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Numerical modeling of three-dimensional stratified tidal flow over Camarinal Sill, Strait of Gibraltar

2011; American Geophysical Union; Volume: 116; Issue: C12 Linguagem: Inglês

10.1029/2011jc007093

2156-2202

José Carlos Sánchez-Garrido, Gianmaria Sannino, Luca Liberti, Jesús García‐Lafuente, Lawrence J. Pratt,

Ocean Waves and Remote Sensing

Journal of Geophysical Research: OceansVolume 116, Issue C12 Free Access Numerical modeling of three-dimensional stratified tidal flow over Camarinal Sill, Strait of Gibraltar J. C. Sánchez-Garrido, J. C. Sánchez-Garrido [email protected] Grupo de Oceanografía Física, Departamento Física Aplicada II, University of Malaga, Malaga, SpainSearch for more papers by this authorG. Sannino, G. Sannino Ocean Modeling Unit, Ente per le Nuove Tecnologie, l'Energia e l'Ambiente, Rome, ItalySearch for more papers by this authorL. Liberti, L. Liberti Istituto Superiore per la Protezione e la Ricerca Ambientale, Rome, ItalySearch for more papers by this authorJ. García Lafuente, J. García Lafuente Grupo de Oceanografía Física, Departamento Física Aplicada II, University of Malaga, Malaga, SpainSearch for more papers by this authorL. Pratt, L. Pratt Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USASearch for more papers by this author J. C. Sánchez-Garrido, J. C. Sánchez-Garrido [email protected] Grupo de Oceanografía Física, Departamento Física Aplicada II, University of Malaga, Malaga, SpainSearch for more papers by this authorG. Sannino, G. Sannino Ocean Modeling Unit, Ente per le Nuove Tecnologie, l'Energia e l'Ambiente, Rome, ItalySearch for more papers by this authorL. Liberti, L. Liberti Istituto Superiore per la Protezione e la Ricerca Ambientale, Rome, ItalySearch for more papers by this authorJ. García Lafuente, J. García Lafuente Grupo de Oceanografía Física, Departamento Física Aplicada II, University of Malaga, Malaga, SpainSearch for more papers by this authorL. Pratt, L. Pratt Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USASearch for more papers by this author First published: 17 December 2011 https://doi.org/10.1029/2011JC007093Citations: 54AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract [1] The baroclinic response to barotropic tidal forcing in the Camarinal Sill area, within the Strait of Gibraltar, is investigated with a three-dimensional, fully nonlinear, nonhydrostatic numerical model. The aim of numerical efforts was the assessment of three-dimensional effects, which are potentially significant in the area because of rather irregular bottom topography, variable background stratification, and complex structure of barotropic tides. Model results reveal a complex baroclinic response under relatively moderate flood tidal currents, which includes the formation of internal hydraulic jumps upstream of the sill, internal cross waves close to the channel walls, and a plunging pycnocline at the lee side of the sill crest. These structures exhibit significant cross-channel spatial dependence and may appear to be aligned together across the channel. This fact makes their identification difficult from the surface pattern captured by remote sensing images. Under strong barotropic forcing (spring tides) the upstream hydraulic jumps are shifted to the lee side of Camarinal Sill, where a single internal hydraulic jump is formed. Significant first- and second-mode hydraulic jumps are also generated near smaller secondary sills in Tangier basin, thus extending the occurrence of intense water mixing and energy dissipation to other zones of the strait. Key Points Three-dimensional baroclinic response to tidal forcing in the Camarinal Sill Different baroclinic response under moderate to strong tidal forcing Generation of multiple internal hydraulic jumps in secondary sills 1. Introduction [2] The Strait of Gibraltar is a prominent spot of the World Ocean connecting the Mediterranean Sea and the Atlantic Ocean through a narrow channel (minimum width of 14 km) characterized by an irregular bottom topography that includes a system of submarine sills (see Figures 1 and 2). Buoyancy losses over the Mediterranean Sea lead to a two-way (or baroclinic) exchange in the strait [Bryden and Kinder, 1991], in which approximately 0.8 Sv (1 Sv = 106 m3 s−1) of salty and dense Mediterranean Water (MW) flows toward the Atlantic in the bottom layer, and a slightly higher volume rate of Atlantic Water (AW), about 0.85 Sv, enters the Mediterranean in the surface layer to compensate for the net evaporative losses over the basin. Figure 1Open in figure viewerPowerPoint (a) Synthetic aperture radar (SAR) image of the Strait of Gibraltar showing the developing internal waves in Camarinal Sill (CS) and the propagation of a previously generated packet of large-amplitude internal waves (LAIWs) in the Alboran Sea (date of reception: 28 November 2005, 22:09; Envisat ASAR data were provided by the