wind stress.

outflow of surface water produced by the wind, in winter and autumn is stronger than spring and summer, the effect of wind stress on salinity decrease is more in spring and summer. This can be caused under the action of lateral and vertical mixing eddies generated by the wind in winter and autumn. In winter and autumn, the bottom saline water under the effect of stirring of mesoscale, mixes with the low-salinity surface water. 4. Conclusion In this work, we employed a three-dimensional hydrodynamic finite-difference model to study thermohaline and winddriven circulation in the Persian Gulf. It is a baroclinic fully non-linear model, solving the Navier–Stokes equations under the hydrostatic approximation and adopting a sigma reference coordinate system in the vertical. Model variables are arranged on an Arakawa staggered C grid and the integration scheme adopted for the advection of momentum and scalars are computationally expensive Total Variance Diminishing (TVD). The model was forced with tidal values prescribed at the eastern open boundary and by climatologic monthly mean atmospheric forcing at 10 m reference height above ground derived of NOAA data.

5902

F. Hosseinibalam et al. / Applied Mathematical Modelling 35 (2011) 5884–5902

The model results show that in summer and autumn, the thermohaline fluxes produce a northwestward surface flow from Hormuz Strait to the head of the Persian Gulf along the Iranian shoreline. In winter and spring main stream of surface inflow driven by thermohaline fluxes follows a westerly course from the Hormuz to the Qatar peninsula and then continues close to the Saudi and Kuwait coasts. In spring-autumn southeastward thermohaline flow along the Kuwait and Saudi Arabia coast, which is stronger in summer, augments the riverine plume. In spring and summer, the wind stress generates southeastern surface currents of magnitude about 5 cm/s along the Saudi and Iranian coast. In addition, both the wind stress and heat fluxes cause the southward currents with speeds of 5–10 cm/s from the Hormuz Strait and main basin of Gulf toward the UAE coast and Bahrain–Qatar shelf. In winter and autumn, the cooling effect of the thermohaline fluxes leads to removal of the thermal stratification and density contrast between the surface and bottom waters. As a result, the static stability of water column weakens significantly and the baroclinic eddies with diameters of about 40–70 km and speeds of about 8– 15 cm/s form in some parts of the Gulf. In addition, the wind stress, due to weak conditions of static stability, leads to shear instability and produce eddies with diameters of 30–120 km and speeds 4–15 cm/s in most parts of the Persian Gulf. The densest waters form in the southern shallows and Bahrain–Qatar shelf under the influence of the heat fluxes during the year. The densest waters are formed in southern shallows and around Bahrain, and the bottom water is driven from these regions toward the Hormuz Strait during the year. The seasonal cycle of intensification of this bottom outflow is associated with the density contrast and the change of sea surface between these regions and water at the Oman–Iran continental shelf outside the Strait. There is a coupling between the strength of the bottom outflow and that of the IOSW inflow into the Persian Gulf, so that the intensified bottom outflow magnifies the influx of IOSW into the Gulf. Both bottom outflow and surface inflow generated by thermohaline fluxes peak in March–April. Wind stress shifts the maximum of inflow/outflow generated by thermohaline to May–June. Comparing the results of sensitivity studies with overall simulation indicate that the heat fluxes are dominant factor in generating residual flow over almost all of the Gulf. Furthermore, under the action of the lateral and vertical mixing eddies produced by the wind, the surface water in winter becomes saltier than summer. The wind stress shifts minimum of salinity from early spring to late spring. Acknowledgments The authors wish to thank the office of Graduate Studies of the University of Isfahan for their support. Reference [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

