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Simulation of wind-driven circulation in the Gulf of Elat (Aqaba)
Journal of Marine Systems 26 Ž2000. 349–365 www.elsevier.nlrlocaterjmarsys
Simulation of wind-driven circulation in the Gulf of Elat žAqaba/ T. Berman a,b, N. Paldor b,) , S. Brenner c a Israel Maritime College, Michmoret 40297, Israel Institute of Earth Sciences, The Hebrew UniÕersity of Jerusalem, GiÕat Ram, Jerusalem 91904, Israel Israel Oceanographic and Limonologic Research, LTD, P.O. Box 8030, Tel-Shikmona, Haifa 31080, Israel b
c
Received 15 May 1999; accepted 12 April 2000
Abstract The Princeton Ocean Model ŽPOM. has been used to investigate the wind-driven circulation in the stratified long and narrow Gulf of Elat ŽAqaba.. Our results indicate that the circulation consists of a series of gyres aligned along the main axis of the basin, and that their size and location are strongly affected by the shoreline and, to a lesser extent, by the hydrography. The seasonality in both the flow and the free surface height ŽFSH. at any specific station are caused mainly by the strong seasonality in the hydrography — the FSH and the magnitude of the currents above the thermocline are inversely related to the thickness of the upper layer. The seasonality in the flow is also manifested in the location and diameter of the gyres. This seasonal change in the gyres’ diameter and location might provide an explanation for the current reversal observed at the northern tip of the western boundary during the month of February. q 2000 Elsevier Science B.V. All rights reserved. Keywords: wind-driven circulation; Gulf of Elat; hydrography
1. Introduction 1.1. The Gulf of Elat The Gulf of Elat is one of the two narrow, northward extensions of the Red Sea ŽFig. 1.. It is 180 km long, 14–26 km wide, and has an average depth of 800 m and a maximum depth of 1800 m. The Gulf is part of the Syrian–African rift valley and is flanked by mountains and desert on both the east and west sides. The southern end of the Gulf is
) Corresponding author. Tel.: q972-2-658-4924; fax: q972-2566-2581. E-mail address: [email protected] ŽN. Paldor..
separated from the Red Sea by a shallow sill Žmaximum depth 270 m. at the Straits of Tiran. Being a semi-enclosed basin, the Gulf is potentially vulnerable to pollution, particularly at its northern tip. The two cities located there, Elat in Israel and Aqaba in Jordan, are both important industrial and tourist centers for their countries. They are also major ports, especially Aqaba, which is Jordan’s only outlet to the sea. The environmental pollution hazards include both continuous sources such as municipal sewage discharge and sporadic ones such as oil spills or shipping accidents. Effective management of the multiple and often conflicting uses of the Gulf Ži.e. industry and shipping vs. tourism. and maintenance of the delicate ecological balance requires a detailed understanding of the physical
0924-7963r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 7 9 6 3 Ž 0 0 . 0 0 0 4 5 - 2
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Fig. 1. ŽA. Location map of the Red Sea with the inset showing in more detail its northeast extension into the Gulf of Elat ŽAqaba.. ŽB. Bathymetry and location of current-meter stations — NT, OP, MBL and MG — in the northern end of the Gulf near the city of Elat.
oceanography of the region. Knowledge of the circulation and its variability is crucial for predicting the ultimate distribution of any pollutant injected into the Gulf. The climate of this region is arid with an average net evaporation of 0.5–1 cm P dayy1 ŽAssaf and Kessler, 1976. and with no permanent rivers flowing into the Gulf. As a result, the waters of the Gulf are among the most saline in the world, with typical salinity values of 40.5 psu or more. Throughout the year, the wind blows predominantly from the north Žover 90% of the time., which further enhances the evaporation and the resulting thermohaline circula-
tion. This thermohaline circulation consists of inflow of fresher water from the Red Sea in the upper layers through the straits, and outflow of more saline water in the lower layer. Early hydrographic observations along the entire Gulf focused solely on the thermohaline circulation and the size Ži.e. northward extension. of the thermohaline cell ŽKlinker et al., 1976; Paldor and Anati, 1979.. The conclusion of these AGulf-longB studies was that the thermohaline cell occupies the upper 300 m and extends all the way to the northern tip. The velocities associated with this thermohaline circulation were estimated at 2–4 cm P sy1 yielding a residence time of a few months. The station spacing in these studies Ž25–30 km. was at least twice the internal Rossby Radius of deformation Ž10 km typically., so that wind-driven gyres and waves could not be addressed in these studies. Later observations employing current meters at several locations; ŽMBL — 8 km south of the north shore and about 200 m east of the west shore; OP — 4 km south of the north shore and about 200 m east of the west shore of; MG — 10 km south of the north shore and about the mid Gulf; and NT — at the northern tip of the Gulf; see Fig. 1. concentrated on the northern tip of the Gulf ŽBrenner et al., 1988, 1989; Goodman et al., 1990; Genin and Paldor, 1991, 1998; Wolf-Vecht et al., 1992. where a very complicated circulation pattern with velocities exceeding 15–20 cm P sy1 was observed. The currents vary significantly in both space and time, with the direction being mainly north–south, along the main axis of the Gulf at the west shore stations. At NT, the currents had a relatively strong east–west component. The spectra of the along- and cross-shore velocity components show a very conspicuous tidal signal, which dominates the spectrum of the sea level too. The progressive vector diagram at MBL has a peculiar reversal of direction during the month of February. The data shown in Fig. 2 for the currents measured at the depth of 12 m at MBL, where the total water depth is 40 m, indicate a clear reversal of flow during February each year Ž1988–1991. from northward to southward. No explanation was offered for this observation, which repeated itself in other years. This flow reversal was not observed at NT and MG. At OP the reversal is much less conspicuous than at MBL, implying that the reversal is a highly
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Fig. 2. Progressive vector diagram for the current measured at MBL station Ž12 m depth, water depth — 40 m. showing clear reversal of flow during February of each year Ž1988–1991. from northward to southward. The opposite reversal takes place during late summer, from Genin and Paldor Ž1998.. Vectors are rotated so that upwards indicates a long-shore current from southwest to northeast Ž37 deg. N.. The full point indicates 1 January and every = indicates a 30-day interval. The squares indicate 1 June.
localized phenomenon. During all years, the measured currents on the west coast ŽMBL and OP. were much stronger than those at MG and this difference in magnitude intensifies in summer when the veloci-
ties are stronger everywhere. Between Dec. 1987 and Mar. 1988, the observations at MBL indicated the existence of an Ekman spiral ŽGenin and Paldor, 1998.. Mean sea level measurements at the northern
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tip of the Gulf revealed higher sea level in winter than in summer. As previously mentioned, the prevailing winds are mainly northerly along the axis of the Gulf. The wind speed varies in both time and space. The temporal variation in wind speed includes both a diurnal and a seasonal signal. The diurnal cycle consists of calm winds at night, increasing winds during morning hours and maximum values in the afternoon in accordance with the daily changes in temperature. On the seasonal scale, the winter winds are the weakest, increasing during spring to their maximum intensity in summer. As for the spatial variation; the wind increases gradually to the south between Elat and Dahab Ž140 km south of Elat. while south of Dahab no data is available in the Gulf itself and just outside the southern edge of the Gulf the winds are much calmer ŽManes et al., 1980.. The internal Rossby radius of deformation is of the same order of magnitude as the basin width. The basin is too small to be influenced by latitudinal variations in the Coriolis parameter Žbeta effect.. In such a system, large-scale vertical displacements of internal density surfaces are trapped near the coast by the earth’s rotation and propagate cyclonically around the basin ŽStrub and Powell, 1986.. This work focuses on the role of the wind in forcing the observed circulation in the Gulf and ignores other forcing such as tides and horizontal thermohaline currents. Tides are expected to average out on the time scales used here while the currents associated with the thermohaline flow do not exceed 2–4 cm P sy1 ŽPaldor and Anati, 1979.. Therefore, this study concentrates on the wind-driven circulation only. The results of the model extarpolate the measurements described above in the northwest corner of the Gulf to the entire a basin.
tion model with a free surface and an imbedded second order turbulence closure based on the scheme of Mellor and Yamada Ž1982.. The turbulence submodel provides vertical mixing coefficients and realistic simulations of both the surface mixed layer and the bottom boundary layer. The prognostic variables are the velocity components, potential temperature, salinity, free surface height ŽFSH., turbulent kinetic energy, and the turbulence macroscale. The horizontal grid consists of orthogonal curvilinear coordinates with the AArakawa CB differencing scheme. The curvilinear grid facilitates the representation of coastlines. In the vertical, the model uses the s coordinate Ži.e. the actual depth scaled by the local total depth of the water column. with a staggered grid. Time differencing is done with a split explicit scheme in which the external and internal modes are integrated using different time steps Žmuch shorter step for the external mode.. The model has been extensively tested and successfully adapted to various estuaries, bays, and semi-enclosed seas including the Hudson–Raritan estuary, Delaware Bay, the Gulf of Mexico, and the Mediterranean Sea.