European Space Agency). (b) Detail of CS area. (c) Barotropic current velocity (depth-averaged velocity) prediction over CS (5°44.64′W, 36°54.78′N) at the time of the image. Figure 2Open in figure viewerPowerPoint (a) Computational grid used in the numerical experiment (for the sake of clarity, only 2% of the grid points are shown). The locations of Camarinal Sill and Tarifa Narrows (TN) are indicated. (b) Bottom topography of the Strait of Gibraltar (isobaths are shown every 100 m). (c) Detailed bottom topography map in the area of the Camarinal Sill (CS), Tangier Basin (TB), Espartel Sill (ES), and Majuan Bank (MB). Dashed line indicates the cross-strait section over CS. [3] The exchange flow is far from being steady. It fluctuates at very different timescales exhibiting tidal, meteorological, seasonal, and interannual [see, e.g., Candela et al., 1989; García Lafuente et al., 2007]. Among all these scales the tidal band is by far the most energetic, with tidal flow exceeding 5 Sv [García Lafuente et al., 2000] and masking the underlying mean baroclinic exchange during important part of the tidal cycle. Furthermore, interaction of flood tidal currents (tidal flow toward the Atlantic) with Camarinal Sill (CS; see Figures 1 and 2), the main sill of Gibraltar, leads to the periodic generation of large-amplitude internal waves (LAIWs) with amplitude exceeding 100 m [Ziegenbein, 1969; Richez, 1994]. After their generation LAIWs propagate eastward carrying a large amount of baroclinic energy that is eventually transferred to turbulence and mixing especially in shallow areas where wave breaking occurs. Consequently these waves play a relevant role in the oceanography of the Strait of Gibraltar and Alboran Sea ecosystems. [4] Observational evidence [Farmer and Armi, 1988; Armi and Farmer, 1988] and numerical results [Brandt et al., 1996; Vázquez et al., 2006] show that LAIWs are the result of the nonlinear evolution of a baroclinic bore (or moving hydraulic jump) generated at CS. Under critical flow conditions the baroclinic bore is trapped in CS until nearly high tide when the barotropic tidal flow weakens. At this time the bore progresses eastward through the strait to the Alboran Sea while transforming into a series of internal solitary waves by nonlinear and dispersive (nonhydrostatic) effects. This process of wave evolution in a dispersive media is well known and has been documented in many works dealing with weakly nonlinear wave theories [Whitham, 1974]. [5] Although the overall generation mechanism of LAIWs in Gibraltar is well understood, there are some important aspects not yet addressed in numerical studies. [6] 1. Numerical models considered laterally averaged (cross-strait) governing equations, thus missing transversal effects associated with across-channel variations of barotropic forcing, background stratification, and bottom topography. These effects are assumed to play a minor role in narrow channels of the World Ocean such as the Strait of Messina in the central Mediterranean [Brandt et al., 1997], or a number of stratified fjords [Armi and Farmer, 2002] where tidally generated LAIWs also occur. Transversal effects are however likely to be significant in the Strait of Gibraltar, where the internal Rossby radius of deformation is comparable to the strait width, originating a nonnegligible cross-strait variation of isopycnal depth (increasing southward), and both surface (barotropic) tides and bottom topography have a complex structure with important across-channel variations [García Lafuente et al., 1990; Candela et al., 1990]. In fact, available synthetic aperture radar (SAR) images of CS area like the one presented in Figure 1 sometimes suggest the three-dimensionality of the baroclinic wavefield. The image was taken at the time when barotropic (depth-averaged) tidal velocity nearly reached its maximum toward the Atlantic (Figure 1c), when presumably the baroclinic bore has not yet been released. Instead of the expected single wavefront, two fronts can be observed in CS area. The front located downstream (to the west) appears in the image almost as a straight line extending all across the strait, but the one located upstream is confined to the southern half of the section. [7] 2. The previously mentioned models were forced only by the M2 tidal constituent. Although this is the most important one, other constituents account for a significant portion of the barotropic energy (S2, O1, K1), and determine clear modulation of the strength of the LAIW packets as observed by Sánchez-Garrido et al. [2008]. In fact, M2 barotropic transport is estimated in 3 Sv [García Lafuente et al., 2000], whereas during spring tides tidal transport can be almost twice that amount. Important differences in the baroclinic response are then expected throughout the neap-spring cycle. [8] This paper presents a numerical investigation on the generation of LAIWs in the Strait of Gibraltar with emphasis on three-dimensional aspects of the generated wavefield. We use a high-resolution, three-dimensional, fully nonlinear and nonhydrostatic model which reproduces the mean two-way exchange of the strait and it is forced by a realistic barotropic tide simulating the neap-spring cycle. Model features and initialization are described in section 2, model results for tidal cycles of increasing strength are discussed in section 3, and a summary and conclusions are presented in section 4. 