Structure of unsteady overflow in the Słupsk Furrow of the Baltic Sea

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011jc007284, 2012 Structure of unsteady overflow in the Słupsk Furrow of the Baltic Sea Victor Zhurbas, 1,2 Jüri Elken, 2 Vadim Paka, 3 Jan Piechura, 4 Germo Väli, 2 Irina Chubarenko, 3 Nikolay Golenko, 3 and Sergey Shchuka 1 Received 10 May 2011; revised 23 February 2012; accepted 4 March 2012; published 17 April [1] A data set of closely spaced CTD profiling performed aboard Russian and Polish research vessels during and numerical modeling are applied to study the variability in the asymmetric transverse structure of salinity/density in the Słupsk Furrow (SF) overflow of the Baltic Sea. The numerical simulations show that, on the one hand, the overflow may be dynamically treated within the SF as a subcritical, eddy-producing gravity current in a wide channel, and on the other, at the sill displays some features peculiar to frictionally controlled rotating flows. Comparison between the field measurements and the simulation results indicates that the variability of the cross-channel density structure is caused mainly by meandering of the gravity current and mesoscale eddies mostly above-halocline cyclones and intrahalocline anticyclones. The meanders and eddies are found to be strongly affected by the bottom topography and wind-forcing. Citation: Zhurbas, V., J. Elken, V. Paka, J. Piechura, G. Väli, I. Chubarenko, N. Golenko, and S. Shchuka (2012), Structure of unsteady overflow in the Słupsk Furrow of the Baltic Sea, J. Geophys. Res., 117,, doi: /2011jc Introduction [2] Bottom gravity currents passing through channel-like topographical constrictions are known to be an important link to the general oceanic circulation [Umlauf and Arneborg, 2009a]. Submarine channels are identified as hot spots of gravity current entrainment and play a key role in the formation of deep water masses [Baringer and Price, 1997; Peters et al., 2005; Mauritzen et al., 2005; Umlauf et al., 2010]. Well-known examples of channelized gravity flows are the Mediterranean outflow [Johnson et al., 1994; Baringer and Price, 1997], the Faroe Bank Channel overflow [Borenäs and Lundberg, 1988; Johnson and Sanford, 1992], and the Red Sea outflow [Peters et al., 2005]. Gravity flows are quite often considered in a steady approach, either due to the limited number of observations and/or the assumptions often made in the rotating hydraulic theory. [3] A striking feature, common to all the above mentioned channelized gravity flows, is the strong asymmetry of the transverse density and velocity structure. The density interface slopes downward in the cross-channel direction to the left of the flow (in the Northern Hemisphere), which is a 1 Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia. 2 Marine Systems Institute, Tallinn University of Technology, Tallinn, Estonia. 3 Atlantic Branch, Shirshov Institute of Oceanology, Russian Academy of Sciences, Kaliningrad, Russia. 4 Institute of Oceanology, Polish Academy of Sciences, Sopot, Poland. Copyright 2012 by the American Geophysical Union /12/2011JC manifestation of geostrophic balance. There is a pronounced spreading and pinching of the pycnocline on the right-hand and left-hand flanks, respectively, so that the interface looks wedge-shaped [e.g., Petrén and Walin, 1976; Borenäs and Lundberg, 1988; Johnson and Sanford, 1992]. In addition, it is often observed that a pool of the densest water lies on the left-hand flank [Paka, 1996; Paka et al., 1998] and downward-bending of near-bottom isopycnals appears on the right-hand flank. Moreover, some observations demonstrate ultimate bending with isopycnals becoming nearly vertical, so that vertical homogeneity and a purely horizontal density gradient are established on the right-hand flank, while the left-hand flank remains essentially free of horizontal density variations [Arneborg et al., 2007; Umlauf and Arneborg, 2009a]. [4] The possible mechanism of the pinching-spreading effect can be easily understood if a two-layer along-channel exchange (a density current below the interface and a return current above it) is assumed in a rotating viscous fluid. The two-layer along-channel flow causes a convergence (divergence) of the Ekman transport on the left-hand (right-hand) flank that may be responsible for the pinching/spreading effect [Johnson and Sanford, 1992; Paka et al., 1998]. In accordance with the theory by Wåhlin [2002, 2004], topographic downward steering of gravity currents along a channel implies that the transverse Ekman transport in the bottom boundary layer (BBL) is balanced by the transverse geostrophic transport due to the down-channel tilt of the interface. Umlauf and Arneborg [2009b] and Umlauf et al. [2010] showed that the nearly geostrophically balanced interfacial jet plays a key role, transporting interfacial fluid to the right of the down-channel flow, with important 1of17