2. Methods The focus of this work is the application of the POM model to the wind-driven circulation in the Gulf of Elat under the prevailing conditions there and when both thermohaline circulation and tidal forcing are ignored. As a preliminary test, in this section we verify that the model does indeed reproduce analytical results known for some idealized configurations that describe conditions and forcing relevant to the Gulf of Elat. 2.1. Verification of the model
1.2. The model We employ the Princeton Ocean Model ŽPOM., which is a state of art, s coordinate, numerical ocean circulation model that has been successfully used intensively in many other coastal settings. A complete description of POM is given by Blumberg and Mellor Ž1987.. Here we only give a brief review of the major features of the model. It is a fully nonlinear, three-dimensional, primitive equa-
The case of a rectangular, barotropic, basin with uniform depth and constant wind stress is simple enough so that its steady state can be calculated analytically. The wind blowing along the basin’s main axis causes water to pile up at the downwind side and ebb upwind. By integrating the along Gulf Ži.e. x . momentum equation, a steady state obtains from a balance between the applied wind stress at the sea surface divided by the density of water, Fw ,
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and the slope of the water column height, hŽ x . Ži.e. the slope of the sea surface in the vertically integrated momentum equation.: gh
dh dx
s Fw
Ž 1.
The solution of Eq. Ž1. is:
(
h s h20 q Ž 2 Fw rg . x
Ž 2.
where h 0 is the water depth at some arbitrary point, x s 0 Žtaken to be the head of the Gulf.. We looked at a test problem with the following values of wind stress and uniform water thickness: 1. Fw s 4 P 10y4 m2 sy2 Žwind of about 15 m P sy1 .; h 0 s 25 m. 2. Fw s 1 P 10y4 m2 sy2 Žwind of about 8 m P sy1 .; h 0 s 25 m. The initial conditions for this verification run are identical with those of Experiment I described below. Fig. 3a and b present the results of the computations for Ž h y h 0 ., which show an excellent agreement between the model solution and the estimates given by Eq. Ž2.. In the first case, of larger wind stress, the maximum relative error is on the order of a few percent only. This agreement between the model result and the analytical values is lost as h 0 increases and for realistic values of 800 m the numerical expected values of Ž h y h 0 . are on the order of 1 mm so that errors dominate the computation. 2.2. Initialization of the model As any other model, the POM model requires initial and boundary conditions as well as wind and thermal forcing in order to apply it to a specific site such as the Gulf of Elat. Specifically, the time dependent surface forcing Žwind stress. and the hydrographic data for initializing the simulation have to be specified Žno river run-off or other data are required in the Gulf.. Obviously, strong thermal forcing prevails in this desert enclosed Gulf. This forcing results in a thermohaline circulation cell, which extends all the way from the straits of Tiran to the Northern Tip of the Gulf near the City of Elat. Despite the intensive
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evaporation in the region Ž0.5–1 cm P dayy1 ., best estimates for the current velocities associated with the thermohaline flow ŽKnudsen relation. are on the order of 3 cm P sy1 only ŽPaldor and Anati, 1979.. The daily heat flux through the sea surface is nearly completely horizontally uniform so spatial density variations are negligible and no flow, other than the thermohaline one mentioned above, results from the thermal forcing. In addition, any, small as they are Žsee the Hydrography subsection below., eustatic sea level differences Ždue to the evaporation in the course of the water flow from the Red Sea northward. are expected to reinforce the N–S difference caused by the piling up of water by the northerly wind. Both effects are therefore ignored in the present study and will be included in a sequel work on the subject. To clarify the various contributions to the dynamics of the wind-driven circulation in the Gulf of Elat Žor other long and narrow stratified basins with similar dimensions., the numerical model was forced with a variety of wind fields, hydrographic conditions and topographic settings. The grid size in all runs was d x s d y s 1.5 km. Two experiments were conducted: The focus of the first one was the effect on the circulation of the thermocline’s depth in a two-layer idealized basin Ži.e. flat, rectangular. when the wind stress is constant. In the second experiment, the combined effects of topography and changing wind stress were added to the real hydrography. The two experiments are described in details, next.
2.2.1. Experiment I In this first experiment, a closed rectangular, flat bottom, two-layer idealized Gulf was used, with dimensions similar to those of the Gulf of Elat Ž18 km = 180 km = 800 m.. A uniform wind stress divided by density of 10y4 m2 P sy2 Žwind speed of about 8 m P sy1 . was directed southwards along the main axis of the idealized Gulf. The hydrographic settings in the runs had a fixed density jump, corresponding to the summer stratification, of DT s 58C and no salinity difference across the interface separating the two layers. The number of levels in the model was 10. The depth-ratio of the two layers occupying the 800 m deep basin varied from 1.0 Ži.e. each layer being 400 m deep. to 0.0 Ži.e. completely homogeneous water column. running through depth
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Fig. 3. Comparison of analytic Žred circle. and model solutions Žblue cross. for FSH. X axis distance in km, Y axis FSH in cm. Ža. Wind stress Ži.e. trr ., Fw s 4 P 10y4 m2 P sy2 Žwind of about 15 m P sy1 .; Žb. wind stress, Fw s 1 P 10y4 m2 P sy2 Žwind of about 8 m P sy1 ..
ratio values of: 266:534, 133:667, 66:733 and 33:767 in between. These are used to approximate the sea-
sonal changes in the thermocline depth. The initial conditions in the experiment were zero velocities and
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free surface elevation, and the lateral boundary conditions used were vanishing of the normal velocities at the walls. 2.2.2. Experiment II The analysis of the actual circulation in the Gulf was studied in the second experiment by adding the real topography Žon the mesh described above., and specifying the observed, seasonally varying wind stress Žas described shortly., and initializing the hydrography in the model with an approximation of the observed hydrography. These initializations of T and S were meant to mimic the observed profiles in the Gulf during the three seasons — Winter, Spring and Summer. The Fall was not simulated since there are no unique hydrographic conditions during this season. In the vertical, the model had 15 layers, five model layers in each of the upper, lower, and middle parts of the water column. The first two parts are intended to capture the dynamics in the surface and bottom boundary layers, respectively, and therefore these layers are relatively thin Žin sigma units.. The sigma range of the central part of the column was 0.75, while the rest was equally shared by the two other parts. Although the model runs on Arakawa’s C grid, we have converted the output at the end of the runs so that velocities are given at the same Žcentral. grid point where the free surface is calculated, by averaging the velocity values in the neighboring grid points. This minimized the artificially large, long-Gulf, velocity components encountered at the last grid point near the shores when the original grid is used for displaying the velocity fields. 2.2.2.1. Bathymetry. Bathymetry data of the Gulf of Elat was digitized from the bathymetric chart of Hall and Ben-Avraham Ž1978. on a 1500-m resolution grid in both long- and cross-Gulf directions. The grid
Fig. 4. Vertically averaged velocity and the free surface height Žin cm. in the idealized basin case for depth ratio of 1.0 Ž400:400.. The X and Y axes denote distances in grid points Žd x sd y s1.5 km. starting from the southwest point Žlower left corner.. The wind is blowing from the north.
