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Wind-induced mesoscale circulation off the Ebro delta, NW Mediterranean: a numerical study
Journal of Marine Systems 16 Ž1998. 235–251
Wind-induced mesoscale circulation off the Ebro delta, NW Mediterranean: a numerical study M. Espino ) , A. S.-Arcilla, M.A. Garcıa ´ Laboratori d’Enginyeria Marıtima, UniÕersitat Politecnica de Catalunya, c r Gran Capitan ´ ` ´ s r n, modul ` D1, 08034 Barcelona, Spain Received 24 October 1996; accepted 23 July 1997
Abstract It is well known that the general circulation on the Catalan continental slope is dominated by a quasi-permanent southwestward geostrophic jet associated to the so-called Catalan front wMillot, C., 1987. Circulation in the western Mediterranean sea. Oceanol Acta 10, 143–149; Font, J., Salat, J., Tintore, ´ J., 1988. Permanent features of the circulation in the Catalan Sea. Oceanol. Acta 9, 51–57x. On the continental shelf, however, the flow is modified by the action of friction which enhances also other nonlinear interactions. Several authors have hypothesized that the shelf circulation is anticyclonic north of the Ebro delta wSalat, J., Manriquez, M., Cruzado, A., 1978. Hidrografia del golfo de Sant Jordi. Campana ˜ Delta ŽAbril 1970.. Investigacion y biologico de ´ Pesquera 42 Ž2., 255–272; Ballester, A., Castellvı, ´ J., 1980. Estudio hidrografico ´ ´ las plataformas continentales espanolas: I. Efecto de los efluentes de una planta de energıa ˜ ´ nuclear en el Golfo de San Jorge ŽFebrero 1975–Octubre 1976.. Informes Tecnicos del Instituto de Investigaciones Pesqueras 76, 70 pp.x. A quasi-3D finite ´ element code based on the shallow-water equations has been used to explore the effect of several mechanisms which might be responsible for such a local circulation pattern, and in particular of wind. The obtained numerical results suggest that the basic anticyclonic structure of the mean flow is controlled by the bathymetry and that the clockwise-rotating mean flow pattern is not a permanent circulation feature. It is seen that the characteristic local wind stress fields—computed through interpolation of the records of a local network of meteo stations—may ‘enhance’ or ‘delete’ the anticyclonic gyre depending on the sign of their relative vorticity. According to the analysis of a 2-yr record of local wind data, the net contribution of wind events with a duration longer than 24 h is to reinforce the anticyclonic circulation Žover 70% of these wind fields supply negative relative vorticity to the study area.. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Ebro delta; mesoscale circulation; wind; Catalan front
1. Introduction The main feature of the mean circulation in the northwestern Mediterranean is a quasi-permanent slope current. This current, which is named the Liguro–Provenc¸al–Catalan Current or simply the )
Corresponding author.
Northern Current, is essentially geostrophic and exhibits continuity from the Gulf of Genova to the Gulf of Valencia ŽMillot, 1987.. Off the Spanish coast, the current is basically southwestward and is linked to the so-called Catalan front, which is a permanent density front associated to strong salinity gradients ŽFont et al., 1988.. The 38.3 psu isohaline and the 29.0 kgrm3 isopycnal can be considered as the
0924-7963r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 7 9 6 3 Ž 9 7 . 0 0 1 1 0 - 3
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hydrographic signatures of the Catalan front. Extensive satellite imagery examined by La Violette et al. Ž1990. reveals important mesoscale activity of the front during most of the year. On the continental shelf, the action of friction and other nonlinear interactions produces a dynamic balance which, in principle, is nongeostrophic. In certain areas such as the Ebro delta continental shelf where the wind is intense, the structure of the local circulation can be very complicated Žsee e.g., Garcıa ´ and Ballester, 1984.. In particular, the spatial smallscale variability of the wind stress can give rise to complex circulation patterns which cannot be explained by just using ‘rules of thumb’. For such an area, the use of numerical modelling techniques to assess the resulting flow patterns is a must Žsee e.g., Han and Kohler, 1982.. The Gulf of St. Jordi is the stretch of the continental shelf extending between Cape Salou and the central lobe of the Ebro delta ŽFig. 1.. In that area, important physical and biogeochemical dispersive processes take place, such as the transport and depo-
Fig. 1. Location of the Gulf of St. Jordi.
Fig. 2. Surface current velocity data collected by Salat et al. Ž1978. during the Delta 70 experiment Žmodified from Salat et al., 1978..
sition of fine sediments and micropollutants discharged by the Ebro river and the dispersion of the thermal plume produced by the refrigeration of the Vandellos ´ nuclear power plant. To assess the physics and the extent of these processes, previous knowledge of the characteristic local mean circulation patterns and flow variability is required. Salat et al. Ž1978. and Ballester and Castellvı´ Ž1980. hypothesized the structure of the mean circulation in the Gulf of St. Jordi on the basis of a limited amount of field observations. In both papers, it was suggested that the local circulation is anticyclonic ŽFigs. 2 and 3., although no physical explanation was proposed by the authors for this flow pattern. Font et al. Ž1986. stated that this clockwise circulation is induced by the bathymetry and that it can be understood as an anticyclonic vortex detached from the general circulation when the slope current veers to the southeast to contour the Ebro Delta. Garcıa ´ Ž1990. performed numerical simulations of the local wind-induced circulation and showed that northwestern wind events supplying negative vorticity to the flow could also be responsible for the clockwise circulation in the Gulf of St. Jordi. The spatial variability of the local wind stress fields was documented by Garcıa ´ Ž1988. and by Cartes and Ž Stefanescu not published.. The aim of this paper is to further the understanding on the circulation schemes proposed for the Gulf
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tion that the velocity field depends on the z-coordinate. the steady-state SWE is read as follows: Continuity equation Ex Ž h q h . U q E y Ž h q h . V s 0
Ž 1.
Momentum equation uE x u q ÕE y u y fÕ s yg
r0
1 Exh y g Ex a r r
q Ex 2 K H Ž Ex u . E y K H Ž Ex Õ q E y u . q Ez K z Ž Ez u . uE x Õ q ÕE y Õ q fu s yg Fig. 3. Surface circulation pattern proposed by Ballester and Castellvı´ Ž1980. after the field data acquired during the Flash VIII survey Žmodified from Ballester and Castellvı, ´ 1980..
of St. Jordi zone using numerical simulation techniques. In particular, the role of the wind on the local mesoscale circulation will be assessed.
2. Model description A steady-state diagnostic model of the shallowwater equations ŽSWE. developed by Espino Ž1994. is the main tool used in this study. This model solves a discretized finite-element version of the SWE using a weighted-residuals Galerkin technique. The model is of the quasi-3D type, in the sense that the vertical variation of the model variables is decomposed in terms of a series of orthogonal basis functions Ževen-number Legendre polynomials are used here., and uses a low order Q1-P0 interpolation scheme in the horizontal Ži.e., four-noded bilinear interpolation for the velocity and piecewise constant interpolation for the pressure field.. The dynamics of the mean flow on continental shelves is such that the vertical advection of momentum can be assumed to be small and the pressure to be approximately hydrostatic. When these hypotheses are applied to the Navier–Stokes equations, we obtain the well-known SWE. If the continuity equation is integrated vertically Žbut keeping the assump-
Ž 2. r0
1 E yh y g E y a r r
q Ex K H Ž Ex Õ q E y u . q Ey 2 K H Ž E yÕ . q Ez K z Ž Ez Õ .