K.O. Emery, Sediments and water of the Persian Gulf, AAPG. Bull. 40 (1956) 2354–2383. J. Kampf, M. Sadrinasab, The circulation of the Persian Gulf: a numerical study, Ocean Sci. 2 (2006) 27–41. T.J. Perrone, Winter shamal in the Persian Gulf, Tech. Rep., Naval Environ. Predict. Res. Facil., Monterey, Calif., 1979, pp. 79–106. M.A.H. Saad, Seasonal variation of some physiochemical condition of shatt-al -Arab estuary, Iraq, Estuarine Coastal Mar.Sci. 6 (1978) 503–513. W.E. Johns, F. Yao, D.B. Olson, S.A. Josey, J.P. Grist, D.A. Smeed, Observation of seasonal exchange through the Straits of Hormuz and the inferred freshwater budgets of the Persian Gulf, J. Geophys. Res., 108(C12), 3391, doi:10. 1029/2003JC001881, 2003. J.L. Wright, A hydrographic and acoustic survey of the Persian Gulf, MSC Thesis, Nav. Postgrad. Sch., Monterey, Calif., 1974. R.M. Reynolds, Physical Oceanography of the Gulf Strait of Hormuz and the Gulf Oman – result from the Mt. Mitchel expedition, Mar. Pol. Bull. 27 (1993) 35–59. M. Tina, W. Shoouhong, Dynamic transition theory for thermohaline circulation, Physica D 239 (2010) 167–189. I. Steinhorn, Salt flux and evaporation, J. Phys. Ocesnogr. 21 (1991) 1681–1683. R.W. Larrdner, W.J. Lehr, R.J. Fraga, M.A. Sarhan, A model of residual currents and pollutant transport in the Gulf, Appl. Math. Modell. 12 (1988) 379– 390. P. Huhges, J.R. Hunter, A proposal for a physical oceanography program and numerical modeling in the KAP region. Project for Kuwait Action Plan2/2, UNESCO, Paris, 1980. J.R. Hunter, The physical oceanography of the Gulf:A review and Theoretical interpretation of previous measurements, in: First Gulf Conference on Environment and Pollution, Kuwait, 1982. J.A. Galt, D.L. Payton, G.M. Torgrimson, G. Watabayashi, Trajectory analysis For the Nowruz oil spill with specific application to Kuwait, Report of National Oceanic and atmospheric Agency, Seattle, Wash, 1983. R.W. lardner, W.J. Lehr, R.J. Fraga, M.A. Sarhan, Residual currents in the Gulf. I: Density-driven flow, Arabian J. Sci. Eng. 12 (1987) 341–354. R.W. Lardner, S.K. Das, On the computation of flows driven by density gradient: residual currents in the Gulf, Appl. Math. Model. 15 (1991) 282–294. S.Y. Chao, T.W. Kao, K.R. Al – Hajri, A numerical investigation of circulation in the Gulf, J. Geophys. Res. 97 (1992) 11219–11236. UNESCO: Tenth report of the joint panel on oceanographic tables ans standards, UNESCO Tech, Pap. In Marine Sci. (36) 1981. P.G. Luyten, J.E. Jones, R. Proctor, A. Tabor, P. Tett, K. Wil-Allen, COHERENS-A Coupled hydrodynamical – ecological model for regional and shelf seas: user documentation, MUMM Rep., Management Unit Mathematical Models of the n-orth sea, 1999. A.A. Elhakeem, W. Elshorbagy, R. Chebbi, Oil spill simulation and validation in the Persian Gulf with special reference to the UAE coast, Water Air Soil Poll. 184 (2007) 243–254. S.A. Swift, A.S Bower, Formation and circulation of dense water in the. Persian Gulf, J. Geophys. Res 108(C1), 3004. doi:10.1029/2002JC001360, 2003. J.R. Hunter, Aspects of the dynamics of the residual circulation of the Gulf, in: H.G. Gade, A. Edwards, H. Svendsen (Eds.), Coastal Oceanography, Plenum Press, 1983, pp. 31–42. S. Hassanzadeh, A. Kiasatpour, F. Hosseinibalam, Statistical techniques analysis Of SST and SLP in the Persian Gulf, Physica A 382 (2007) 586–596. R.H. Stewart, Introduction to Physical Oceanography, Department of Oceanography Texas A and M University, 2008.