Table 1 Hydrographic conditions used for initializing the model in the different seasons
Winter Spring Summer
T0 w8Cx
S0 wpsux
H wmx
20.5 23 26
40.6 40.55 40.65
homogenous water column 130 300
obtained using this mesh size consists of 25 = 137 points. 2.2.2.2. Wind. The daily surface wind forcing data was compiled from data collected by Manes et al.
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Ž1980. at three locations along the Gulf — the City of Elat, Nueiba Ž70 km south of Elat. and Dahab Ž140 km south of Elat.. These data represent hourly values calculated by averaging month-long measurements arranged into hourly bins. The hourly wind speeds for the months of January, April and July were used in the model for the surface forcing during the winter, spring and summer seasons, respectively. The wind between the three stations was calculated by linear interpolation between stations, while south of Dahab the winds were assumed to be the same as those in Dahab as no better data are available. 2.2.2.3. Initial conditions Hydrography. The initial salinity Ž S . and temperature ŽT . profiles were assumed uniform over the entire Gulf as variations in S and T between the north and south ends of the Gulf rarely exceed 0.3 psu and 0.78C, respectively ŽKlinker et al., 1976.. The chosen continuous temperature profiles, T Ž z ., were taken as the exponential best fit to the data of Wolf-Vecht et al. Ž1992.: T Ž z . s T` q Ž T0 y T` . eyz r H
Ž 3.
where T` is 20.58C in all seasons, T0 is the SST during a particular season and H is the depth of the seasonal thermocline during that season.
Similarly, the initial salinity profiles, SŽ z ., were calculated by: S Ž z . s S` q Ž S0 y S` . eyz r H
Ž 4.
where S` is 40.6 psu throughout the year and S0 is the surface salinity at the particular season. The surface and bottom salinity values are not as well defined as those for temperature, but the overall salinity effect on the density is hardly noticeable. The values of these parameters for the three seasons are given in Table 1. Velocity and free surface. The current velocity initial conditions were u s 0 s Õ s w s h. 2.2.2.4. Boundary conditions. Along the east, west and north coasts of the Gulf as well as on the artificial southern boundary, a condition of no normal flow was assumed, i.e. u s 0 on the east and west coasts and Õ s 0 on the north and south boundaries. The Straits of Tiran in the south are allowed to remain open Ži.e. flow through them is permitted in the model. to the Red Sea by placing the southern boundary Žassumed to be a wall. 15 km south of the straits. Moving this boundary any farther away from the straits had a negligible effect on the circulation inside the Gulf.
Fig. 5. The FSH difference between the north and south ends of the idealized basin Žtotal depth — 800 m. as a function of the thickness of the upper layer.
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2.3. Consistency checks As an additional validation of the model’s results, we checked the consistency of the model under a slightly different numerical setup. The model was run three times in summer configuration Žas described above.: The first time using the grid size and number of vertical layers as described above; the second time, with d x s 1 km instead of 1.5 km; while in the third run we used 10 vertical layers instead of 15. The differences in results among the three runs were negligible.
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are shown in Fig. 4 for a basin with a depth ratio of 400:400. The calculated fields are consistent with the expected result. Along the centerline of the Gulf currents are weakest and directed cross-wind. When the run was repeated but with a vanishing Coriolis
3. Results The results presented here are snapshot fields at a time much longer than the spin-up period of the model. The fields were considered fully spun-up when the kinetic energy associated with the calculated daily-averaged currents at all model points reached an asymptotic value. In all experiments, this saturation value was reached within 20 days and the model was run for at least 20 additional days to ensure both stability and complete spin-up. Superimposed on this asymptotic value was a daily cycle caused by the daily cycle in wind stress. To further establish the spin-up of the model, we examined the time series of the FSH at several points in the domain. After 15 days, there is no long-term trend in FSH and the only deviation from steady state is the repeating diurnal cycle, associated with the wind forcing. The snapshots presented are therefore representative of the fully spun-up circulation. The fields described here pertain to day 40 from the initial time at 00:00 h. In the following, we present the resulting fields in the two experiments. 3.1. Experiment I In this idealized basin experiment, the combined effects of the constant wind stress acting at the sea surface, the viscous drag at the interface separating model layers and the Coriolis force, result in a steady, cyclonic circulation around the basin ŽCsanady and Scott, 1974; Strub and Powell, 1986.. The vertically averaged velocity field Žweighted by the thickness of each layer. and the FSH distribution
Fig. 6. Diurnal variations Žhourly bins. in month-long means of wind speed in Elat, Nueiba and Dahab in: Ža. January, Žb. April, Žc. July. ŽAdapted from Manes et al. 1980...
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parameter Žits value was set at 10y1 0 sy1 ., this asymmetry was lost, which indicates that it is the rotation of the earth which is responsible for this east–west asymmetry. When the upper layer Žthe layer above the thermocline. becomes thinner we expect the sea surface
slope to increase as the action of the wind stress is distributed throughout a shallower layer. This is indeed the result obtained in Fig. 5, where the FSH difference between the north end and the south end increases as the thermocline is made shallower Ži.e. depth ratio decreases.. The vertically averaged veloc-
Fig. 7. Vertically averaged velocity over the upper 50 m and the FSH Žin cm. during Winter. The X and Y axes denote distances in grid points Žd x s d y s 1.5 km. starting from the southwest point Žlower left corner.. The FSH difference is negligible.
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ities decrease as the depth of the upper layer increases Žnot shown.. These different values of the depth-ratio approximate the seasonal changes in the hydrographic conditions in the Gulf and as such will aid in interpreting the results of the next subsection where the model is applied to the real Gulf.
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3.2. Experiment II When the real topography, hydrography and diurnal wind stress ŽTable 1 and Fig. 6. are added, the simple scenario of the idealized Gulf is greatly altered. The single, basin scale gyre is replaced by a
Fig. 8. As Fig. 7, during Spring.
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series of gyres distributed along the Gulf. The locations and sizes of these gyres vary seasonally. The results pertaining to the various seasons are described next.
3.2.1. Winter During this season, the water column is homogeneous and, as is expected from Experiment I, north– south FSH difference is negligible Žless than 0.5 cm.
Fig. 9. As Fig. 7, during Summer.
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as are the weighted average velocities over the upper 50 m shown in Fig. 7. There are three gyres in the northern half of the Gulf; the northernmost gyre is anticyclonic with an 18-km diameter. In contrast to this, the southern half is occupied by a single cyclonic gyre, associated with strong currents along the boundaries and weak velocities at the center. The weak, cross-Gulf distribution of the Žsmall. sea surface slope in this southern gyre is symmetrical, which gives rise to the anti-symmetric current along the east–west boundaries gyres. 3.2.2. Spring The fairly clear winter scenario becomes much more complex during spring. The weighted average current velocity over the upper 50 m and the FSH for this season are shown in Fig. 8. As before, there are three gyres in the northern half, but now the circulation in the southern half cannot be described by a simple circulation pattern. In general, the currents in the southern half are weaker than in the north. The winter east–west symmetry in the FSH disappears and the complicated flow is consistent with this loss
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of symmetry. The north–south FSH difference reaches a value close to 2.1 cm. 3.2.3. Summer The structure of the currents and FSH in this season, shown in Fig. 9, both lack the east–west symmetry similar to the circumstances encountered in spring. The overall north–south FSH difference reaches its maximal value of 2.5 cm due to the increase in wind stress during this season. The northernmost gyre is cyclonic with a 10-km diameter. The overall picture that emerges from these results are that the magnitude of the typical currents in summer and spring are much larger than that of winter. The results of daily changes in both current and FSH are that there is no clear correlation between the current’s magnitude and the wind but the FSH closely follows the daily wind cycle. The daily changes in FSH at a point 1.5 km south of the north coast ŽMid-Gulf., shown in Fig. 10 for the summer conditions, closely follows those of the wind. It decreases Žincreases. when the wind increases Ždecreases. in accordance with the wind set-up scenario
Fig. 10. Daily changes in FSH at a point 1.5 km south of the north coast Žblue. in cm and daily changes in wind velocity Žgreen. in m P sy1 . FSH at this point is negatively correlated with the wind: it decreases Žincreases. when the wind increases Ždecreases..