2 Figure 1. (left) Bathymetric map of the Baltic Sea and (right) close-up of SF. White lines, numbered 0 3, depict the cross-sections of the Furrow used in Section 3.2 to demonstrate the simulation results. implications for the evolution of the density field and the entrainment process. However, the mechanisms controlling the secondary circulation and the related asymmetry of the cross-channel density structure are currently not well understood [Umlauf et al., 2010], because potential explanations include, apart from the bottom Ekman transport and the interfacial geostrophic jet, the rotating hydraulic theory [e.g., Hogg, 1983]. [5] Laboratory experiments on gravity currents over a flat sloping bottom in a rotating system [Cenedese et al., 2004] have shown that, depending on the value of non-dimensional parameters the Froude (Fr) and Ekman (Ek) numbers the following three flow types were realized: a laminar regime in which the dense current had a constant thickness behind the head (Fr < 1, Ek > 0. 1), a wave regime in which wavelike disturbances appeared on the interface between the dense and fresh fluids (Fr 1), and an eddy regime in which periodic formation of cyclonic eddies in the fresh overlying ambient fluid was observed (Fr < 1, Ek < 0. 1). In the case of turbulent flow, instead of the laminar regime one has to consider a stable (i.e., non- wave- and non-eddy) regime. We suggest that the above classification of flow regimes based on Fr and Ek values can also be applied to channelized, turbulent rotating gravity currents, though the marginal value of Ek for the transition between stable and eddy regimes may differ from 0.1, depending on the ratio of some length scale controlling the width of the gravitational current to the channel width, and, probably, the Reynolds number. [6] The Baltic Sea contains a number of submarine channels (the Bornholm Strait, the Słupsk Furrow, and the Hoburg Channel) that connect a chain of deeper basins (the Arkona, the Bornholm, and the Gdansk/Eastern Gotland basins). These channels are the pathways for gravity currents transporting saline/dense water of North Sea origin from the Danish Straits toward the Gotland Deep. Because of the relatively small dimensions of the sea 1600 km long and on average 200 km wide and 55 m deep transient weather patterns with a time scale of a few days superimpose significant perturbations in deep water transport due to compensation flows [e.g., Krauss and Brügge, 1991]. Gravity current transport in SF was recently calculated by Borenäs et al. [2007] using the rotating hydraulic and frictional theories. The transverse structure of the Bornholm Strait and the SF overflows has been examined by Petrén and Walin [1976], Paka [1996], Paka et al. [1998] and Piechura and Beszczyńska-Möller [2003]. A comprehensive study of the quasi-stationary bottom gravity currents passing through a small (approximately 10 m thick and 10 km wide) channellike constriction in the western Baltic Sea was recently undertaken, including highly resolved measurements of stratification, velocity and turbulence parameters [Arneborg et al., 2007; Umlauf and Arneborg, 2009a], analytical considerations [Arneborg et al., 2007; Umlauf and Arneborg, 2009b] and numerical modeling [Burchard et al., 2009; Umlauf et al., 2010]. [7] The geographical focus of our study is the Słupsk Furrow (SF), a channel-like topographic constriction in the southern Baltic Sea between the Bornholm Basin and the Eastern Gotland/Gdansk basins (Figure 1). It is approximately 90 km long, km wide (as estimated by the distance between 50 m isobaths) and m deep at the deepest connection. The Furrow is the only pathway for saline water from the North Sea to enter the deep basins of the Baltic Proper and ventilate them laterally. [8] The objectives of this study are as follows: (1) to present an overview of different types of observed cross-channel density structure and produce geostrophic estimates of the volume rate of the overflow using data from extensive CTD profiling in SF and (2) to estimate, on the basis of field data and numerical simulation results, non-dimensional dynamic parameters of the gravity current in SF, determine the flow regime, and identify the dynamic processes responsible for the variability in the cross-channel density structure. 2. Empirical Data Analysis 2.1. Data [9] We used the data from closely spaced CTD profiles with a horizontal resolution of m, approaching the bottom as close as 1 2 m. The first time such measurements were carried out in SF was in April 1993 using a winch-operated tow-yo technique at a speed of 5 knots [Paka, 1996]. A little later, such a technique became customary during the cruises of the Polish research vessel Oceania [e.g., Piechura and 2of17

3 Figure 2. Salinity cross-sections of SF of various shapes. The labels identify the name of the research vessel, the date of measurements and the longitude of the cross-section. Beszczyńska-Möller, 2003]. Since then, a large number of CTD cross-sections have been carried out in SF during different seasons with different meteorological/wind conditions. The typical time scale required for taking one of the crosschannel transects was 3 h, so they can be considered synoptic. Here, the results of 51 cross-sections of the Furrow, performed during 25 cruises of the R.V. Oceania and 5 cruises of the Russian R.V. Professor Shtokman, Sergei Vavilov and Shelf, over the period of will be presented Variety of Cross-Furrow Salinity Distributions [10] The different shapes of the salinity contours in the cross-sections of SF are illustrated in Figure 2. Since temperature makes a minor contribution to the density change in the Baltic halocline (no more than a few percent of the salinity contribution), the salinity distribution is almost identical to the density distribution, so the former can be used to characterize the asymmetry effect. The sections in Figure 2 were selected to demonstrate the different visual intensities of the asymmetry effect in different parts of SF: Figures 2a and 2b refer to the western part, Figures 2c 2f to the mid part, and Figures 2g and 2h to the eastern part. [11] The asymmetry effect is clearly seen in Figures 2a, 2b, 2g and 2f; the difference is that the Figures 2a, 2b and 2g are characterized by visually almost vertical salinity contours 3 of 17