2. Model Description and Initialization [9] The Massachusetts Institute of Technology general circulation model (MITgcm) has been used for this work. The MITgcm solves the fully nonlinear, nonhydrostatic Navier–Stokes equations under the Boussinesq approximation for an incompressible fluid with a spatial finite-volume discretization on a curvilinear computational grid. The model formulation, which includes implicit free surface and partial step topography, is described in detail by Marshall et al. [1997a, 1997b] and its source code and documentation are available at the MITgcm Group Web site (http://mitgcm.org/sealion/online_documents/node2.html). [10] The model domain extends from 6.3°W to 4.78°W and was discretized by a nonuniform curvilinear orthogonal grid of 1440 × 210 points (Figure 2a). Spatial resolution along the longitudinal axis of the strait, Δx, (across the strait axis, Δy,) ranges between 46 and 63 m (175–220 m) in the CS area and mesh size is always less than 70 m (340 m) in the middle of the strait between Espartel Sill (the westernmost sill of Gibraltar, hereinafter ES) and CS, and less than 70 m (200 m) between CS and Tarifa Narrows, the narrowest section of the strait. To adequately resolve the pycnocline the model has 53 vertical z levels with a thickness of 7.5 m in the upper 300 m gradually increasing to a maximum of 105 m for the remaining 13 bottom levels. [11] Model topography (Figures 2b and 2c) has been obtained by merging the ETOPO2 bathymetry [NOAA, 2006] with the very high resolution bathymetry chart of [Sanz et al., 1991]. No-slip conditions were imposed at the bottom and lateral solid boundaries. [12] The selected tracer advection scheme is a third-order direct space-time flux limited scheme [Hundsdorfer et al., 1995], which is unconditionally stable and does not require additional diffusion. Following the numerical experiments conducted by Vlasenko et al. [2009] to investigate the 3-D evolution of LAIWs in the Strait of Gibraltar, the turbulent closure parametrization for vertical viscosity and diffusivity proposed by Pacanowski and Philander [1981] was used, where Ri = N2(z)/(uz2 + vz2) is the Richardson number, νb = 1.5 × 10−4 m2 s−1, κb = 1 × 10−7 m2 s−1 are background values, and ν0 = 1.5 × 10−2 m2 s−1, α = 5 and n = 1 are adjustable parameters. Horizontal diffusivity coefficient is κh = 1 × 10−2 m2 s−1, whereas variable horizontal viscosity follows the parameterization of Leith [1968]. [13] Initial conditions for temperature and salinity were derived from the climatologic Medar-MedAtlas Database [MEDAR Group, 2002] for the month of April. The mean two-way exchange is obtained by laterally forcing the model through the imposition of the mean baroclinic velocities and tracers extracted from the intermediate resolution model developed by Sannino et al. [2009] to study the water exchange through the strait and its hydraulic behavior. Therefore, the present model can be viewed as a nested model of the one described by Sannino et al. [2009]. The model initially ran for 11 days without tidal forcing in order to reach a quasi-steady two-way exchange. Subsequently, tidal forcing was introduced by prescribing at the open boundaries the main diurnal (O1, K1) and semidiurnal (M2, S2) barotropic tidal currents, extracted from the intermediate resolution model. The simulation was then extended for 8 more days in order to attain a stable time periodic solution. Finally, the actual numerical experiment was carried out by running the model for a full tropical month. Wave reflections at the open boundaries are minimized by adding a Newtonian relaxation term to the tracer equations over the boundary area and adopting the flow relaxation scheme proposed by Carter and Merrifield [2007] for the velocity field. [14] The most apparent difference between the intermediate and the nested model results concerns diapycnal mixing, which is better simulated in the latter because of its higher spatial resolution and nonhydrostatic formulation (the impact of a more realistic representation of water mixing on the exchange flow and hydraulics of the strait will be the subject of a future work). Mean and barotropic tidal currents obtained in the present numerical experiment are similar to the ones obtained in the intermediate model, which in turn were in good agreement with historical observations collected in the strait [Sánchez-Román et al., 2009]. Example of the good performance of the model is