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discussed in Experiment I. Of course, a very similar pattern exists for the overall north–south FSH difference across the entire Gulf Žnot shown.. The velocities shown in Figs. 7, 8, and 9 represent the average current in the top 50 m of the water column while the average currents in the top 10 m exceeds 20 cm sy1 Žnot shown. in accordance with the decrease of speed with depth in the surface Ekman layer.
4. Discussion and conclusions The results presented in the preceding section demonstrate that the seasonality in the flow and in FSH in the Gulf of Elat is caused mainly by the strong seasonality in the hydrography ŽTable 1.. Both the magnitudes of the currents in the upper layer, above the thermocline, and the FSH are inversely related to the thickness of that layer. The weak seasonality in wind stress ŽFig. 6. amplifies this pattern — weaker winds in winter when the thermocline reaches its maximal depth. These findings are consistent with observations on seasonal changes in FSH reported in Genin and Paldor Ž1998., where it is shown that sea surface heights near the city of Elat are highest in winter and lowest in summer. The practical aspect of our results is that pollutant dispersal in the upper layer in the Gulf will be more efficient in summer and spring than in winter. During the entire year, our model results show that the circulation in the Gulf is made up of a series of permanent gyres oriented along its main axis. The location and diameter of these gyres can change in accordance with the depth of the thermocline. This can be invoked to explain a peculiar observation noted in Genin and Paldor Ž1998. as well as Wolf Ž1990.. Both of these studies report a reversal of the current direction along the west coast near the northern end of the Gulf. The progressive vector diagram at a depth of 12 m is directed northward until mid-February when it abruptly changes to southward. The opposite reversal of direction in summer occurs on different dates each year. Attempts to correlate this reversal to winds and atmospheric pressure have failed ŽWolf, 1990.. The present study provides an explanation for this reversal in terms of the hydrographic conditions rather than in terms of
external forcing. As the depth of the thermocline becomes large enough a transition from summer to winter circulation is triggered which, in turn, causes a change in the location of the centers of the gyres as well as in their diameters ŽFig. 11a and b.. As a result, the progressive vector diagram at a fixed point along the northwest end of the Gulf can shift from northward to southward Žor from southward to northward depending on the precise location. due only to the change in hydrographic conditions. The explanation given above for the current reversal has its origin in the vertically averaged Žhorizontal. velocity, i.e. the horizontal flux in the upper layer. Our model also allows an alternative explanation for this reversal of current based on the change in vertical profile of horizontal velocity rather than the horizontal arrangement of the gyres. The velocity profile shown in Fig. 12 at a point 13 km south of the north shore and 750 m east of the west coast also changes between summer and winter: In winter, the profile is unidirectional throughout the upper layer, while in summer, the velocity changes its direction between layers. Thus, at any given depth Žand grid point., a reversal in the direction of the current can take place even if the gyres remain unaltered. Of course, a heuristic, quantitative, explanation for this flow reversal is provided by the seasonal change in the wind stress, which results in a change in the depth of the Ekman layer and the depth scale of the Ekman spiral. Current meters moored at a constant depth of 12 m measure different parts of the spiral in different seasons. A comparison between current measurements at 12 and at 37 m ŽGenin and Paldor, 1999. is consistent with an Ekman flow there. The existence of gyres in the circulation seems, therefore, to be of utmost importance in trying to explain the various observations in the Gulf. It is natural at this point to examine the reason for the presence of these gyres. To do so, we ran Experiment I once again but this time with disturbed shorelines Ža guitar-shaped basin. rather than the straight, rectangular, ones used previously. The resulting circulation is shown in Fig. 13, which should be compared with Fig. 4. Instead of a single cell of cyclonic flow, which extends throughout the entire Gulf, a series of gyres develops along the main axis of the basin. It is obvious that the topography of the shoreline determines the direction of the local cur-
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Fig. 11. Vertically averaged velocity over the upper 50 m and the FSH Žin cm. during Winter Ža. and Summer Žb. in the northern part of the Gulf of Elat. The X and Y axes denote distances in grid points Žd x s d y s 1.5 km. starting from the southwest point located 17 grid points south of the northwest corner of Fig. 7. The changes in the gyral system in Ža. and Žb. result from the seasonal changes in hydrography and wind stress. As a result of these changes, the progressive vector diagram at a fixed point along the northwest end of the Gulf point can shift from northward to southward Žor from southward to northward depending upon the precise location..
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model was run for 2 days, only a Kelvin wave that propagates cyclonically around the Gulf was encountered. This wave dissipates as time goes on and steady state is established when the explicit, as well as implicit, dissipation terms in the model equations balance the energy input by the wind.
Fig. 12. Model results for the vertical profile of the long-shore velocity component at a point 13 km south of the north shore and 750 m east of the west coast for summer and winter. X axis — longshore velocity in cm sy1 , Y axis — depth in m. In winter, the profile is unidirectional throughout the upper layer, while in summer, the velocity changes its direction with depth.
rent via the boundary condition of tangential flow only. This is also the reason why more gyres develop in the narrow northern half of the Gulf where the curved coastlines have a greater effect. Consequently, in Experiment II, the equivalent of the idealized single, basin-wide cyclonic gyre appeared only in the southern half of the Gulf. Unlike the thermocline depth and wind stress, the density jump across the thermocline does not seem to have an effect on the circulation. We reran Experiment I, this time, with a temperature jump of 18C, i.e. a density jump of 0.283 su Žwhile in the original experiment it was 1.455 su .. Although the density jump was reduced by a factor of 5, the resulting circulations in the two cases were indistinguishable. Hence, the magnitude of the density jump does not have an effect on the circulation in our model, and only the wind stress and thermocline depth determine the intensity of the current. Although the focus of the study as described above applies to much longer times as compared with the spin-up of the model, a brief description of the results on shorter times is in order. When the
Fig. 13. An ideal basin with a wavy shoreline. A series of gyres develops along the main axis of the basin instead of the single cyclonic one, which obtains in the straight shoreline case ŽFig. 4.. This experiment demonstrates the effect of curved shorelines in determining the gyral structure of the circulation.
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Acknowledgements Financial support for this study was provided by the Israel Ministry of National Infrastructures via a research grant to The Hebrew University of Jerusalem. The discussions held with Drs. A. Genin and B. Lazar of HU greatly helped clarify the conditions at the Gulf.
References Assaf, G., 1976. Climate and energy exchange in Gulf of Aqaba ŽEilat.. Mon. Weather Rev. 104, 381–385. Blumberg, A.F., Mellor, G.L., 1987. Description of a three dimensional coastal ocean circulation model. In: Heaps, N.S. ŽEd.., Three Dimensional Coastal Models. American Geophysical Union, Washington, DC, 456 pp. Brenner, S., Rosentraub, Z., Bishop, Y., 1988. Current measurements in the Gulf of Elat, IOLR Rep. H3r88, 38 pp. Brenner, S., Rosentraub, Z., Bishop, Y., 1989. Current measurements in the Gulf of Elat 1988r89. IOLR Rep. H8r89, 31 pp. Csanady, G.T., Scott, J.T., 1974. Baroclinic coastal jets in Lake Ontario during IFYGL. J. Phys. Oceanogr. 4, 524–541. Genin, A., Paldor, N., 1991. Currents in the northern Gulf of Elat. Interuniversity Institute of Eilat, Research Report, 17 pp.