4 below the salinity interface (i.e., the contours drop almost vertically after detachment from the interface), while in Figure 2f, the contours display a wedge-shaped spreading toward the south (right-hand flank) without a clear tendency to drop down vertically. The term almost vertical means that the slope of isohalines below the salinity interface becomes much larger than that of the bottom line and the overlying salinity contours, so that the near-bottom layer is almost vertically uniform in salinity, even though it has a considerable horizontal gradient. Note that vertically aligned salinity/density contours were also observed in the transects across a bottom gravity current passing through a channel north of the Kriegers Shoal in the Arkona Basin of the Baltic Sea [Umlauf and Arneborg, 2009a]. [12] Figures 2c, 2d, 2e and 2h present examples of salinity cross-sections of the Furrow where a weakly pronounced asymmetry effect is masked by superimposed mesoscale features such as, probably, a subsurface cyclonic eddy/ negative lens (c and d) and an anticyclonic subsurface eddy/ positive lens (e and h). Similar cyclonic eddies have been observed and numerically simulated in SF by Zhurbas et al. [2004]. Figure 2c illustrates the evolution of an interior transverse density gradient (strongly tilted isopycnals near the northern rim, probably due to a flow reversal) as it is normally only observed near the southern rim. Finally, Figures 2g and 2h, illustrate the opposite tendencies observed in the eastern part of SF: a case of asymmetry effect with almost vertical salinity contours on the southern flank (Figure 2g), and a case when a pinching effect is visible on the southern flank instead of the northern one (Figure 2h). [13] The above data of CTD profiling in SF and their empirical analysis revealed some features that require further effort to be properly explained. What dynamic processes cause the observed variability of asymmetric cross-channel salinity/ density structures remains an open question. For example, why are the wedge-shaped interfacial contours, clearly seen in Figures 2a, 2b, 2d, 2e, 2f and 2g, accompanied by downwardbending in Figures 2a, 2b and 2g, but not in Figures 2d, 2e and 2f? We hope to obtain some explanations and answers to the above questions by means of numerical modeling. Figure 3. Scatterplot of geostrophic estimates of the salt water volume rate through SF, obtained from data of CTD profiling versus the NE component of wind stress Geostrophic Estimates of Salt Water Volume Rate [14] The closely spaced CTD profiling data, presented above, can be used to estimate the volume transport of overflow water by means of the geostrophic relation. Since the gravity current is localized in near bottom layers while the overlying layers are presumably less dynamically active, the along-channel component of the velocity is calculated from density cross-sections using the geostrophic relation with a reference (zero velocity) level taken at 30 m depth, i.e., above the permanent halocline. The salt water volume rate, V overflow, is defined as a volume of water with salinity above 8 that has passed through a cross-section of SF per second. [15] Geostrophic estimates of V overflow obtained from 51 CTD cross-sections of SF varied in the range from m 3 s 1 to m 3 s 1 with a mean value of m 3 s 1. Note that Pedersen [1977] estimated the SF salt water volume rate to range from to m 3 s 1, taking into account the mass balance and entrainment calculations. A numerical study [Meier and Kauker, 2003] encompassing the period shows that the longterm average of this deep-water transport may have a lower limit of around m 3 s 1. On the other hand, by applying the different setups of a rotating hydraulic maximaltransport formalism [Whitehead et al., 1974; Borenäs and Lundberg, 1986] and the frictional theory by Lundberg [1983] to the climatological averages of the density stratification in the Bornholm and Gdansk basins, Borenäs et al. [2007] obtained somewhat higher volume rate estimates in the range of ( ) 10 4 m 3 s 1. Therefore, our mean value of the salt water volume rate through SF obtained from CTD profiling ( m 3 s 1 ) is close to the lower limit of the above estimates. [16] Easterly and northerly (westerly and southerly) winds are known to contribute to (prevent) the eastward overflow in SF [Krauss and Brügge, 1991]. For this reason one may expect a negative correlation between V overflow and the NE component of the wind velocity vector and, therefore, a positive correlation between V overflow and the NE p component of the wind stress vector, t NE ¼ ðt N þ t E Þ= ffiffi 2, where