Ž 3.
where h is the free surface height, Ž u,Õ . the horizontal velocity components, ŽU,V . the vertically integrated horizontal velocity components, h is the depth, f is the Coriolis parameter, r is the density, g the gravity acceleration, K H and K z are the horizontal and vertical eddy viscosity and a the integral of r between a generic depth z and the sea level at rest. Our FEM model solves the nonlinear steady-state Eqs. Ž1. – Ž3. by means of the Newton–Raphson technique and uses a macroelement technique combined with a generalized Uzawa algorithm to avoid ‘checkerboarding’ spurious modes in the pressure solutions Žsee Fortin and Boivin, 1990.. A direct frontal method is used to solve the system of equations at each iteration. The model is currently supported by a DEC ALPHA AXP 7000 architecture. 3. Local characteristic wind fields According to Garcıa ´ Ž1982., the typical wind events in the Ebro delta region can be classified into three groups: Ži. onshore winds—mainly northeasterlies and easterlies—related to storms generated in the western Mediterranean basin Ž lleÕants .; Žii. southwesterlies, which are typically summer winds linked to fair weather conditions Ž garbins .; and Žiii. strong northwesterlies Ž mestrals ., which are forced either geostrophically or as cross-isobaric jets down the Ebro valley Žbreezes are obviously not included in any of these wind types..
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Fig. 4 gives an idea of the relevance of land topography in the vicinity of the Ebro delta. It clearly suggests that wind fields acting on neighbouring marine areas such as the Gulf of St. Jordi may have an important spatial small-scale variability, as Garcıa ´ Ž1988. and Cartes and Stefanescu Ž1980, personal communication. have evidenced. The small-scale structure of the wind fields may play a key role on the local mesoscale circulation. Furthermore, this variability has to be included in the wind stress forcing of the circulation model to produce realistic results. To assess the small-scale structure of the typical wind fields in the study area, we have considered the time series of wind data acquired at the Casablanca, Vandellos ´ and Deltebre weather stations simultaneously between March 1988 and March 1990 Žsee Fig. 4.. The Casablanca station Ž40843X N, 01821X E, relative height of the anemometer z s 71 m. was operated by Repsol Exploracion ´ at the Casablanca oil rig off the Ebro delta and produced mean wind velocity and wind direction records each 6 h. The Vandellos ´ station Ž40857X N, 00852X E, relative height of the
anemometer z s 10 m. was run by Hifrensa at the Vandellos ´ I nuclear power plant and produced synops of the mean wind velocity and wind direction at 0 h, 7 h, 13 h and 18 h local time. The wind direction was discriminated in 16 directional sectors in the synop observations. As for Deltebre Ž40843X N, 00845X E, relative height of the anemometer z s 17 m., the automatic weather station was managed by the Direccio´ General de Ports i Costes of the Catalan Regional Government with a sampling interval of 10 min. Using Deltebre as master station, each wind record in the period March 1988–March 1990 has been coarsely classified as lleÕant, garbı´ or mestral, according to the following directional rules: -lleÕant: wind direction comprised between 08 and 1358 -garbı: ´ wind direction comprised between 1358 and 2708 -mestral: wind direction comprised between 2708 and 3608. A wind event has been defined as an interval during which the wind records belong to the same
Fig. 4. Land topography in the vicinity of the Ebro delta and location of the Casablanca, Vandellos ´ and Deltebre meteo stations.
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directional class without loss of continuity. Breezes have been then filtered out by considering only the wind events whose duration exceeded 24 h Žin fact, it was assumed that only the relatively long-lasting wind events are able to have a remarkable influence on the local mean circulation. and computing the vector-averaged wind velocity for the period corresponding to each event Žusing log-corrected values for a z s 10 m height.. The same vector-averages have been then computed for the Casablanca and
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Vandellos ´ data sets. The roughness length parameters Ž z 0 . considered for the log-correction of each wind data set depend on the nature of the local surface. We have taken z 0 s 5.10y3 m for Casablanca, z 0 s 10y2 m for Vandellos ´ and z 0 s 3.10y2 m for Deltebre. In this way, 36 wind events have been identified according to the previous criteria, which are listed in Table 1. This table includes an estimate of the relative vorticity of the mean wind velocity field
Table 1 Wind events with duration exceeding 24 h, for the March 1988–March 1990 period Number
Initial date
Final date
Duration Žh.
Type
Module Žmrs.
Direction Ž8.
Vorticity Ž)10y7 .
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
11r04r88 25r04r88 05r05r88 09r06r88 22r07r88 04r11r88 10r11r88 06r12r88 30r01r89 06r02r89 07r02r89 14r02r89 20r03r89 26r03r89 29r03r89 13r04r89 16r04r89 22r04r89 25r04r89 27r04r89 09r05r89 23r05r89 07r06r89 12r06r89 03r07r89 05r07r89 23r07r89 31r08r89 07r10r89 09r10r89 16r10r89 23r10r89 26r10r89 13r11r89 01r03r90 03r03r90
13r04r88 27r04r88 06r05r88 10r06r88 24r07r88 06r11r88 12r11r88 08r12r88 31r01r89 07r02r89 08r02r89 15r02r89 22r03r89 29r03r89 31r03r89 14r04r89 17r04r89 24r04r89 26r04r89 29r04r89 11r05r89 26r05r89 09r06r89 14r06r89 04r07r89 06r07r89 24r07r89 02r09r89 09r10r89 10r10r89 18r10r89 24r10r89 27r10r89 16r11r89 02r03r90 05r03r90
65.33 33.67 24.33 49.16 39.33 44.50 44.50 42.83 31.33 30.50 25.67 25.17 40.50 54.33 39.50 32.83 28.67 59.33 25.00 35.33 28.00 92.33 30.17 30.00 29.83 41.83 27.17 30.00 27.83 24.50 48.17 23.83 29.00 68.50 26.50 39.17
garbı´ levante levante levante garbı´ levante levante mestral levante levante levante mestral mestral levante levante mestral mestral levante mestral mestral garbı´ levante levante levante garbı´ levante levante mestral mestral mestral levante levante levante levante mestral levante
0.92 4.90 3.34 2.79 2.15 4.01 5.45 9.26 3.05 3.82 3.15 8.59 9.37 5.19 6.84 9.35 6.28 3.48 5.82 9.82 3.82 7.32 3.76 1.99 3.96 5.60 3.16 6.96 10.35 6.37 4.43 3.86 4.16 4.32 4.44 3.88
185.77 45.41 83.64 78.85 181.86 52.30 71.59 328.51 75.96 67.06 70.13 318.95 313.66 67.73 71.23 304.95 302.05 75.36 322.97 314.55 123.69 69.29 69.59 80.16 131.93 70.59 75.92 318.73 320.96 319.91 67.72 79.71 81.01 79.46 318.66 68.72
y2.73 y4.87 y2.99 q1.71 y2.82 y5.46 y11.89 y4.96 y0.11 y7.3 y2.31 q9.66 q6.26 y16.21 y31.66 q23.20 q5.35 y1.94 q6.42 q37.40 y47.50 y28.70 y6.24 y0.19 y45.81 y14.95 y1.01 y27.14 y4.18 y23.31 y11.19 y4.24 y3.19 y0.01 q14.1 y1.56
Variables listed are: number of wind event, initial date, end date, duration Žin hours., type of wind, module Žmrs. and direction Ž8. of the vector-averaged wind velocity at Deltebre and vorticity estimate Žmrs 2 ..