provided in Figure 3, which shows semidiurnal tidal amplitudes and phases of modeled barotropic tidal currents across CS along with depth-averaged values of harmonic tidal analysis presented by Candela et al. [1990]. Amplitudes and phases increase toward the south both in numerical outputs and observations, although M2 amplitudes are somewhat higher in the model results. Much better agreement is found with acoustic Doppler current profiler (ADCP) observations encompassing nearly the whole water column over CS (black dots; see data set description by García Lafuente et al. [2007]), suggesting that the lack of information in the upper layer in the data presented by Candela et al. [1990] is the source of discrepancy. Figure 3Open in figure viewerPowerPoint (a) Semidiurnal (solid line, M2; dashed line, S2) tidal amplitudes of barotropic currents in the CS cross section (dashed line in Figure 2c). Gray symbols correspond to observations reported by Candela et al. [1990], and black symbols correspond to acoustic Doppler current profiler (ADCP) observations collected within the INGRES projects (see text for details). Dots (circles) indicate the amplitude of tidal constituent M2 (S2). (b) Same as Figure 3a for tidal phases. 3. Models Results [15] Model results reveal that nonlinear internal waves propagating as internal bores and solitary waves develop for a maximum barotropic tidal transport Trmax > 3.0 Sv, approximately the tidal transport associated with the M2 tidal constituent. Our analysis focuses on this upper range of tidal forcing, which has been split into two different cases considering qualitatively different baroclinic response over CS. Moderate Tidal Forcing 3.1.1. Two-Dimensional Surface Pattern Produced by the Baroclinic Field [16] We start our analysis by examining the less energetic case looking at a tidal cycle characterized by Trmax = 3.65 Sv, which can be classified as a moderate tidal forcing cycle. An effective procedure to trace the evolution of the internal or baroclinic field consists of monitoring the spatial gradient of surface velocity. The superposition of baroclinic and barotropic currents gives rise to areas of strong horizontal convergence/divergence of the flow characterized by short-scale surface roughness which can be captured by SARs [Alpers, 1985]. This allows for the identification of baroclinic structures such as internal hydraulic jumps or free propagating internal waves through the observation of the ocean surface. [17] Figure 4 shows the surface zonal velocity gradient evolution in the sills area of the strait during the flood tide. Figure 4a corresponds to the beginning of the flood tide, when barotropic tidal flow over CS is null. In spite of this, two noticeable surface signatures appear in shallow areas nearby CS close to the channel walls. The one in the north is especially significant, resembling a wavefront that extends over great distance roughly along z = 50 m isobath. Minor surface signatures can be also observed in the proximity of Majuan Bank (∼6°57′W, 36°55′N, Figure 2), the seamount immediately north ES. The origin of these local features is analyzed in detail later. Figure 4Open in figure viewerPowerPoint (a–f) Time evolution of surface zonal velocity gradient (× 10−3 s−1) during the flood tide. Solid lines represent bottom depth contours (isobaths 50, 100, 150 m, etc.). The time origin is taken at the beginning of the flood tide. Dashed lines S1, S2, and S3 in Figure 4a indicate cross sections mentioned in the text. (g) Barotropic tidal transport during the time series. [18] The surface pattern looks more complex when the barotropic flow increases (Figure 4b). In addition to some residual features in shallow areas to the north, two structures emerge in the centre of the channel, which at the moment of maximum tidal flow evolve into a pair of wavefronts (Figure 4c). One of them appears next to the θ = 5°45′W meridian and encompasses almost the entire channel width, whereas the second, located further upstream, leaves a clearer trace at the south of the strait. The pattern clearly resembles the SAR image shown in Figure 1. [19] The subsequent evolution corresponds to the relaxation of the tidal forcing. Weakening of the barotropic tidal flow triggers the release of the longer wavefront that propagates eastward under the effect of wave dispersion, as shown by the appearance of a dispersive wave tail (Figures 4d–4f). The front generated upstream however remains almost stationary and as a result eventually collides with the wave propagating behind (Figure 4e). Despite this complex evolution the wavefield finally entering Tarifa Narrows is a rather regular wave packet of LAIWs (Figure 4f). [20] The last remark about Figure 4 concerns the small-scale structures generated west of CS, immediately downstream of the main wavefront (Figures 4b and 4c). They arise only at the time of maximum tidal flow, and vanish as soon as the flow slackens. Another interesting feature is the slanted front moving together with the main wave train close to the south channel wall (Figures 4d–4f). 