tn and t E are the northerly and easterly components of the wind stress vector. [17] To check whether the geostrophic estimates of V overflow we obtained are correlated with wind-forcing, the NCEP/ NCAR reanalysis gridded meteorology data set was used. From the data set we retrieved the rows of x and y components of the 10mlevelwindvelocitywith6hintervalsattheclosestsealocated grid point to SF, then calculated the wind stress components and averaged them over a one-day period immediately before CTD measurements of a cross-section were started. [18] The scatterplot of (t NE, V overflow ) is shown in Figure 3. It does not show any significant correlation between the geostrophic estimates of the overflow volume rate and windforcing, which is surprising in view of the expectations based on the results of simulations by Krauss and Brügge [1991]. To explain such a discrepancy we suggest that the geostrophic estimate of V overflow based on data of a single CTD crosssection of SF may differ much from the real value of V overflow. 4of17

5 A detailed discussion of this issue in the context of our simulation results will be undertaken in Section Definition of Bulk Parameters and Non-dimensional Numbers of a Gravity Flow [19] Before proceeding to the simulation results, let us introduce some dynamic parameters of gravity currents to be used in the posterior analysis. [20] To check whether a rotating gravity current is frictionally controlled, one has to estimate the different terms of bulk (vertically integrated) down-channel momentum balance and non-dimensional Froude and Ekman numbers characterizing a variety of flow regimes. Following Arneborg et al. [2007], the bulk buoyancy B and thickness H of a gravity current may be defined according to BH ¼ Z 1 2 BH2 ¼ bdz z b Z z b bz ð z b Þdz ; ð1þ where b = g(r r )/r is the negative buoyancy of gravity flow with respect to the overlying ambient fluid of density r and zero buoyancy (b 0atz ), and the lower integration limit lies at the bottom (z = z b ); g =9.81ms 2 is the acceleration due to gravity. The Froude number, Fr, and the Ekman number, Ek, and the Ekman depth, d E, are introduced as Du Fr ¼ ð BHÞ ;Ek ¼ d E 1=2 H ;d E ¼ u2 fu ; where U and Du are the characteristic velocity scales, either the vertically averaged velocity of the gravity current (U) or the velocity difference between the gravity current and the above-lying layer (Du), u 2 * = t Bx /r is the squared friction velocity, t Bx is the down-channel bottom stress, and f is the Coriolis parameter. Note that the Ekman number used by pffiffiffiffiffiffiffiffiffiffi 2 Cenedese et al. [2004] is defined as Ek ¼ 2n=f =H, where n is the kinematic viscosity, which can be combined into the bulk definition of Ek given in (2) because the bottom friction velocity in their experiments follows a drag law of the form u * 2 = C D U 2 with the drag coefficient scaling as C D n/(hu). [21] Note that there are other definitions of the Ekman depth in turbulent flows, e.g., d E = 0.4u * /f [Cushman-Roisin, 1994]. The latter expression is more likely to correspond to the thickness affected by frictional effects [Umlauf and Arneborg, 2009a] and yields substantially larger values for the Ekman depth than the expression d E = u * 2 /( fu) based on the momentum budget. [22] Two methods can be suggested for estimating the lateral size of the channelized gravity current. If the gravity current is governed by rotating hydraulics rules, the width of the current can be estimated from straightforward measurements using the formula [Whitehead et al., 1974] ð2þ pffiffiffiffiffiffiffiffiffiffi 2g*h R HC ¼ ; ð3þ f where h is the upstream reservoir elevation of the density interface relatively to the channel s depth at the entrance (in our case relative to the Słupsk Sill depth (63 m)), and g* =g Dr /r is the reduced gravity based on Dr, the horizontal density difference between the upstream basin and the channel (i.e., between the Bornholm Basin and SF). If the gravity current is frictionally controlled, an alternative expression for the width of the current is valid [Darelius and Wåhlin, 2007] R FC ¼ d E S x ; where S x is the down-channel interface slope. Note that Darelius and Wåhlin [2007] originally defined d E = K/f, where K is the linear drag coefficient, which should be replaced by K = u 2 * /U to arrive at the definition of the Ekman depth given in equation (2). [23] The bulk down-channel baroclinic and barotropic pressure gradient forces, BC x and BT x respectively, as well as the Coriolis force, CO x, acting on the gravity current can be estimated as BC x ¼ CO x ¼ Z z Z b zi Z z z b b x dz dz; BT x ¼ fv 0 ðz i z b Þ; ð4þ z b fv dz; ð5þ where v 0 is the y-component of the geostrophic velocity at the sea surface, v is the y-component of the flow velocity, and z = z i corresponds to the upper boundary of the dense layer. [24] However, we suggest that for the real geometry of SF shown in Figure 1 the channel axis is not strictly directed along the x axis, and the gravity current, in turn, is skewed relative to both the channel axis and the x axis. Based on this suggestion, we can perform a standard transformation from the zonally meridionally oriented Cartesian coordinates, xy, to the downstream-oriented ones, x y, using the constraint CO x = 0, where x is the downstream