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associated to each event computed with the assumption that the spatial variation of the wind velocity across the study area is linear, which is an acceptable hypothesis given the dimensions of the study area. Some interesting conclusions emerge from this analysis: Ø The most intense winds are the mestrals Žaverage velocity of the order of 4–11 mrs., whereas the garbins are the weakest Ž0–4 mrs.. The average velocities of the lleÕants fall within the 2–8 mrs interval. Ø The wind event duration is longest for the lleÕants and the garbins, whereas the persistence of the mestrals is always below 45 h with the criteria adopted here. Ø Seventy-two percent of the mean wind velocity fields have negative relative vorticity. In particular, all garbins and 86% of the lleÕants have associated mean wind velocity fields with negative relative vorticity. As for the mestrals, only 37% of them produce negative relative vorticity in the mean wind velocity field. Ø In general terms, moderate wind events Žaverage wind velocities of the order of 3–6 mrs in Deltebre. produce mean wind velocity fields with negative relative vorticity, whereas relative vorticity can be either positive or negative in events with average wind velocities under 3 mrs or over 6 mrs. Ø The relative vorticity of the mean wind velocity fields linked to wind events lasting more than 35 h is mainly negative. There is no such clear predominance in the shorter wind events. Although some of the previous results may partially be artifacts due to the criteria used to define wind events Že.g., the relatively low persistence of the mestrals ., they provide sufficient indication that the prevailing winds—and associated wind stress fields—acting on the Gulf of St. Jordi tend to introduce negative vorticity in the area. Section 4 studies how this influences the local circulation.
4. Numerical experiments and results Several numerical experiments have been designed to evaluate the effects of wind stress fields representing typical wind conditions on the back-
ground mean circulation in the Gulf of St. Jordi by using the model described in Section 2: -Case 1: no wind -Case 2: wind stress field associated to the lleÕant wind event starting on 29.03.89, 08:30 h Žwind velocity distribution with negative relative vorticity. -Case 3: wind stress field associated to the mestral wind event starting on 27.08.89 at 22:50 h Žwind velocity distribution with positive relative vorticity.. The domain considered for these modelling exercises is limited by the coastline, the 100 m isobath and two cross-shore transects off Cape Salou and Cape Tortosa. The computational grid used consists of 384 elements and 425 nodes Žsee Fig. 5., with a characteristic element size of 2 km = 2 km. The number of vertical degrees of freedom Žs number of basis functions. considered per node is 2. The wind stress Žt s . forcing has been evaluated using a conventional quadratic parameterization of the form:
t s s ra C D < u10 < u10
Ž 4.
where ra is the air density, C D is a constant drag coefficient and ra C D s 0.0018 kgrm3. The value of the wind velocity at 10 m over the sea surface Ž u10 . at each node has been derived from a linear interpolationrextrapolation fit on the basis of the Casablanca, Vandellos ´ and Deltebre wind data. The wind stress distributions derived for cases 2 and 3 are depicted in Fig. 6. A linear relationship between the bottom stress Žt b . and the near-bottom velocity namely:
t xb s g b Ž u b y Õ b . t yb s g b Ž u b q Õ b . Žwith g b being the bottom friction coefficient and u b , Õ b the horizontal components of the near bottom velocity. has been considered following the assumption that the bottom boundary layer is governed by the Ekman dynamics. Since the main goal in this paper is to better understand the action of wind forcing, all simulations have been performed with a closed Ebro river mouth and assuming an homogeneous density field Ž r s 1025 kgrm3 .. As regards to the model ‘free’ param-
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Fig. 5. Ža. Bathymetry of the study area. Žb. Numerical grid.
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eters, homogeneous horizontal and vertical eddy viscosity coefficients Ž K H s 50 m2rs and K z s 10y2 m2rs. have been considered together with values for the bottom friction coefficients Žg b . ranging from 0.001 to 10 kgrm2 s, which give a reasonable approximate representation of the physics. An error radius eps s 0.01 mrs has been fixed for the convergence criterion. The values selected for the eddy viscosity and bottom friction coefficients fall within the ranges recommended by the oceanographic literature. A value of g b has been selected for each simulation such that the surface stress exerted by the wind and the bottom stress are of the same order of magnitude, which is known to be the case in shallow water domains. The availability of current measurements obtained at the Casablanca oil rig near the southestward corner of the study domain Žsee e.g., Font, 1990. has been taken into account for the definition of the boundary conditions. For the first vertical degree of freedom, which corresponds to the vertically-averaged velocity, an along-isobath flow of 10 cmrs on the outer boundary has been prescribed Žthis is a means to reproduce the action of the slope jet existing off the shelf edge.. A uniform southward flow of 10 cmrs on the southern boundary and a no-slip condition at the coastline have also been selected as reasonable boundary prescriptions. On the northern boundary, an homogeneous Neumann Žor free-flow. condition has been imposed. For the second vertical degree of freedom, which produces the vertical structure in the current velocity profiles, homogeneous
Neumann conditions have been specified for the northern, outer and southern boundaries, together with an homogeneous Dirichlet Žno-slip. boundary condition for the coastline. Given the iterative penalty approach used in our model for the continuity equation Žgeneralized Uzawa algorithm., which allows iterative explicit elimination of the pressure as a function of the velocity and the penalty parameter, no boundary condition needs to be specified for the pressure. Fig. 7 shows the model solutions for case 1 Žno wind forcing.. The vertically-integrated circulation is anticyclonic, just as the surface and the bottom current velocity fields are. The differences between the surface, the bottom and the vertically-averaged fields are negligible due to the fact that there is no agent driving vertical velocity gradients. The topography of the sea surface roughly parallels the streamlines, which suggests that the mean circulation is basically in geostrophic balance. The numerical solutions for case 2 Ž lleÕant wind introducing negative vorticity in the study area. are reported in Fig. 8. It can be seen that the verticallyintegrated circulation is again anticyclonic and that it is strengthened by the wind Žthe maximum velocity values exceed those of case 1 by about 6 cmrs.. The pattern of the surface current velocity field is also anticyclonic but not that of the bottom flow. Only near the coast of the Ebro delta that the bottom current velocities reach relevant values. The results of case 3 Ž mestral wind introducing positive vorticity. are very interesting Žsee Fig. 9..