3.1.2. Baroclinic Wavefield Over CS [21] In this section we analyze in detail the baroclinic field generated over CS. Figure 5 provides a first insight into the internal wavefield by depicting the evolution of the isopycnal σθ = 27.5 (approximately coincident with the pycnocline) along zonal sections S2 and S3 (Figure 4a). Section S3 covers the south central part of the channel, where two prominent surface features appear as flood current increases (Figure 4b), i.e., the southern portion of the longer front over the sill crest, and the shorter front generated further upstream. Figure 5a reveals that these two surface signatures are caused by a double plunge of isopycnals, the first over the western flank of the sill (feature A; ∼5°45′W) and the second over the lee side of a 50 m bump situated at the eastern edge of the sill crest (feature B; ∼5°43′W). Figure 5Open in figure viewerPowerPoint (a–d) Time evolution of σθ = 27.5 isopycnal along cross sections S2 (black) and S3 (gray) shown in Figure 4a. Features A, B, C, and D indicate baroclinic features mentioned in the text. The bottom axis indicates distance (km) from the center of Camarinal Sill, whereas the axis on the top indicates minutes to the west of the meridian 5°W. (e) Barotropic tidal transport during the time series. [22] Figure 5b shows a more complex baroclinic structure, with the formation of two upstream internal hydraulic jumps. One appears in the northern section S2 (feature C; Figure 5b) aligned along θ = 5°45′W with the southern plunging pycnocline formed at the lee side of the sill. These two baroclininc structures are merged together in a single feature that forms the westernmost surface signature presented in Figure 4c and the SAR image of Figure 1. The second hydraulic jump is formed at the south section S3 over the eastern edge of the sill (feature D; Figure 5b). Weakening of the tidal flux leads to the release of both the southern plunging pycnocline and the northern upstream hydraulic jump, which gradually disintegrates into a series of solitary-like internal waves. The hydraulic jump at the southeast edge of the sill crest also progresses eastward with slack currents, but much slower than the waves propagating behind, and is eventually absorbed by them (Figures 5c and 5d). [23] Let us now analyze in more detail the fronts formed in the proximity of the channel walls. They can be distinguished throughout the whole flood period, even when the net tidal flux is null. Barotropic tidal velocities can be locally strong in coastal areas, even though the total tidal flow is weak. This can be seen in Figure 6b, which shows the barotropic velocity at the beginning of the flood tide. Velocities are small in the centre of the channel, but they are relatively large near the lateral boundaries of the channel, where the circulation is characterized by short-scale eddies. The stratification is generally weak in these shallow areas, although occasionally, a layer of relatively dense water can be present, as is shown in Figure 7 where a tongue of interface water (salinity ∼37, mixture of Atlantic and Mediterranean waters) of 15–20 m thick intrudes onto the northern shelf beneath the Atlantic surface water (salinity ∼36–36.5). If the stratified flow is simplified to a two-layer system, relatively large current velocities, weak stratification, and thin layers result in a locally supercritical flow in coastal areas (see shaded contours in Figures 6c and 6f). The assessment of the flow criticality is made in terms of the composite Froude number G2 for a two-layer flow [Armi, 1986]: where Fn = (un2 + vn2)/(g′Dn); un, vn and Dn are horizontal components of velocity and thickness of layer n, and g′ the reduced gravity. The interface in the two-layer approximation of the stratified flow is taken as the depth of maximum vertical density gradient, whereas un, ρn are obtained by averaging velocity and density in layer n. Figure 6Open in figure viewerPowerPoint (a) Close up of the surface velocity gradient (× 10−3 s−1) in CS area at t = 00:00 (see Figure 4a). Arrows indicate the position of cross waves. (b) Barotropic current velocity field at t = 00:00. (c) Criticality of the flow at t = 00:00. Shaded (unshaded) areas indicate local internal supercritical (subcritical) flow. (d–f) Same as Figures 6a–6c at t = 04:40. Transversal lines in Figure 6f indicate locations of hydraulic transitions according to the generalized composite internal Froude number for a two-layer flow (Gw2 = 1). Figure 7Open in figure viewerPowerPoint Salinity field along cross section S4 (see Figure 6a) at t = 00:00. [24] Therefore, the lateral wavefronts can be thought of as oblique internal hydraulic jumps or stationary cross waves that can only exist where the flow is "locally supercritical". Here an analogy can be