axis, and formulate the downstream momentum budget instead of that of the downchannel. [25] The downstream parameters u * 2, U, and Du along with B and H, were substituted instead of the down-channel parameters u * 2, U, and Du into equation (2) to calculate Fr, Ek and d E. The downstream constituents of the bulk momentum budget, BC x + BT x and u * 2, as well as abovedefined parameters B, H, U, Du, Fr, Ek and d E, were calculated for a medial point of the gravity current in the four cross-sections of SF shown in Figure 1. The medial point at a given cross-section x = const and a given time moment t was defined as the point y(x, t), where the transport of the gravity current, T x ¼ Z zi z b u dz; ð6þ reaches a maximum. The upper boundary of the dense layer, z i, was defined as the level where the salinity is equal to 8, 5of17

6 Table 1. Parameters of the Gravity Current in SF, the No-Wind Case, Averaged Over a 30-Day Simulation Period Parameter Section 0 Section 1 Section 2 Section 3 Downstream bottom stress (u 2 *,m 2 s 2 ) Dense layer thickness, H (m) Bulk buoyancy, B (m s 2 ) Mean velocity of gravity current, U (m s 1 ) Velocity jump, Du (m s 1 ) Mean downstream angle, a (deg) Ekman layer depth, d E = u 2 * f 1 U 1 (m) Ekman layer depth, d E = 0.4 u * f 1 (m) Froude number, Fr = Du ( BH) 1/2 Ekman number, Ek =(u 2 * f 1 U 1 )/H Ekman number, Ek = (0.4 u * f 1 )/H Gravity current width, R HC =(2g*h) 1/2 /f (km) Gravity current width, R FC = u 2 * f 1 U 1 S 1 x (km) i.e., is slightly above S 0 = 7.5, the undisturbed value of the upper-layer salinity (see equation (7)). 4. Simulation 4.1. Model Setup [26] To simulate the variability of saline water overflow in SF caused by the interplay of gravity current and windforcing effects, we applied the Princeton Ocean Model POM [Blumberg and Mellor, 1987]. POM is a free-surface, hydrostatic, sigma-coordinate hydrodynamic model with an imbedded second and a half moment turbulence closure submodel [Mellor and Yamada, 1982]. A detailed description of the model setup with reference to the Baltic Sea was given by Zhurbas et al. [2004], so we take the liberty of mentioning here only some of the principal model setup features. [27] The model domain includes the whole Baltic Sea, closed in the west at 12 E and at the narrowest section of the Sound. The grid cell size along latitude and longitude, Dx and Dy, was varying spatially from Dx = (1/120) and Dy = (1/240) (or Dx Dy 0.5 km) in SF and its vicinity to Dx = (1/15) and Dy = (1/30) in distant parts of the Baltic Sea. Such a grid refinement was good enough to resolve the details of mesoscale variability in the SF cross-sections, including mesoscale eddies with sizes of the order of the baroclinic Rossby radius L R. (Note that L R varies from 2 to 5 km in the region of interest [Fennel et al., 1991].) [28] The model grid was created using the digitized bottom topography of the Baltic Sea by Seifert and Kayser [1995]. There were 32 s-layers whose thickness was of the total water depth in the main water body and logarithmically refined to in BBL. [29] When formulating the initial conditions, we tried to reproduce the principal features of thermohaline fields in the Baltic Sea by using simple analytical parameterizations. [30] The initial salinity was parameterized by a simple analytical form 8 S 0 at 0 z z 0 >< z z 0:2 Sx; ð y; zþ ¼ 0 S 0 þ ðs 1 S 0 Þ at z 0 > z z 1 ; ð7þ >: z 1 z 0 S 1 þ S z ðz z 1 Þ at z < z 1 where z 0 (x, y) and z 1 (x, y) are the values of the z coordinate at the upper and lower boundaries of the halocline, S 0 (x, y) and S 1 (x, y) are the salinity values at z = z 0 and z = z 1, respectively, and S z is the deep layer salinity gradient. These parameters are taken as constant within each of the Baltic basins (i.e., the salinity is horizontally homogeneous within each basin). In accordance with the observations, the following values of parameters are used: S 0 =7.5,S z = m 1 (the whole Baltic Sea), z 0 = 35 m, z 1 = 48 m, S 1 =18 (the Arkona Basin), z 0 = 45 m, z 1 = 90 m, S 1 =16(the Bornholm Basin), z 0 = 60 m, z 1 = 90 m, S 1 =13(the Słupsk Furrow), z 0 = 70 m, z 1 = 100 m, S 1 =11.5(therest of the Baltic Sea). [31] Since thermal stratification is of secondary importance for the dynamics of the gravitational currents in the Baltic halocline, the initial temperature field was taken as uniform at 5 C within the whole water body. [32] The boundaries between the basins were drawn through the sills or the shallowest connections. In order to remove the discontinuity of the salinity field at the boundaries, a spatial smoothing of the initial salinity field has been applied. The smoothing procedure consists of low-pass filtering the values of z 0, z 1, S 0, S 1 over approximately of the nearest grid nodes. Heat and salt fluxes across the sea surface are taken as zero. [33] Two model runs lasting 60 days are examined here: (1) a no-wind case when the SF overflow can be treated as a pure gravity current and (2) a case of spatially uniform timevarying (easterly-westerly) wind when the x component of the wind stress changes sinusoidally with a period of 6 days a typical value of the natural synoptic period for Europe (see and and an amplitude of 0.15 Nm 2 (i.e., the wind speed amplitude is about 10 ms 1, which is not extraordinary for Baltic