Fig. 6. Ža. Wind stress forcing for case 2. Žb. Wind stress forcing for case 3. Scales are given by the length of the longest vector in figures Ž0.147 N Wrm2 in figure a, 0.257 N Wrm2 in figure b.. Fig. 7. Model solutions for case 1 Ž K H s 50 m2rs, K z s 10y2 m2 rs and g b s 0.001 kgrm2 s.. Ža. Vertically-integrated current velocity Žmrs.. Žb. Surface current velocity Žmrs.. Žc. Bottom current velocity Žmrs.. Žd. Sea surface elevation Žin meters relative to arbitrary zero level.. Scales in figures a, b and c are given by the length of the longest vectors Ž0.109 mrs in all figures.. Fig. 8. Model solutions for case 2 Ž K H s 50 m2 rs, K z s 10y2 m2 rs and g b s 1 kgrm2 s.. Ža. Vertically-integrated current velocity Žmrs.. Žb. Surface current velocity Žmrs.. Žc. Bottom current velocity Žmrs.. Žd. Sea surface elevation Žin meters relative to arbitrary zero level.. Scales in figures a, b and c are given by the length of the longest vectors Ž0.163 mrs in figure a, 0.222 mrs in figure b and 0.183 mrs in figure c.. Fig. 9. Model solutions for case 3 Ž K H s 50 m2rs, K z s 10y2 m2 rs and g b s 10 kgrm2 s.. Ža. Vertically-integrated current velocity Žmrs.. Žb. Surface current velocity Žmrs.. Žc. Bottom current velocity Žmrs.. Žd. Sea surface elevation Žin meters relative to arbitrary zero level.. Scales in figures a, b and c are given by the length of the longest vectors Ž0.243 mrs in figure a, 0.387 mrs in figure b and 0.183 mrs in figure c..
M. Espino et al.r Journal of Marine Systems 16 (1998) 235–251
Fig. 6.
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Fig. 7.
M. Espino et al.r Journal of Marine Systems 16 (1998) 235–251
Fig. 7 Žcontinued..
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Fig. 8.
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Fig. 8 Žcontinued..
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Fig. 9.
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Fig. 9 Žcontinued..
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The background anticyclonic pattern of the vertically-averaged circulation has been totally offset by the wind forcing. The surface flow is essentially along isobaths with a predominant southward component, whereas the bottom circulation is much weaker and complex. Again the bottom current velocities are highest in the vicinity of the Ebro delta. The modelled sea surface elevation field reveals water-piling near the Ebro delta coast, showing the dominance of the momentum induced by wind in determining the surface elevation.
5. Discussion The previous modelling exercises have been designed to gain insight into the effect of local winds on the mean circulation in the Gulf of St. Jordi area. Our results support the hypothesis of Salat et al. Ž1978. and Ballester and Castellvı´ Ž1980. in the sense that the obtained background mean circulation is anticyclonic Žsee Fig. 7.. This circulation pattern can be regarded as a by-product to vorticity adjustment of the alongslope jet associated to the Catalan front, which is forced to acquire positive relative Žand potential. vorticity south of Cape Salou due to slope curvature related to shelf width increase. From the same point of view, the introduction of positive Žnegative. vorticity via the wind stress forcing applied to the sea surface has to result in a weakening Žstrengthening. of the anticyclonic circulation pattern. The obtained model results are consistent with this behaviour, which means that the final circulation pattern will depend on the relative importance of the two forcing mechanisms Žin fact of their respective induced vorticity.. Furthermore, the previous numerical results point out that there might be important differences between the surface and the near-bed flows. ŽNote: the obtained ‘bottom’ current velocities are, strictly speaking, flow velocities derived for the uppermost level of a bottom boundary layer. See Espino, 1994 for more details.. The vertical structure of the model solutions, obtained here with just 2 vertical degrees of freedom, is probably valid only in a qualitative sense, so runs with higher vertical resolution would be needed to achieve solutions suitable for a realistic computation of stresses acting on bottom sediments,
which is beyond the present goals. On the other hand, neither the winds events in the area nor the boundary conditions are really steady, so time-dependent simulations of the wind-induced flow Žin which the steady circulation is reached after model spinning-up. should be performed to compare with detailed field observations when they are available. Moreover, further runs for stratification conditions and with vertically-varying eddy viscosities should be undertaken to assess the different effect of the wind action when the vertical density gradients are important. Finally, additional simulations with the Ebro river mouth open should be carried out to study the details of the circulation in the area influenced by the river discharge.
6. Conclusions A quasi-3D finite element code of the shallowwater equations has been used to investigate the effect of wind forcing on the mesoscale circulation in the Gulf of St. Jordi area. The obtained numerical results suggest that the mean flow is anticyclonic under no-wind conditions, which is in agreement with the statements by Salat et al. Ž1978. and Ballester and Castellvı´ Ž1980.. Nevertheless, the characteristic local wind stress fields may strengthen or weaken the anticyclonic circulation depending on the sign of their relative vorticity. Furthermore, they introduce vertical structure in the current velocity profiles. Given the fact that over 70% of the local wind events recorded during a 2-yr period and exceeding 24 h in duration have associated wind velocity distributions with negative relative vorticity, we conclude that the net effect of local winds is to reinforce the clockwise mesoscale circulation.
Acknowledgements The authors wish to thank Repsol Exploracion, ´ Hifrensa and the Direccio´ General de Ports i Costes of the Generalitat de Catalunya for making available their meteo data sets to us. This study has been partially funded by the Spanish Comision ´ Interministerial de Ciencia y Tecnologıa ´ Žgrant no. AMB92-
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0251-C02-02. and the European Commission, MAST EU Programme ŽFANS project, contract no. MAS3CT95-0037. References Ballester, A., Castellvı, y biologico ´ J., 1980. Estudio hidrografico ´ ´ de las plataformas continentales espanolas: I. Efecto de los ˜ efluentes de una planta de energıa ´ nuclear en el Golfo de San Jorge ŽFebrero 1975–Octubre 1976.. Informes Tecnicos del ´ Instituto de Investigaciones Pesqueras 76, 70. Espino, M., 1994. Estabilizacion ´ de la superficie libre en la solucion ´ de ecuaciones shallow-water por elementos finitos. Aplicaciones oceanograficas. PhD thesis, Universitat ´ Politecnica de Catalunya, 443 pp. ` Font, J., 1990. Marine circulation along the Ebro continental margin. Mar. Geol. 95, 165–177. Font, J., Julia, J., 1986. ` A., Rovira, J., Salat, J., Sanchez-Pardo, ´ Circulacion ´ marina en la plataforma continental del Ebro determinada a partir de la distribucion ´ de masas de agua y los microcontaminantes organicos en el sedimento. Acta Geol. ´ Hispanica 21–22, 483–489. ´ Font, J., Salat, J., Tintore, ´ J., 1988. Permanent features of the circulation in the Catalan Sea. Oceanol. Acta 9, 51–57.