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Genin, A., Paldor, N., 1998. Changes in the circulation and current spectrum near the tip of the narrow, seasonally mixed Gulf of Elat. Isr. J. Earth Sci. 47, 87–92. Goodman, L., Brenner, S., Rosentraub, Z., Bishop, Y., 1990. Current measurement in the Gulf of Elat 1989r90. IOLR Rep. H5r90, 27 pp. Hall, J.K., Ben-Avraham, Z., 1978. Bathymetric Chart of the Gulf of Elat. Israel Geological Survey, Jerusalem, Israel. Klinker, J., Reiss, Z., Kropach, C., Levanon, I., Harpaz, H., Halicz, E., Assaf, G., 1976. Observation on the circulation pattern in the Gulf of Elat ŽAqaba.. Isr. J. Earth Sci. 25, 85–103. Manes, A., Rindsberger, M., Segal, L., 1980. Wind power resources in Israel and Eastern Mediterranean. Internal Report, Ministry of Transport, Israel Meteorological Service. Mellor, G.L., Yamada, T., 1982. Development of turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys. 20, 851–875. Paldor, N., Anati, D., 1979. Seasonal variations of temperature and salinity in the Gulf of Elat ŽAqaba., Red Sea. Deep-Sea Res. 26, 661–672. Strub, P.T., Powell, T.M., 1986. Wind-driven surface transport in stratified closed basins: direct versus residual circulation. J. Geophys. Res. 91, 8497–8508. Wolf, A., 1990. Hydrography, currents and wind effect at the head of the Gulf of Elat. MSc Thesis, The Hebrew University, Jerusalem, Israel. Wolf-Vecht, A., Paldor, N., Brenner, S., 1992. Hydrograpic indication of advectionrconvection effects in the Gulf of Elat. Deep-Sea Res. 39, 1393–1401.
Simulation of wind-driven circulation in the Gulf of Elat žAqaba/ T. Berman a,b, N. Paldor b,) , S. Brenner c a Israel Maritime College, Michmoret 40297, Israel Institute of Earth Sciences, The Hebrew UniÕersity of Jerusalem, GiÕat Ram, Jerusalem 91904, Israel Israel Oceanographic and Limonologic Research, LTD, P.O. Box 8030, Tel-Shikmona, Haifa 31080, Israel b
c
Received 15 May 1999; accepted 12 April 2000
Abstract The Princeton Ocean Model ŽPOM. has been used to investigate the wind-driven circulation in the stratified long and narrow Gulf of Elat ŽAqaba.. Our results indicate that the circulation consists of a series of gyres aligned along the main axis of the basin, and that their size and location are strongly affected by the shoreline and, to a lesser extent, by the hydrography. The seasonality in both the flow and the free surface height ŽFSH. at any specific station are caused mainly by the strong seasonality in the hydrography — the FSH and the magnitude of the currents above the thermocline are inversely related to the thickness of the upper layer. The seasonality in the flow is also manifested in the location and diameter of the gyres. This seasonal change in the gyres’ diameter and location might provide an explanation for the current reversal observed at the northern tip of the western boundary during the month of February. q 2000 Elsevier Science B.V. All rights reserved. Keywords: wind-driven circulation; Gulf of Elat; hydrography
1. Introduction 1.1. The Gulf of Elat The Gulf of Elat is one of the two narrow, northward extensions of the Red Sea ŽFig. 1.. It is 180 km long, 14–26 km wide, and has an average depth of 800 m and a maximum depth of 1800 m. The Gulf is part of the Syrian–African rift valley and is flanked by mountains and desert on both the east and west sides. The southern end of the Gulf is
) Corresponding author. Tel.: q972-2-658-4924; fax: q972-2566-2581. E-mail address: [email protected] ŽN. Paldor..
separated from the Red Sea by a shallow sill Žmaximum depth 270 m. at the Straits of Tiran. Being a semi-enclosed basin, the Gulf is potentially vulnerable to pollution, particularly at its northern tip. The two cities located there, Elat in Israel and Aqaba in Jordan, are both important industrial and tourist centers for their countries. They are also major ports, especially Aqaba, which is Jordan’s only outlet to the sea. The environmental pollution hazards include both continuous sources such as municipal sewage discharge and sporadic ones such as oil spills or shipping accidents. Effective management of the multiple and often conflicting uses of the Gulf Ži.e. industry and shipping vs. tourism. and maintenance of the delicate ecological balance requires a detailed understanding of the physical
0924-7963r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 7 9 6 3 Ž 0 0 . 0 0 0 4 5 - 2
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Fig. 1. ŽA. Location map of the Red Sea with the inset showing in more detail its northeast extension into the Gulf of Elat ŽAqaba.. ŽB. Bathymetry and location of current-meter stations — NT, OP, MBL and MG — in the northern end of the Gulf near the city of Elat.
oceanography of the region. Knowledge of the circulation and its variability is crucial for predicting the ultimate distribution of any pollutant injected into the Gulf. The climate of this region is arid with an average net evaporation of 0.5–1 cm P dayy1 ŽAssaf and Kessler, 1976. and with no permanent rivers flowing into the Gulf. As a result, the waters of the Gulf are among the most saline in the world, with typical salinity values of 40.5 psu or more. Throughout the year, the wind blows predominantly from the north Žover 90% of the time., which further enhances the evaporation and the resulting thermohaline circula-
tion. This thermohaline circulation consists of inflow of fresher water from the Red Sea in the upper layers through the straits, and outflow of more saline water in the lower layer. Early hydrographic observations along the entire Gulf focused solely on the thermohaline circulation and the size Ži.e. northward extension. of the thermohaline cell ŽKlinker et al., 1976; Paldor and Anati, 1979.. The conclusion of these AGulf-longB studies was that the thermohaline cell occupies the upper 300 m and extends all the way to the northern tip. The velocities associated with this thermohaline circulation were estimated at 2–4 cm P sy1 yielding a residence time of a few months. The station spacing in these studies Ž25–30 km. was at least twice the internal Rossby Radius of deformation Ž10 km typically., so that wind-driven gyres and waves could not be addressed in these studies. Later observations employing current meters at several locations; ŽMBL — 8 km south of the north shore and about 200 m east of the west shore; OP — 4 km south of the north shore and about 200 m east of the west shore of; MG — 10 km south of the north shore and about the mid Gulf; and NT — at the northern tip of the Gulf; see Fig. 1. concentrated on the northern tip of the Gulf ŽBrenner et al., 1988, 1989; Goodman et al., 1990; Genin and Paldor, 1991, 1998; Wolf-Vecht et al., 1992. where a very complicated circulation pattern with velocities exceeding 15–20 cm P sy1 was observed. The currents vary significantly in both space and time, with the direction being mainly north–south, along the main axis of the Gulf at the west shore stations. At NT, the currents had a relatively strong east–west component. The spectra of the along- and cross-shore velocity components show a very conspicuous tidal signal, which dominates the spectrum of the sea level too. The progressive vector diagram at MBL has a peculiar reversal of direction during the month of February. The data shown in Fig. 2 for the currents measured at the depth of 12 m at MBL, where the total water depth is 40 m, indicate a clear reversal of flow during February each year Ž1988–1991. from northward to southward. No explanation was offered for this observation, which repeated itself in other years. This flow reversal was not observed at NT and MG. At OP the reversal is much less conspicuous than at MBL, implying that the reversal is a highly
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Fig. 2. Progressive vector diagram for the current measured at MBL station Ž12 m depth, water depth — 40 m. showing clear reversal of flow during February of each year Ž1988–1991. from northward to southward. The opposite reversal takes place during late summer, from Genin and Paldor Ž1998.. Vectors are rotated so that upwards indicates a long-shore current from southwest to northeast Ž37 deg. N.. The full point indicates 1 January and every = indicates a 30-day interval. The squares indicate 1 June.