Sea weather). Case (2) presents the combined effect of a gravity current and a wind-driven overflow in SF. The analysis of the simulated overflow focuses upon four cross-sections of the Furrow: a transect at E passing through the Słupsk Sill (section 0), a transect at E in the western part of SF where the channel tilts eastward with a slope of about g = (section 1), a transect at E in the eastern part of the Furrow where the channel displays the opposite tendency of becoming shallower toward the east (section 2), and a skewed transect at the eastern outlet of SF between (18 00 E, N) and (17 35 E, N) (section 3). The locations of the four sections are shown in Figure Simulation Results [34] Time series of the downstream constituents of the bulk momentum budget, BC x + BT x and u * 2, as well as a, the angle of the downstream axis, calculated for the no-wind case simulation in the four cross-sections of SF, are given in 6of17

7 Figure 4. Time series of the downstream bulk momentum budget constituents of the gravity current, BC x + BT x and u 2 *, as well as the downstream angle a, calculated for the medial point of the gravity current in the four cross-sections of SF shown in Figure 1 (the no-wind case simulation). Figure 4, while Table 1 presents the mean values (averaged over a 30 day period) of the gravity current parameters defined in Section 3. To calculate R HC and R FC from expressions (3) and (4), we took h =63m 45 m = 18 m, g* = ms 2 (in accordance with the numbers next to equation (7)), S x = (a climatic value of the downchannel interfacial slope in SF given by Borenäs et al. [2007]) and f = s 1. [35] The Froude number in sections 0 3 varies from 0.42 to 0.19, so the gravity flow can be definitely treated as subcritical. In sections 0 and 3, respectively located at the Słupsk Sill and at the eastern outlet of SF, the downstream pressure gradient force balances the bottom friction force within approximately 30% accuracy (see Figure 4), so the gravity current is frictionally controlled. In contrast, in sections 1 and 2, located in the inner parts of SF, BC x + BT x does not balance u * 2, therefore frictional control is not confirmed. Such ambiguous situations correspond well to the changes in the Ekman number Ek =0.4u * /( fh), which is found to be above 1 in sections 0 and 3, and below 1 in sections 2 and 3 (see Table 1). [36] With respect to the Ekman number defined as Ek = u * 2 /( fu H), its value is found to be above 0.1 (the marginal value between the steady and eddy regimes in laboratory experiments by Cenedese et al. [2004]) for marginal sections 0 and 3 (Ek = 0.37 and 0.19) and below 0.1 in inner sections 1 and 2 (Ek = and 0.041). However, since the threshold of u * 2 /( fu H) = 0.1 was established for laminar gravity currents over a flat sloping bottom, there is no guarantee that the same value will be valid for a channelized gravity current in the sea like that of SF. [37] To check directly whether the modeled gravity current in SF does belong to the eddy regime, let us examine maps of current velocity at 40 m and 60 m depth at different points in time (Figure 5). The velocity maps show that the gravity flow is accompanied by the generation of eddies. Cyclonic eddies of a size comparable with the channel width are formed just above the pycnocline (two cyclones clearly identified on the 40 m depth velocity maps are scarcely visible on the 60 m depth velocity maps), and anticyclonic eddies of smaller radius are found within the pycnocline in the eastern part of SF (see the 60 m depth velocity maps). Attached as they are to the gravity current, the eddies are slowly translated to the east. The periodicity of the abovehalocline cyclonic eddy generation is about 25 days (this 7of17

8 Figure 5. Snapshots of current velocity at 40 m and 60 m depth presented for different points of time (the no-wind case simulation). estimate was obtained from the 60-day simulation run, while the results presented in Figures 4 10 refer to the first 30 days of the simulation period). Therefore, the modeled gravity current in SF should undoubtedly refer to the eddy regime. Note that the above-halocline cyclonic eddies are formed in the vicinity of the Słupsk Sill and translated eastward within SF until the bottom begins to rise in the flow direction (cf. Figures 1 and 5). As a result, the above-halocline cyclonic eddies cannot pass through whole length of SF and remain trapped within it. [38] The typical distributions of simulated salinity and along-channel velocity versus the cross-channel distance and depth for the no-wind case are presented in Figure 6. In section 1, the gravity current is attached to the right-hand 8of17