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Fortin, M., Boivin, S., 1990. Iterative stabilization of the bilinear velocity constant pressure element. Int. J. Numerical Meth. Fluids 2, 25–42. Garcıa, ´ M.A., 1982. Aproximacion ´ al comportamiento estadıstico ´ del viento en el delta del Ebro Estudio de la velocidad escalar. Investigacion ´ Pesquera 46 Ž3., 349–377. Garcıa, ´ M.A., 1988. Analisi ` i proposta de solucions per a estabilitzar el delta de l’Ebre. El vent en el delta de l’Ebre. Ed. Direccio´ General de Ports i Costes, Generalitat de Catalunya, 22 pp. Garcıa, ´ M.A., 1990. Contribucion ´ al estudio de la circulacion ´ marina mediante el metodo de los elementos finitos. PhD ´ Thesis, Universitat Politecnica de Catalunya, 321 pp. ` Garcıa, ´ M.A., Ballester, A., 1984. Notas acerca de la meteorologıa ´ y la circulacion ´ local en la region ´ del delta del Ebro Ž1980– 1981.. Investigacion ´ Pesquera 48 Ž3., 469–493. Han, G., Kohler, K., 1982. Observed and modelled circulation on the Spanish Mediterranean continental shelf near Rıo ´ Ebro. Rep. NA82RAC000222, 1-424-12-500, Sci. Appl., 70 pp. La Violette, P.E., Tintore, ´ J., Font, J., 1990. The surface circulation of the Balearic Sea. J. Geophys. Res. 95 ŽC2., 1559–1568. Millot, C., 1987. Circulation in the western Mediterranean Sea. Oceanol. Acta 10, 143–149. Salat, J., Manrıquez, M., Cruzado, A., 1978. Hidrografia del golfo ´ de Sant Jordi. Campana ˜ ‘Delta’ ŽAbril 1970.. Investigacion ´ Pesquera 42 Ž2., 255–272.
Wind-induced mesoscale circulation off the Ebro delta, NW Mediterranean: a numerical study M. Espino ) , A. S.-Arcilla, M.A. Garcıa ´ Laboratori d’Enginyeria Marıtima, UniÕersitat Politecnica de Catalunya, c r Gran Capitan ´ ` ´ s r n, modul ` D1, 08034 Barcelona, Spain Received 24 October 1996; accepted 23 July 1997
Abstract It is well known that the general circulation on the Catalan continental slope is dominated by a quasi-permanent southwestward geostrophic jet associated to the so-called Catalan front wMillot, C., 1987. Circulation in the western Mediterranean sea. Oceanol Acta 10, 143–149; Font, J., Salat, J., Tintore, ´ J., 1988. Permanent features of the circulation in the Catalan Sea. Oceanol. Acta 9, 51–57x. On the continental shelf, however, the flow is modified by the action of friction which enhances also other nonlinear interactions. Several authors have hypothesized that the shelf circulation is anticyclonic north of the Ebro delta wSalat, J., Manriquez, M., Cruzado, A., 1978. Hidrografia del golfo de Sant Jordi. Campana ˜ Delta ŽAbril 1970.. Investigacion y biologico de ´ Pesquera 42 Ž2., 255–272; Ballester, A., Castellvı, ´ J., 1980. Estudio hidrografico ´ ´ las plataformas continentales espanolas: I. Efecto de los efluentes de una planta de energıa ˜ ´ nuclear en el Golfo de San Jorge ŽFebrero 1975–Octubre 1976.. Informes Tecnicos del Instituto de Investigaciones Pesqueras 76, 70 pp.x. A quasi-3D finite ´ element code based on the shallow-water equations has been used to explore the effect of several mechanisms which might be responsible for such a local circulation pattern, and in particular of wind. The obtained numerical results suggest that the basic anticyclonic structure of the mean flow is controlled by the bathymetry and that the clockwise-rotating mean flow pattern is not a permanent circulation feature. It is seen that the characteristic local wind stress fields—computed through interpolation of the records of a local network of meteo stations—may ‘enhance’ or ‘delete’ the anticyclonic gyre depending on the sign of their relative vorticity. According to the analysis of a 2-yr record of local wind data, the net contribution of wind events with a duration longer than 24 h is to reinforce the anticyclonic circulation Žover 70% of these wind fields supply negative relative vorticity to the study area.. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Ebro delta; mesoscale circulation; wind; Catalan front
1. Introduction The main feature of the mean circulation in the northwestern Mediterranean is a quasi-permanent slope current. This current, which is named the Liguro–Provenc¸al–Catalan Current or simply the )
Corresponding author.
Northern Current, is essentially geostrophic and exhibits continuity from the Gulf of Genova to the Gulf of Valencia ŽMillot, 1987.. Off the Spanish coast, the current is basically southwestward and is linked to the so-called Catalan front, which is a permanent density front associated to strong salinity gradients ŽFont et al., 1988.. The 38.3 psu isohaline and the 29.0 kgrm3 isopycnal can be considered as the
0924-7963r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 7 9 6 3 Ž 9 7 . 0 0 1 1 0 - 3
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hydrographic signatures of the Catalan front. Extensive satellite imagery examined by La Violette et al. Ž1990. reveals important mesoscale activity of the front during most of the year. On the continental shelf, the action of friction and other nonlinear interactions produces a dynamic balance which, in principle, is nongeostrophic. In certain areas such as the Ebro delta continental shelf where the wind is intense, the structure of the local circulation can be very complicated Žsee e.g., Garcıa ´ and Ballester, 1984.. In particular, the spatial smallscale variability of the wind stress can give rise to complex circulation patterns which cannot be explained by just using ‘rules of thumb’. For such an area, the use of numerical modelling techniques to assess the resulting flow patterns is a must Žsee e.g., Han and Kohler, 1982.. The Gulf of St. Jordi is the stretch of the continental shelf extending between Cape Salou and the central lobe of the Ebro delta ŽFig. 1.. In that area, important physical and biogeochemical dispersive processes take place, such as the transport and depo-
Fig. 1. Location of the Gulf of St. Jordi.
Fig. 2. Surface current velocity data collected by Salat et al. Ž1978. during the Delta 70 experiment Žmodified from Salat et al., 1978..
sition of fine sediments and micropollutants discharged by the Ebro river and the dispersion of the thermal plume produced by the refrigeration of the Vandellos ´ nuclear power plant. To assess the physics and the extent of these processes, previous knowledge of the characteristic local mean circulation patterns and flow variability is required. Salat et al. Ž1978. and Ballester and Castellvı´ Ž1980. hypothesized the structure of the mean circulation in the Gulf of St. Jordi on the basis of a limited amount of field observations. In both papers, it was suggested that the local circulation is anticyclonic ŽFigs. 2 and 3., although no physical explanation was proposed by the authors for this flow pattern. Font et al. Ž1986. stated that this clockwise circulation is induced by the bathymetry and that it can be understood as an anticyclonic vortex detached from the general circulation when the slope current veers to the southeast to contour the Ebro Delta. Garcıa ´ Ž1990. performed numerical simulations of the local wind-induced circulation and showed that northwestern wind events supplying negative vorticity to the flow could also be responsible for the clockwise circulation in the Gulf of St. Jordi. The spatial variability of the local wind stress fields was documented by Garcıa ´ Ž1988. and by Cartes and Ž Stefanescu not published.. The aim of this paper is to further the understanding on the circulation schemes proposed for the Gulf
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tion that the velocity field depends on the z-coordinate. the steady-state SWE is read as follows: Continuity equation Ex Ž h q h . U q E y Ž h q h . V s 0
Ž 1.