localized phenomenon. During all years, the measured currents on the west coast ŽMBL and OP. were much stronger than those at MG and this difference in magnitude intensifies in summer when the veloci-
ties are stronger everywhere. Between Dec. 1987 and Mar. 1988, the observations at MBL indicated the existence of an Ekman spiral ŽGenin and Paldor, 1998.. Mean sea level measurements at the northern
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tip of the Gulf revealed higher sea level in winter than in summer. As previously mentioned, the prevailing winds are mainly northerly along the axis of the Gulf. The wind speed varies in both time and space. The temporal variation in wind speed includes both a diurnal and a seasonal signal. The diurnal cycle consists of calm winds at night, increasing winds during morning hours and maximum values in the afternoon in accordance with the daily changes in temperature. On the seasonal scale, the winter winds are the weakest, increasing during spring to their maximum intensity in summer. As for the spatial variation; the wind increases gradually to the south between Elat and Dahab Ž140 km south of Elat. while south of Dahab no data is available in the Gulf itself and just outside the southern edge of the Gulf the winds are much calmer ŽManes et al., 1980.. The internal Rossby radius of deformation is of the same order of magnitude as the basin width. The basin is too small to be influenced by latitudinal variations in the Coriolis parameter Žbeta effect.. In such a system, large-scale vertical displacements of internal density surfaces are trapped near the coast by the earth’s rotation and propagate cyclonically around the basin ŽStrub and Powell, 1986.. This work focuses on the role of the wind in forcing the observed circulation in the Gulf and ignores other forcing such as tides and horizontal thermohaline currents. Tides are expected to average out on the time scales used here while the currents associated with the thermohaline flow do not exceed 2–4 cm P sy1 ŽPaldor and Anati, 1979.. Therefore, this study concentrates on the wind-driven circulation only. The results of the model extarpolate the measurements described above in the northwest corner of the Gulf to the entire a basin.
tion model with a free surface and an imbedded second order turbulence closure based on the scheme of Mellor and Yamada Ž1982.. The turbulence submodel provides vertical mixing coefficients and realistic simulations of both the surface mixed layer and the bottom boundary layer. The prognostic variables are the velocity components, potential temperature, salinity, free surface height ŽFSH., turbulent kinetic energy, and the turbulence macroscale. The horizontal grid consists of orthogonal curvilinear coordinates with the AArakawa CB differencing scheme. The curvilinear grid facilitates the representation of coastlines. In the vertical, the model uses the s coordinate Ži.e. the actual depth scaled by the local total depth of the water column. with a staggered grid. Time differencing is done with a split explicit scheme in which the external and internal modes are integrated using different time steps Žmuch shorter step for the external mode.. The model has been extensively tested and successfully adapted to various estuaries, bays, and semi-enclosed seas including the Hudson–Raritan estuary, Delaware Bay, the Gulf of Mexico, and the Mediterranean Sea.
2. Methods The focus of this work is the application of the POM model to the wind-driven circulation in the Gulf of Elat under the prevailing conditions there and when both thermohaline circulation and tidal forcing are ignored. As a preliminary test, in this section we verify that the model does indeed reproduce analytical results known for some idealized configurations that describe conditions and forcing relevant to the Gulf of Elat. 2.1. Verification of the model
1.2. The model We employ the Princeton Ocean Model ŽPOM., which is a state of art, s coordinate, numerical ocean circulation model that has been successfully used intensively in many other coastal settings. A complete description of POM is given by Blumberg and Mellor Ž1987.. Here we only give a brief review of the major features of the model. It is a fully nonlinear, three-dimensional, primitive equa-
The case of a rectangular, barotropic, basin with uniform depth and constant wind stress is simple enough so that its steady state can be calculated analytically. The wind blowing along the basin’s main axis causes water to pile up at the downwind side and ebb upwind. By integrating the along Gulf Ži.e. x . momentum equation, a steady state obtains from a balance between the applied wind stress at the sea surface divided by the density of water, Fw ,
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and the slope of the water column height, hŽ x . Ži.e. the slope of the sea surface in the vertically integrated momentum equation.: gh
dh dx
s Fw
Ž 1.
The solution of Eq. Ž1. is:
(
h s h20 q Ž 2 Fw rg . x
Ž 2.
where h 0 is the water depth at some arbitrary point, x s 0 Žtaken to be the head of the Gulf.. We looked at a test problem with the following values of wind stress and uniform water thickness: 1. Fw s 4 P 10y4 m2 sy2 Žwind of about 15 m P sy1 .; h 0 s 25 m. 2. Fw s 1 P 10y4 m2 sy2 Žwind of about 8 m P sy1 .; h 0 s 25 m. The initial conditions for this verification run are identical with those of Experiment I described below. Fig. 3a and b present the results of the computations for Ž h y h 0 ., which show an excellent agreement between the model solution and the estimates given by Eq. Ž2.. In the first case, of larger wind stress, the maximum relative error is on the order of a few percent only. This agreement between the model result and the analytical values is lost as h 0 increases and for realistic values of 800 m the numerical expected values of Ž h y h 0 . are on the order of 1 mm so that errors dominate the computation. 2.2. Initialization of the model As any other model, the POM model requires initial and boundary conditions as well as wind and thermal forcing in order to apply it to a specific site such as the Gulf of Elat. Specifically, the time dependent surface forcing Žwind stress. and the hydrographic data for initializing the simulation have to be specified Žno river run-off or other data are required in the Gulf.. Obviously, strong thermal forcing prevails in this desert enclosed Gulf. This forcing results in a thermohaline circulation cell, which extends all the way from the straits of Tiran to the Northern Tip of the Gulf near the City of Elat. Despite the intensive
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evaporation in the region Ž0.5–1 cm P dayy1 ., best estimates for the current velocities associated with the thermohaline flow ŽKnudsen relation. are on the order of 3 cm P sy1 only ŽPaldor and Anati, 1979.. The daily heat flux through the sea surface is nearly completely horizontally uniform so spatial density variations are negligible and no flow, other than the thermohaline one mentioned above, results from the thermal forcing. In addition, any, small as they are Žsee the Hydrography subsection below., eustatic sea level differences Ždue to the evaporation in the course of the water flow from the Red Sea northward. are expected to reinforce the N–S difference caused by the piling up of water by the northerly wind. Both effects are therefore ignored in the present study and will be included in a sequel work on the subject. To clarify the various contributions to the dynamics of the wind-driven circulation in the Gulf of Elat Žor other long and narrow stratified basins with similar dimensions., the numerical model was forced with a variety of wind fields, hydrographic conditions and topographic settings. The grid size in all runs was d x s d y s 1.5 km. Two experiments were conducted: The focus of the first one was the effect on the circulation of the thermocline’s depth in a two-layer idealized basin Ži.e. flat, rectangular. when the wind stress is constant. In the second experiment, the combined effects of topography and changing wind stress were added to the real hydrography. The two experiments are described in details, next.
2.2.1. Experiment I In this first experiment, a closed rectangular, flat bottom, two-layer idealized Gulf was used, with dimensions similar to those of the Gulf of Elat Ž18 km = 180 km = 800 m.. A uniform wind stress divided by density of 10y4 m2 P sy2 Žwind speed of about 8 m P sy1 . was directed southwards along the main axis of the idealized Gulf. The hydrographic settings in the runs had a fixed density jump, corresponding to the summer stratification, of DT s 58C and no salinity difference across the interface separating the two layers. The number of levels in the model was 10. The depth-ratio of the two layers occupying the 800 m deep basin varied from 1.0 Ži.e. each layer being 400 m deep. to 0.0 Ži.e. completely homogeneous water column. running through depth
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Fig. 3. Comparison of analytic Žred circle. and model solutions Žblue cross. for FSH. X axis distance in km, Y axis FSH in cm. Ža. Wind stress Ži.e. trr ., Fw s 4 P 10y4 m2 P sy2 Žwind of about 15 m P sy1 .; Žb. wind stress, Fw s 1 P 10y4 m2 P sy2 Žwind of about 8 m P sy1 ..