drawn with supercritical open-channel flows where cross waves are formed close to the lateral boundaries as a result of the turning effect produced by curved walls [Chow, 1959]. Although near the coast the flow remains supercritical almost permanently, cross waves only become apparent when the stratification is significant; that is to say, when the tongue of dense water intrudes onto shallow areas. They mainly appear in the northern part of the channel during the early stage of the tidal cycle because the pycnocline is shallow there (because of the Earth's rotation). It is during the ebb tide that cross waves are clear near the south coast (Figures 4d–4f), when the dense layer has been able to flood the southern shelf as a result of the overall rising of isopycnals produced by flood tidal currents (see Figure 8). Figure 8Open in figure viewerPowerPoint (a–e) Time evolution of the potential density field along the central axis of the strait (cross section S1 in Figure 4) during moderate tidal cycle. Isopycnals σθ = 26.80,27.05,…,28.80,29.02 are shown. Arrows indicate local current velocity. Shaded contours are areas where Ri < 1/4, which are prone to the development of shear instabilities and occurrence of water mixing. Dashed thick lines indicate the evolution of two second-mode baroclinic bores. Feature SS in Figure 8e indicates the location of the secondary sill mentioned in the text. (f) Barotropic tidal transport during the time series. [25] The map of local G2 deserves further discussion (Figure 6c). The flow is locally supercritical in marginal areas, but also downstream the western flank of the sill crest, where the Mediterranean undercurrent accelerates downslope (see also Figure 8a). This configuration is similar to a crest-controlled flow, where a subcritical-to-supercritical hydraulic transition occurs just over the sill crest; the flow then turns to supercritical along the western slope of the obstacle, and recovers the subcritical state in Tangier Basin (the basin separating Camarinal and Espartel sills, Figures 2b and 2c, hereinafter TB) through an internal hydraulic jump. Increase of tidal flow originates a control section well upstream of the sill at the eastern proximity of the obstacle (∼5°40′W, see shaded contour across the channel in Figure 6f). Moving downstream the flow then switches again to subcritical upstream of the sill, according to the subcritical patch encompassing the central northern part of the channel at ∼5°44′W. This supercritical-to-subcritical hydraulic transition corresponds to the abrupt drop in isopycnal height "C" shown in Figure 5b, supporting the idea that the feature in question is a hydraulic jump. Further downstream the flow becomes supercritical close to the sill crest, to finally turn to subcritical in TB. [26] The above hydraulic analysis is local and does not speak to the question of overall control of the exchange flow. The value of G2 at any point may give information about localized disturbances (as shown in the Appendix A), G2 ≥ 1 is a necessary condition for the existence of local cross waves, provided that the upper and lower layer velocity are more or less parallel. On the other hand the hydraulic of the flow as a whole depends on its properties over the entire cross section in question and involves wave with a cross-strait modal structure. The judgment of the flow criticality as a whole is based on the generalized composite Froude number Gw2, considering transversal variations of layer thickness and velocity [Pratt, 2008; Sannino et al., 2009] where wI is the channel width at the interface depth, and ∫Y denotes across-channel integral. [27] The locations of sections of critical flow with respect to Gw2 are indicated by solid lines in Figure 6f. They indicate subcritical flow Gw2 < 1 to the east and west of the general area surrounding CS and including the upstream hydraulic jump. As one moves from west to east through this region, several transitions between subcritical and supercritical flow occur, possibly because of the irregular nature of the flow caused by numerous, short-wave disturbances generated by topography. The main conclusion that one should draw from this is that the exchange flow is hydraulically controlled, though it is difficult to interpret this in terms of classical hydraulic theory. 3.1.3. Baroclinic Wavefield Over TB and ES [28] Although prominent surface signatures related to the baroclinic field are mainly found in the CS area (Figure 4), the internal dynamics are also remarkable in TB and ES. The weak surface trace left by internal hydraulic jumps in these areas is attributable to the great depth of the pycnocline (smaller current velocity associated to internal disturbances in the thick upper layer than in the bottom layer) downstream CS, especially over ES, as is shown below. [29] Figure 8 shows isopycnals and velocity currents evolution along section S1 (Figure 4). Even at slack tide two additi