Momentum equation uE x u q ÕE y u y fÕ s yg
r0
1 Exh y g Ex a r r
q Ex 2 K H Ž Ex u . E y K H Ž Ex Õ q E y u . q Ez K z Ž Ez u . uE x Õ q ÕE y Õ q fu s yg Fig. 3. Surface circulation pattern proposed by Ballester and Castellvı´ Ž1980. after the field data acquired during the Flash VIII survey Žmodified from Ballester and Castellvı, ´ 1980..
of St. Jordi zone using numerical simulation techniques. In particular, the role of the wind on the local mesoscale circulation will be assessed.
2. Model description A steady-state diagnostic model of the shallowwater equations ŽSWE. developed by Espino Ž1994. is the main tool used in this study. This model solves a discretized finite-element version of the SWE using a weighted-residuals Galerkin technique. The model is of the quasi-3D type, in the sense that the vertical variation of the model variables is decomposed in terms of a series of orthogonal basis functions Ževen-number Legendre polynomials are used here., and uses a low order Q1-P0 interpolation scheme in the horizontal Ži.e., four-noded bilinear interpolation for the velocity and piecewise constant interpolation for the pressure field.. The dynamics of the mean flow on continental shelves is such that the vertical advection of momentum can be assumed to be small and the pressure to be approximately hydrostatic. When these hypotheses are applied to the Navier–Stokes equations, we obtain the well-known SWE. If the continuity equation is integrated vertically Žbut keeping the assump-
Ž 2. r0
1 E yh y g E y a r r
q Ex K H Ž Ex Õ q E y u . q Ey 2 K H Ž E yÕ . q Ez K z Ž Ez Õ .
Ž 3.
where h is the free surface height, Ž u,Õ . the horizontal velocity components, ŽU,V . the vertically integrated horizontal velocity components, h is the depth, f is the Coriolis parameter, r is the density, g the gravity acceleration, K H and K z are the horizontal and vertical eddy viscosity and a the integral of r between a generic depth z and the sea level at rest. Our FEM model solves the nonlinear steady-state Eqs. Ž1. – Ž3. by means of the Newton–Raphson technique and uses a macroelement technique combined with a generalized Uzawa algorithm to avoid ‘checkerboarding’ spurious modes in the pressure solutions Žsee Fortin and Boivin, 1990.. A direct frontal method is used to solve the system of equations at each iteration. The model is currently supported by a DEC ALPHA AXP 7000 architecture. 3. Local characteristic wind fields According to Garcıa ´ Ž1982., the typical wind events in the Ebro delta region can be classified into three groups: Ži. onshore winds—mainly northeasterlies and easterlies—related to storms generated in the western Mediterranean basin Ž lleÕants .; Žii. southwesterlies, which are typically summer winds linked to fair weather conditions Ž garbins .; and Žiii. strong northwesterlies Ž mestrals ., which are forced either geostrophically or as cross-isobaric jets down the Ebro valley Žbreezes are obviously not included in any of these wind types..
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Fig. 4 gives an idea of the relevance of land topography in the vicinity of the Ebro delta. It clearly suggests that wind fields acting on neighbouring marine areas such as the Gulf of St. Jordi may have an important spatial small-scale variability, as Garcıa ´ Ž1988. and Cartes and Stefanescu Ž1980, personal communication. have evidenced. The small-scale structure of the wind fields may play a key role on the local mesoscale circulation. Furthermore, this variability has to be included in the wind stress forcing of the circulation model to produce realistic results. To assess the small-scale structure of the typical wind fields in the study area, we have considered the time series of wind data acquired at the Casablanca, Vandellos ´ and Deltebre weather stations simultaneously between March 1988 and March 1990 Žsee Fig. 4.. The Casablanca station Ž40843X N, 01821X E, relative height of the anemometer z s 71 m. was operated by Repsol Exploracion ´ at the Casablanca oil rig off the Ebro delta and produced mean wind velocity and wind direction records each 6 h. The Vandellos ´ station Ž40857X N, 00852X E, relative height of the
anemometer z s 10 m. was run by Hifrensa at the Vandellos ´ I nuclear power plant and produced synops of the mean wind velocity and wind direction at 0 h, 7 h, 13 h and 18 h local time. The wind direction was discriminated in 16 directional sectors in the synop observations. As for Deltebre Ž40843X N, 00845X E, relative height of the anemometer z s 17 m., the automatic weather station was managed by the Direccio´ General de Ports i Costes of the Catalan Regional Government with a sampling interval of 10 min. Using Deltebre as master station, each wind record in the period March 1988–March 1990 has been coarsely classified as lleÕant, garbı´ or mestral, according to the following directional rules: -lleÕant: wind direction comprised between 08 and 1358 -garbı: ´ wind direction comprised between 1358 and 2708 -mestral: wind direction comprised between 2708 and 3608. A wind event has been defined as an interval during which the wind records belong to the same
Fig. 4. Land topography in the vicinity of the Ebro delta and location of the Casablanca, Vandellos ´ and Deltebre meteo stations.
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directional class without loss of continuity. Breezes have been then filtered out by considering only the wind events whose duration exceeded 24 h Žin fact, it was assumed that only the relatively long-lasting wind events are able to have a remarkable influence on the local mean circulation. and computing the vector-averaged wind velocity for the period corresponding to each event Žusing log-corrected values for a z s 10 m height.. The same vector-averages have been then computed for the Casablanca and
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Vandellos ´ data sets. The roughness length parameters Ž z 0 . considered for the log-correction of each wind data set depend on the nature of the local surface. We have taken z 0 s 5.10y3 m for Casablanca, z 0 s 10y2 m for Vandellos ´ and z 0 s 3.10y2 m for Deltebre. In this way, 36 wind events have been identified according to the previous criteria, which are listed in Table 1. This table includes an estimate of the relative vorticity of the mean wind velocity field
Table 1 Wind events with duration exceeding 24 h, for the March 1988–March 1990 period Number
Initial date
Final date
Duration Žh.
Type
Module Žmrs.
Direction Ž8.
Vorticity Ž)10y7 .