ratio values of: 266:534, 133:667, 66:733 and 33:767 in between. These are used to approximate the sea-
sonal changes in the thermocline depth. The initial conditions in the experiment were zero velocities and
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free surface elevation, and the lateral boundary conditions used were vanishing of the normal velocities at the walls. 2.2.2. Experiment II The analysis of the actual circulation in the Gulf was studied in the second experiment by adding the real topography Žon the mesh described above., and specifying the observed, seasonally varying wind stress Žas described shortly., and initializing the hydrography in the model with an approximation of the observed hydrography. These initializations of T and S were meant to mimic the observed profiles in the Gulf during the three seasons — Winter, Spring and Summer. The Fall was not simulated since there are no unique hydrographic conditions during this season. In the vertical, the model had 15 layers, five model layers in each of the upper, lower, and middle parts of the water column. The first two parts are intended to capture the dynamics in the surface and bottom boundary layers, respectively, and therefore these layers are relatively thin Žin sigma units.. The sigma range of the central part of the column was 0.75, while the rest was equally shared by the two other parts. Although the model runs on Arakawa’s C grid, we have converted the output at the end of the runs so that velocities are given at the same Žcentral. grid point where the free surface is calculated, by averaging the velocity values in the neighboring grid points. This minimized the artificially large, long-Gulf, velocity components encountered at the last grid point near the shores when the original grid is used for displaying the velocity fields. 2.2.2.1. Bathymetry. Bathymetry data of the Gulf of Elat was digitized from the bathymetric chart of Hall and Ben-Avraham Ž1978. on a 1500-m resolution grid in both long- and cross-Gulf directions. The grid
Fig. 4. Vertically averaged velocity and the free surface height Žin cm. in the idealized basin case for depth ratio of 1.0 Ž400:400.. The X and Y axes denote distances in grid points Žd x sd y s1.5 km. starting from the southwest point Žlower left corner.. The wind is blowing from the north.
Table 1 Hydrographic conditions used for initializing the model in the different seasons
Winter Spring Summer
T0 w8Cx
S0 wpsux
H wmx
20.5 23 26
40.6 40.55 40.65
homogenous water column 130 300
obtained using this mesh size consists of 25 = 137 points. 2.2.2.2. Wind. The daily surface wind forcing data was compiled from data collected by Manes et al.
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Ž1980. at three locations along the Gulf — the City of Elat, Nueiba Ž70 km south of Elat. and Dahab Ž140 km south of Elat.. These data represent hourly values calculated by averaging month-long measurements arranged into hourly bins. The hourly wind speeds for the months of January, April and July were used in the model for the surface forcing during the winter, spring and summer seasons, respectively. The wind between the three stations was calculated by linear interpolation between stations, while south of Dahab the winds were assumed to be the same as those in Dahab as no better data are available. 2.2.2.3. Initial conditions Hydrography. The initial salinity Ž S . and temperature ŽT . profiles were assumed uniform over the entire Gulf as variations in S and T between the north and south ends of the Gulf rarely exceed 0.3 psu and 0.78C, respectively ŽKlinker et al., 1976.. The chosen continuous temperature profiles, T Ž z ., were taken as the exponential best fit to the data of Wolf-Vecht et al. Ž1992.: T Ž z . s T` q Ž T0 y T` . eyz r H
Ž 3.
where T` is 20.58C in all seasons, T0 is the SST during a particular season and H is the depth of the seasonal thermocline during that season.
Similarly, the initial salinity profiles, SŽ z ., were calculated by: S Ž z . s S` q Ž S0 y S` . eyz r H
Ž 4.
where S` is 40.6 psu throughout the year and S0 is the surface salinity at the particular season. The surface and bottom salinity values are not as well defined as those for temperature, but the overall salinity effect on the density is hardly noticeable. The values of these parameters for the three seasons are given in Table 1. Velocity and free surface. The current velocity initial conditions were u s 0 s Õ s w s h. 2.2.2.4. Boundary conditions. Along the east, west and north coasts of the Gulf as well as on the artificial southern boundary, a condition of no normal flow was assumed, i.e. u s 0 on the east and west coasts and Õ s 0 on the north and south boundaries. The Straits of Tiran in the south are allowed to remain open Ži.e. flow through them is permitted in the model. to the Red Sea by placing the southern boundary Žassumed to be a wall. 15 km south of the straits. Moving this boundary any farther away from the straits had a negligible effect on the circulation inside the Gulf.
Fig. 5. The FSH difference between the north and south ends of the idealized basin Žtotal depth — 800 m. as a function of the thickness of the upper layer.
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2.3. Consistency checks As an additional validation of the model’s results, we checked the consistency of the model under a slightly different numerical setup. The model was run three times in summer configuration Žas described above.: The first time using the grid size and number of vertical layers as described above; the second time, with d x s 1 km instead of 1.5 km; while in the third run we used 10 vertical layers instead of 15. The differences in results among the three runs were negligible.
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are shown in Fig. 4 for a basin with a depth ratio of 400:400. The calculated fields are consistent with the expected result. Along the centerline of the Gulf currents are weakest and directed cross-wind. When the run was repeated but with a vanishing Coriolis
3. Results The results presented here are snapshot fields at a time much longer than the spin-up period of the model. The fields were considered fully spun-up when the kinetic energy associated with the calculated daily-averaged currents at all model points reached an asymptotic value. In all experiments, this saturation value was reached within 20 days and the model was run for at least 20 additional days to ensure both stability and complete spin-up. Superimposed on this asymptotic value was a daily cycle caused by the daily cycle in wind stress. To further establish the spin-up of the model, we examined the time series of the FSH at several points in the domain. After 15 days, there is no long-term trend in FSH and the only deviation from steady state is the repeating diurnal cycle, associated with the wind forcing. The snapshots presented are therefore representative of the fully spun-up circulation. The fields described here pertain to day 40 from the initial time at 00:00 h. In the following, we present the resulting fields in the two experiments. 3.1. Experiment I In this idealized basin experiment, the combined effects of the constant wind stress acting at the sea surface, the viscous drag at the interface separating model layers and the Coriolis force, result in a steady, cyclonic circulation around the basin ŽCsanady and Scott, 1974; Strub and Powell, 1986.. The vertically averaged velocity field Žweighted by the thickness of each layer. and the FSH distribution
Fig. 6. Diurnal variations Žhourly bins. in month-long means of wind speed in Elat, Nueiba and Dahab in: Ža. January, Žb. April, Žc. July. ŽAdapted from Manes et al. 1980...
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parameter Žits value was set at 10y1 0 sy1 ., this asymmetry was lost, which indicates that it is the rotation of the earth which is responsible for this east–west asymmetry. When the upper layer Žthe layer above the thermocline. becomes thinner we expect the sea surface
slope to increase as the action of the wind stress is distributed throughout a shallower layer. This is indeed the result obtained in Fig. 5, where the FSH difference between the north end and the south end increases as the thermocline is made shallower Ži.e. depth ratio decreases.. The vertically averaged veloc-
Fig. 7. Vertically averaged velocity over the upper 50 m and the FSH Žin cm. during Winter. The X and Y axes denote distances in grid points Žd x s d y s 1.5 km. starting from the southwest point Žlower left corner.. The FSH difference is negligible.
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ities decrease as the depth of the upper layer increases Žnot shown.. These different values of the depth-ratio approximate the seasonal changes in the hydrographic conditions in the Gulf and as such will aid in interpreting the results of the next subsection where the model is applied to the real Gulf.
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3.2. Experiment II When the real topography, hydrography and diurnal wind stress ŽTable 1 and Fig. 6. are added, the simple scenario of the idealized Gulf is greatly altered. The single, basin scale gyre is replaced by a
Fig. 8. As Fig. 7, during Spring.
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series of gyres distributed along the Gulf. The locations and sizes of these gyres vary seasonally. The results pertaining to the various seasons are described next.
3.2.1. Winter During this season, the water column is homogeneous and, as is expected from Experiment I, north– south FSH difference is negligible Žless than 0.5 cm.
Fig. 9. As Fig. 7, during Summer.