9 Figure 6. (left) Simulated salinity and (right) along-channel velocity for the no-wind case in crosssections 1, 2, 3 at different points in time. The locations of the transects as lines superimposed on snapshots of current velocity are shown in Figure 5. (southern) slope, where the salinity contours display a clear tendency toward vertical density/salinity homogenization and to establish almost purely lateral gradients in BBL (Figure 6a). On the left-hand (northern) flank, a reverse, westward flow forms above the interface, attributed to a cyclonic eddy causing a local bulge of the interface (cf. Figure 5). As a result, the pinching of salinity/density contours is observed due to the southward interfacial Ekman transport and, probably, the southward geostrophically balanced transverse interfacial jet [Umlauf and Arneborg, 2009b; Umlauf et al., 2010]. [39] Further to the east, the gravity current detaches from the right-hand (southern) flank (Figures 6b and 6c). As a result, the vertical homogenization and almost purely horizontal gradients are no longer formed on the southern flank. The gravity current shifts to the Furrow s thalweg (Figure 6b) or to the left-hand (northern) flank (Figure 6c), while the return flow embraces it from both south and north. The combination of the gravity current on the left-hand (northern) flank and the return flow on the right-hand (southern) flank forms an anticyclonic circulation in the halocline and, in view of geostrophic equilibration, a lenslike swelling of salinity/density contours (Figure 6c). By 9 of 17

10 Figure 7. (left) Simulated salinity and (right) cross-section component of velocity (either u or v) for the no-wind case in (a) cross-channel and (b) along-channel sections passing though the center of an abovehalocline cyclonic eddy (17 19 E, N), as well as in (c) a cross-channel section (17 41 E) passing through an intrahalocline cyclonic eddy (negative lens) at t = days. The locations of the transects as lines superimposed on snapshots of current velocity are shown in Figure 5. combining the vertical-transverse views of Figure 6 with the plan views of Figure 5 we find that the return flows in Figure 6 are actually caused by eddies, namely the abovehalocline cyclonic eddies (Figures 6a and 6d), and the intrahalocline anticyclonic eddies (Figures 6b and 6c). [40] As in section 1, the gravity current in the easternmost cross-section of SF (section 3) is often pressed to the southern slope, displaying a tendency toward vertical density/salinity homogenization and establishing almost purely lateral gradients in BBL (Figure 6d). However, in contrast to section 1, where the vertical homogenization and establishment of purely lateral gradients were found to be a permanent feature of the salinity/density contours due to the relatively stable position of the gravity current on the right-hand (southern) flank, in section 3 the gravity flow meanders between the southern and northern flanks of SF, so that any of the salinity contour patterns shown in Figure 6 can be observed. [41] More examples demonstrating the variability in the simulated salinity/density structure of the SF overflow in relation to eddy activity are presented in Figure 7. Salinity contours in the cross-channel (Figure 7a) and along-channel (Figure 7b) transects passing through the center of an abovehalocline cyclonic eddy (17 19 E, N at t = days; cf. Figure 5) display a local bulge of the permanent halocline and tilted (downward-bending) isopycnals near the northern rim as a result of a flow reversal. Figure 7c demonstrates local squeezing of salinity/density contours (negative lens) related to the weak intrahalocline cyclonic eddy displayed in Figure 5, bottom right, at E. [42] All the simulated features of the cross-section salinity distribution, described above, correspond well to observations (cf. Figure 2 with Figures 6 and 7). For example, there is a clear resemblance between Figures 2a and 2b and Figures 6a, between Figure 2g and Figure 6d (a tendency toward vertical density/salinity homogenization and the establishment of almost purely lateral gradients in BBL related to the right-hand rim alignment of the gravity current), between Figure 2f and Figure 6b, (an intrahalocline anticyclonic eddy near the right-hand rim and the gravity current in the middle), between Figure 2e and Figure 6c (an 10 of 17

11 Figure 8. Snapshots of the gravity current transport, Tx, presented in the plane view at different points in time (the no-wind case simulation). The thick black line is the 50 m depth contour, the thin black lines are the 60, 70, 80 and 90 m contours, and the thick red line is the deepest connection line of SF (thalweg). intrahalocline anticyclonic eddy in the middle and the gravity current near the left-hand rim), between Figure 2c and Figure 7a (tilted isopycnals near the left-hand rim due to a flow reversal related to an above-halocline cyclonic eddy), and between Figure 2d and Figure 7c (an intrahalocline cyclonic eddy near the right-hand rim and the gravity current near the left-hand rim). [43] The horizontal structure of the gravity flow and its meandering are illustrated in Figure 8, where snapshots of the gravity current transport, Tx, calculated by equation (6), are presented in the plane view at different points in time. In the western part of SF, the position of the gravity current is relatively stable: it passes along the right-hand flank of the Furrow south of the thalweg. Somewhere between E and E the gravity current crosses the thalweg and then moves eastward along the left-hand flank north of the thalweg. Finally, at the eastern outlet of the Furrow (18 00 E) the gravity current displays a comeback tendency toward the thalweg. The meandering mostly takes place in the eastern part of the Furrow, e.g., at E (section 2) the gravity current can be found both near to the thalweg and 10 km away from it (to the north). [44] The