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
11r04r88 25r04r88 05r05r88 09r06r88 22r07r88 04r11r88 10r11r88 06r12r88 30r01r89 06r02r89 07r02r89 14r02r89 20r03r89 26r03r89 29r03r89 13r04r89 16r04r89 22r04r89 25r04r89 27r04r89 09r05r89 23r05r89 07r06r89 12r06r89 03r07r89 05r07r89 23r07r89 31r08r89 07r10r89 09r10r89 16r10r89 23r10r89 26r10r89 13r11r89 01r03r90 03r03r90
13r04r88 27r04r88 06r05r88 10r06r88 24r07r88 06r11r88 12r11r88 08r12r88 31r01r89 07r02r89 08r02r89 15r02r89 22r03r89 29r03r89 31r03r89 14r04r89 17r04r89 24r04r89 26r04r89 29r04r89 11r05r89 26r05r89 09r06r89 14r06r89 04r07r89 06r07r89 24r07r89 02r09r89 09r10r89 10r10r89 18r10r89 24r10r89 27r10r89 16r11r89 02r03r90 05r03r90
65.33 33.67 24.33 49.16 39.33 44.50 44.50 42.83 31.33 30.50 25.67 25.17 40.50 54.33 39.50 32.83 28.67 59.33 25.00 35.33 28.00 92.33 30.17 30.00 29.83 41.83 27.17 30.00 27.83 24.50 48.17 23.83 29.00 68.50 26.50 39.17
garbı´ levante levante levante garbı´ levante levante mestral levante levante levante mestral mestral levante levante mestral mestral levante mestral mestral garbı´ levante levante levante garbı´ levante levante mestral mestral mestral levante levante levante levante mestral levante
0.92 4.90 3.34 2.79 2.15 4.01 5.45 9.26 3.05 3.82 3.15 8.59 9.37 5.19 6.84 9.35 6.28 3.48 5.82 9.82 3.82 7.32 3.76 1.99 3.96 5.60 3.16 6.96 10.35 6.37 4.43 3.86 4.16 4.32 4.44 3.88
185.77 45.41 83.64 78.85 181.86 52.30 71.59 328.51 75.96 67.06 70.13 318.95 313.66 67.73 71.23 304.95 302.05 75.36 322.97 314.55 123.69 69.29 69.59 80.16 131.93 70.59 75.92 318.73 320.96 319.91 67.72 79.71 81.01 79.46 318.66 68.72
y2.73 y4.87 y2.99 q1.71 y2.82 y5.46 y11.89 y4.96 y0.11 y7.3 y2.31 q9.66 q6.26 y16.21 y31.66 q23.20 q5.35 y1.94 q6.42 q37.40 y47.50 y28.70 y6.24 y0.19 y45.81 y14.95 y1.01 y27.14 y4.18 y23.31 y11.19 y4.24 y3.19 y0.01 q14.1 y1.56
Variables listed are: number of wind event, initial date, end date, duration Žin hours., type of wind, module Žmrs. and direction Ž8. of the vector-averaged wind velocity at Deltebre and vorticity estimate Žmrs 2 ..
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associated to each event computed with the assumption that the spatial variation of the wind velocity across the study area is linear, which is an acceptable hypothesis given the dimensions of the study area. Some interesting conclusions emerge from this analysis: Ø The most intense winds are the mestrals Žaverage velocity of the order of 4–11 mrs., whereas the garbins are the weakest Ž0–4 mrs.. The average velocities of the lleÕants fall within the 2–8 mrs interval. Ø The wind event duration is longest for the lleÕants and the garbins, whereas the persistence of the mestrals is always below 45 h with the criteria adopted here. Ø Seventy-two percent of the mean wind velocity fields have negative relative vorticity. In particular, all garbins and 86% of the lleÕants have associated mean wind velocity fields with negative relative vorticity. As for the mestrals, only 37% of them produce negative relative vorticity in the mean wind velocity field. Ø In general terms, moderate wind events Žaverage wind velocities of the order of 3–6 mrs in Deltebre. produce mean wind velocity fields with negative relative vorticity, whereas relative vorticity can be either positive or negative in events with average wind velocities under 3 mrs or over 6 mrs. Ø The relative vorticity of the mean wind velocity fields linked to wind events lasting more than 35 h is mainly negative. There is no such clear predominance in the shorter wind events. Although some of the previous results may partially be artifacts due to the criteria used to define wind events Že.g., the relatively low persistence of the mestrals ., they provide sufficient indication that the prevailing winds—and associated wind stress fields—acting on the Gulf of St. Jordi tend to introduce negative vorticity in the area. Section 4 studies how this influences the local circulation.
4. Numerical experiments and results Several numerical experiments have been designed to evaluate the effects of wind stress fields representing typical wind conditions on the back-
ground mean circulation in the Gulf of St. Jordi by using the model described in Section 2: -Case 1: no wind -Case 2: wind stress field associated to the lleÕant wind event starting on 29.03.89, 08:30 h Žwind velocity distribution with negative relative vorticity. -Case 3: wind stress field associated to the mestral wind event starting on 27.08.89 at 22:50 h Žwind velocity distribution with positive relative vorticity.. The domain considered for these modelling exercises is limited by the coastline, the 100 m isobath and two cross-shore transects off Cape Salou and Cape Tortosa. The computational grid used consists of 384 elements and 425 nodes Žsee Fig. 5., with a characteristic element size of 2 km = 2 km. The number of vertical degrees of freedom Žs number of basis functions. considered per node is 2. The wind stress Žt s . forcing has been evaluated using a conventional quadratic parameterization of the form:
t s s ra C D < u10 < u10
Ž 4.
where ra is the air density, C D is a constant drag coefficient and ra C D s 0.0018 kgrm3. The value of the wind velocity at 10 m over the sea surface Ž u10 . at each node has been derived from a linear interpolationrextrapolation fit on the basis of the Casablanca, Vandellos ´ and Deltebre wind data. The wind stress distributions derived for cases 2 and 3 are depicted in Fig. 6. A linear relationship between the bottom stress Žt b . and the near-bottom velocity namely:
t xb s g b Ž u b y Õ b . t yb s g b Ž u b q Õ b . Žwith g b being the bottom friction coefficient and u b , Õ b the horizontal components of the near bottom velocity. has been considered following the assumption that the bottom boundary layer is governed by the Ekman dynamics. Since the main goal in this paper is to better understand the action of wind forcing, all simulations have been performed with a closed Ebro river mouth and assuming an homogeneous density field Ž r s 1025 kgrm3 .. As regards to the model ‘free’ param-
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Fig. 5. Ža. Bathymetry of the study area. Žb. Numerical grid.