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as are the weighted average velocities over the upper 50 m shown in Fig. 7. There are three gyres in the northern half of the Gulf; the northernmost gyre is anticyclonic with an 18-km diameter. In contrast to this, the southern half is occupied by a single cyclonic gyre, associated with strong currents along the boundaries and weak velocities at the center. The weak, cross-Gulf distribution of the Žsmall. sea surface slope in this southern gyre is symmetrical, which gives rise to the anti-symmetric current along the east–west boundaries gyres. 3.2.2. Spring The fairly clear winter scenario becomes much more complex during spring. The weighted average current velocity over the upper 50 m and the FSH for this season are shown in Fig. 8. As before, there are three gyres in the northern half, but now the circulation in the southern half cannot be described by a simple circulation pattern. In general, the currents in the southern half are weaker than in the north. The winter east–west symmetry in the FSH disappears and the complicated flow is consistent with this loss
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of symmetry. The north–south FSH difference reaches a value close to 2.1 cm. 3.2.3. Summer The structure of the currents and FSH in this season, shown in Fig. 9, both lack the east–west symmetry similar to the circumstances encountered in spring. The overall north–south FSH difference reaches its maximal value of 2.5 cm due to the increase in wind stress during this season. The northernmost gyre is cyclonic with a 10-km diameter. The overall picture that emerges from these results are that the magnitude of the typical currents in summer and spring are much larger than that of winter. The results of daily changes in both current and FSH are that there is no clear correlation between the current’s magnitude and the wind but the FSH closely follows the daily wind cycle. The daily changes in FSH at a point 1.5 km south of the north coast ŽMid-Gulf., shown in Fig. 10 for the summer conditions, closely follows those of the wind. It decreases Žincreases. when the wind increases Ždecreases. in accordance with the wind set-up scenario
Fig. 10. Daily changes in FSH at a point 1.5 km south of the north coast Žblue. in cm and daily changes in wind velocity Žgreen. in m P sy1 . FSH at this point is negatively correlated with the wind: it decreases Žincreases. when the wind increases Ždecreases..
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discussed in Experiment I. Of course, a very similar pattern exists for the overall north–south FSH difference across the entire Gulf Žnot shown.. The velocities shown in Figs. 7, 8, and 9 represent the average current in the top 50 m of the water column while the average currents in the top 10 m exceeds 20 cm sy1 Žnot shown. in accordance with the decrease of speed with depth in the surface Ekman layer.
4. Discussion and conclusions The results presented in the preceding section demonstrate that the seasonality in the flow and in FSH in the Gulf of Elat is caused mainly by the strong seasonality in the hydrography ŽTable 1.. Both the magnitudes of the currents in the upper layer, above the thermocline, and the FSH are inversely related to the thickness of that layer. The weak seasonality in wind stress ŽFig. 6. amplifies this pattern — weaker winds in winter when the thermocline reaches its maximal depth. These findings are consistent with observations on seasonal changes in FSH reported in Genin and Paldor Ž1998., where it is shown that sea surface heights near the city of Elat are highest in winter and lowest in summer. The practical aspect of our results is that pollutant dispersal in the upper layer in the Gulf will be more efficient in summer and spring than in winter. During the entire year, our model results show that the circulation in the Gulf is made up of a series of permanent gyres oriented along its main axis. The location and diameter of these gyres can change in accordance with the depth of the thermocline. This can be invoked to explain a peculiar observation noted in Genin and Paldor Ž1998. as well as Wolf Ž1990.. Both of these studies report a reversal of the current direction along the west coast near the northern end of the Gulf. The progressive vector diagram at a depth of 12 m is directed northward until mid-February when it abruptly changes to southward. The opposite reversal of direction in summer occurs on different dates each year. Attempts to correlate this reversal to winds and atmospheric pressure have failed ŽWolf, 1990.. The present study provides an explanation for this reversal in terms of the hydrographic conditions rather than in terms of
external forcing. As the depth of the thermocline becomes large enough a transition from summer to winter circulation is triggered which, in turn, causes a change in the location of the centers of the gyres as well as in their diameters ŽFig. 11a and b.. As a result, the progressive vector diagram at a fixed point along the northwest end of the Gulf can shift from northward to southward Žor from southward to northward depending on the precise location. due only to the change in hydrographic conditions. The explanation given above for the current reversal has its origin in the vertically averaged Žhorizontal. velocity, i.e. the horizontal flux in the upper layer. Our model also allows an alternative explanation for this reversal of current based on the change in vertical profile of horizontal velocity rather than the horizontal arrangement of the gyres. The velocity profile shown in Fig. 12 at a point 13 km south of the north shore and 750 m east of the west coast also changes between summer and winter: In winter, the profile is unidirectional throughout the upper layer, while in summer, the velocity changes its direction between layers. Thus, at any given depth Žand grid point., a reversal in the direction of the current can take place even if the gyres remain unaltered. Of course, a heuristic, quantitative, explanation for this flow reversal is provided by the seasonal change in the wind stress, which results in a change in the depth of the Ekman layer and the depth scale of the Ekman spiral. Current meters moored at a constant depth of 12 m measure different parts of the spiral in different seasons. A comparison between current measurements at 12 and at 37 m ŽGenin and Paldor, 1999. is consistent with an Ekman flow there. The existence of gyres in the circulation seems, therefore, to be of utmost importance in trying to explain the various observations in the Gulf. It is natural at this point to examine the reason for the presence of these gyres. To do so, we ran Experiment I once again but this time with disturbed shorelines Ža guitar-shaped basin. rather than the straight, rectangular, ones used previously. The resulting circulation is shown in Fig. 13, which should be compared with Fig. 4. Instead of a single cell of cyclonic flow, which extends throughout the entire Gulf, a series of gyres develops along the main axis of the basin. It is obvious that the topography of the shoreline determines the direction of the local cur-
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Fig. 11. Vertically averaged velocity over the upper 50 m and the FSH Žin cm. during Winter Ža. and Summer Žb. in the northern part of the Gulf of Elat. The X and Y axes denote distances in grid points Žd x s d y s 1.5 km. starting from the southwest point located 17 grid points south of the northwest corner of Fig. 7. The changes in the gyral system in Ža. and Žb. result from the seasonal changes in hydrography and wind stress. As a result of these changes, the progressive vector diagram at a fixed point along the northwest end of the Gulf point can shift from northward to southward Žor from southward to northward depending upon the precise location..
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model was run for 2 days, only a Kelvin wave that propagates cyclonically around the Gulf was encountered. This wave dissipates as time goes on and steady state is established when the explicit, as well as implicit, dissipation terms in the model equations balance the energy input by the wind.
Fig. 12. Model results for the vertical profile of the long-shore velocity component at a point 13 km south of the north shore and 750 m east of the west coast for summer and winter. X axis — longshore velocity in cm sy1 , Y axis — depth in m. In winter, the profile is unidirectional throughout the upper layer, while in summer, the velocity changes its direction with depth.
rent via the boundary condition of tangential flow only. This is also the reason why more gyres develop in the narrow northern half of the Gulf where the curved coastlines have a greater effect. Consequently, in Experiment II, the equivalent of the idealized single, basin-wide cyclonic gyre appeared only in the southern half of the Gulf. Unlike the thermocline depth and wind stress, the density jump across the thermocline does not seem to have an effect on the circulation. We reran Experiment I, this time, with a temperature jump of 18C, i.e. a density jump of 0.283 su Žwhile in the original experiment it was 1.455 su .. Although the density jump was reduced by a factor of 5, the resulting circulations in the two cases were indistinguishable. Hence, the magnitude of the density jump does not have an effect on the circulation in our model, and only the wind stress and thermocline depth determine the intensity of the current. Although the focus of the study as described above applies to much longer times as compared with the spin-up of the model, a brief description of the results on shorter times is in order. When the
Fig. 13. An ideal basin with a wavy shoreline. A series of gyres develops along the main axis of the basin instead of the single cyclonic one, which obtains in the straight shoreline case ŽFig. 4.. This experiment demonstrates the effect of curved shorelines in determining the gyral structure of the circulation.
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Acknowledgements Financial support for this study was provided by the Israel Ministry of National Infrastructures via a research grant to The Hebrew University of Jerusalem. The discussions held with Drs. A. Genin and B. Lazar of HU greatly helped clarify the conditions at the Gulf.
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