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eters, homogeneous horizontal and vertical eddy viscosity coefficients Ž K H s 50 m2rs and K z s 10y2 m2rs. have been considered together with values for the bottom friction coefficients Žg b . ranging from 0.001 to 10 kgrm2 s, which give a reasonable approximate representation of the physics. An error radius eps s 0.01 mrs has been fixed for the convergence criterion. The values selected for the eddy viscosity and bottom friction coefficients fall within the ranges recommended by the oceanographic literature. A value of g b has been selected for each simulation such that the surface stress exerted by the wind and the bottom stress are of the same order of magnitude, which is known to be the case in shallow water domains. The availability of current measurements obtained at the Casablanca oil rig near the southestward corner of the study domain Žsee e.g., Font, 1990. has been taken into account for the definition of the boundary conditions. For the first vertical degree of freedom, which corresponds to the vertically-averaged velocity, an along-isobath flow of 10 cmrs on the outer boundary has been prescribed Žthis is a means to reproduce the action of the slope jet existing off the shelf edge.. A uniform southward flow of 10 cmrs on the southern boundary and a no-slip condition at the coastline have also been selected as reasonable boundary prescriptions. On the northern boundary, an homogeneous Neumann Žor free-flow. condition has been imposed. For the second vertical degree of freedom, which produces the vertical structure in the current velocity profiles, homogeneous
Neumann conditions have been specified for the northern, outer and southern boundaries, together with an homogeneous Dirichlet Žno-slip. boundary condition for the coastline. Given the iterative penalty approach used in our model for the continuity equation Žgeneralized Uzawa algorithm., which allows iterative explicit elimination of the pressure as a function of the velocity and the penalty parameter, no boundary condition needs to be specified for the pressure. Fig. 7 shows the model solutions for case 1 Žno wind forcing.. The vertically-integrated circulation is anticyclonic, just as the surface and the bottom current velocity fields are. The differences between the surface, the bottom and the vertically-averaged fields are negligible due to the fact that there is no agent driving vertical velocity gradients. The topography of the sea surface roughly parallels the streamlines, which suggests that the mean circulation is basically in geostrophic balance. The numerical solutions for case 2 Ž lleÕant wind introducing negative vorticity in the study area. are reported in Fig. 8. It can be seen that the verticallyintegrated circulation is again anticyclonic and that it is strengthened by the wind Žthe maximum velocity values exceed those of case 1 by about 6 cmrs.. The pattern of the surface current velocity field is also anticyclonic but not that of the bottom flow. Only near the coast of the Ebro delta that the bottom current velocities reach relevant values. The results of case 3 Ž mestral wind introducing positive vorticity. are very interesting Žsee Fig. 9..
Fig. 6. Ža. Wind stress forcing for case 2. Žb. Wind stress forcing for case 3. Scales are given by the length of the longest vector in figures Ž0.147 N Wrm2 in figure a, 0.257 N Wrm2 in figure b.. Fig. 7. Model solutions for case 1 Ž K H s 50 m2rs, K z s 10y2 m2 rs and g b s 0.001 kgrm2 s.. Ža. Vertically-integrated current velocity Žmrs.. Žb. Surface current velocity Žmrs.. Žc. Bottom current velocity Žmrs.. Žd. Sea surface elevation Žin meters relative to arbitrary zero level.. Scales in figures a, b and c are given by the length of the longest vectors Ž0.109 mrs in all figures.. Fig. 8. Model solutions for case 2 Ž K H s 50 m2 rs, K z s 10y2 m2 rs and g b s 1 kgrm2 s.. Ža. Vertically-integrated current velocity Žmrs.. Žb. Surface current velocity Žmrs.. Žc. Bottom current velocity Žmrs.. Žd. Sea surface elevation Žin meters relative to arbitrary zero level.. Scales in figures a, b and c are given by the length of the longest vectors Ž0.163 mrs in figure a, 0.222 mrs in figure b and 0.183 mrs in figure c.. Fig. 9. Model solutions for case 3 Ž K H s 50 m2rs, K z s 10y2 m2 rs and g b s 10 kgrm2 s.. Ža. Vertically-integrated current velocity Žmrs.. Žb. Surface current velocity Žmrs.. Žc. Bottom current velocity Žmrs.. Žd. Sea surface elevation Žin meters relative to arbitrary zero level.. Scales in figures a, b and c are given by the length of the longest vectors Ž0.243 mrs in figure a, 0.387 mrs in figure b and 0.183 mrs in figure c..
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Fig. 6.
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Fig. 7.
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Fig. 7 Žcontinued..
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Fig. 8.
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Fig. 8 Žcontinued..
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Fig. 9.
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Fig. 9 Žcontinued..
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The background anticyclonic pattern of the vertically-averaged circulation has been totally offset by the wind forcing. The surface flow is essentially along isobaths with a predominant southward component, whereas the bottom circulation is much weaker and complex. Again the bottom current velocities are highest in the vicinity of the Ebro delta. The modelled sea surface elevation field reveals water-piling near the Ebro delta coast, showing the dominance of the momentum induced by wind in determining the surface elevation.
5. Discussion The previous modelling exercises have been designed to gain insight into the effect of local winds on the mean circulation in the Gulf of St. Jordi area. Our results support the hypothesis of Salat et al. Ž1978. and Ballester and Castellvı´ Ž1980. in the sense that the obtained background mean circulation is anticyclonic Žsee Fig. 7.. This circulation pattern can be regarded as a by-product to vorticity adjustment of the alongslope jet associated to the Catalan front, which is forced to acquire positive relative Žand potential. vorticity south of Cape Salou due to slope curvature related to shelf width increase. From the same point of view, the introduction of positive Žnegative. vorticity via the wind stress forcing applied to the sea surface has to result in a weakening Žstrengthening. of the anticyclonic circulation pattern. The obtained model results are consistent with this behaviour, which means that the final circulation pattern will depend on the relative importance of the two forcing mechanisms Žin fact of their respective induced vorticity.. Furthermore, the previous numerical results point out that there might be important differences between the surface and the near-bed flows. ŽNote: the obtained ‘bottom’ current velocities are, strictly speaking, flow velocities derived for the uppermost level of a bottom boundary layer. See Espino, 1994 for more details.. The vertical structure of the model solutions, obtained here with just 2 vertical degrees of freedom, is probably valid only in a qualitative sense, so runs with higher vertical resolution would be needed to achieve solutions suitable for a realistic computation of stresses acting on bottom sediments,
which is beyond the present goals. On the other hand, neither the winds events in the area nor the boundary conditions are really steady, so time-dependent simulations of the wind-induced flow Žin which the steady circulation is reached after model spinning-up. should be performed to compare with detailed field observations when they are available. Moreover, further runs for stratification conditions and with vertically-varying eddy viscosities should be undertaken to assess the different effect of the wind action when the vertical density gradients are important. Finally, additional simulations with the Ebro river mouth open should be carried out to study the details of the circulation in the area influenced by the river discharge.
6. Conclusions A quasi-3D finite element code of the shallowwater equations has been used to investigate the effect of wind forcing on the mesoscale circulation in the Gulf of St. Jordi area. The obtained numerical results suggest that the mean flow is anticyclonic under no-wind conditions, which is in agreement with the statements by Salat et al. Ž1978. and Ballester and Castellvı´ Ž1980.. Nevertheless, the characteristic local wind stress fields may strengthen or weaken the anticyclonic circulation depending on the sign of their relative vorticity. Furthermore, they introduce vertical structure in the current velocity profiles. Given the fact that over 70% of the local wind events recorded during a 2-yr period and exceeding 24 h in duration have associated wind velocity distributions with negative relative vorticity, we conclude that the net effect of local winds is to reinforce the clockwise mesoscale circulation.
Acknowledgements The authors wish to thank Repsol Exploracion, ´ Hifrensa and the Direccio´ General de Ports i Costes of the Generalitat de Catalunya for making available their meteo data sets to us. This study has been partially funded by the Spanish Comision ´ Interministerial de Ciencia y Tecnologıa ´ Žgrant no. AMB92-
M. Espino et al.r Journal of Marine Systems 16 (1998) 235–251
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