displacement of the gravity current from the right-hand flank to the left-hand flank in the middle part of the Furrow and its comeback at the eastern exit of SF seems to be a quasi-permanent feature (see Figure 8). Comparing the snapshots of the gravity current plan views shown in Figures 5 and 8 with the bathymetric map (see Figure 1 or the depth contours on Figure 8), we would suggest that this quasi-permanent meander is bathymetrically controlled, being caused by local shallowing of the Furrow in the downstream direction. The shallowing forces the squeezing of a moving parcel and, in view of the tendency to conserve potential vorticity, the gravity current acquires a negative (anticyclonic) relative vorticity, which implies the displacement of the velocity maxima toward the left-hand (northern) flank. The quasi-permanent character of the meander in the eastern part of SF is confirmed by estimates of the mean ¼19 and 23 in sections 2 and 3, downstream angle: a respectively (see Table 1). The same tendency of a bathymetrically controlled, northward shift of the gravity current is also seen in the data: the downward-bending effect has been frequently observed in the western part and at the outlet but never in the eastern part of the Furrow (see Figure 2). [45] It is worth mentioning that there is a link between the development of the above-halocline cyclonic eddy, the meander, and the intrahalocline anticyclonic eddy south of the gravity current meander (see Figure 5). The above-halocline cyclone, the point where the gravity current crosses the thalweg, and the intrahalocline anticyclone display a coherent movement to the east, and the process has a cyclic character: the eastward translation of a new-born above-halocline cyclonic eddy is accompanied by the formation of a new meander and new intrahalocline anticyclones. Figure 5 demonstrates only one cycle with an approximately 25-day period, but within the 60-day simulation span more than two cycles were observed. 11 of 17

12 Figure 9. Time series of salt water volume rate for sections 0 (blue), 1 (black), 2 (red) and 3 (green) simulated in the (top) no-wind and (bottom) variable wind cases. The dashed lines represent the baroclinic part of the volume rate calculated from the geostrophic relation with a zero-velocity level at 30 m depth. The thin black line at the bottom represents the wind stress time series (t x ). [46] The width of the simulated gravity current, roughly estimated from Figure 8 as the width of the region with positive eastward velocities, varies from approximately 10 km in the central part of SF to approximately 20 km at the Słupsk Sill and the eastern outlet. These estimates of the gravity current width are comparable with calculations from the expression R FC = u * 2 f 1 U 1 S x 1, whereas the expression R HC =(2g*h) 1/2 /f underestimates the simulated values by a factor of 2 (see Table 1). Based on the simulation results shown in Figures 5 8, as well as from the reasonably good correspondence of the observations (Figure 2) and simulations (Figures 6 and 7), the real width of the gravity current in the SF interior was found to be less than the Furrow breadth by a factor of (30 32 km between 50-m isobaths). Therefore, SF may be considered a wide channel, which explains the possibility of meandering. The notion of a wide channel can also explain the applicability of the Cenedese et al. [2004] criterion (u * 2 f 1 U 1 )/H = 0.1 for the margin between the stable and eddy regimes and the Darelius and Wåhlin [2007] expression (equation (4)) for the gravity current width, which were not originally applied to a channel-like bottom topography. [47] The simulated time series of the salt water volume rate, V overflow are illustrated in Figure 9 for the cases of (1) the no-wind, purely gravitational current and (2) the interplay of the gravity current and the variable wind-driven overflow. After an initial growth period of 3 5 days, the salt water volume rate, calculated for sections 0 3, approaches an asymptotic value of about m 3 s 1 in case 1, and undulates between m 3 s 1 and zero in case 2. Undulations of V overflow and the x-component of wind stress are highly coherent with the time lag from a few hours for section 0 located at the Słupsk Sill to approximately 1 day for section 3 located at the eastern outlet. With respect to the geostrophic estimates of V overflow obtained from the simulated density field and the zero velocity level taken at 30 m depth, they were found to be quite different from true values of V overflow ; the difference can be attributed to the barotropic component of transport. The only exception is section 0, where the true values and geostrophic estimates of V overflow display relatively high coherence. The discrepancy between simulated values of V overflow and their geostrophic estimates can explain the absence of a correlation between the geostrophic estimates of the SF salt water volume rate from the field CTD measurements and the NE component of wind stress (Figure 3). [48] To illustrate changes in velocity and density structures of the SF overflow caused by wind forcing, let us look at Figures 10 and 11. These present the plane view of velocity vectors at 40 and 60 m depth (Figure 10) and salinity and along-channel velocity versus distance and depth in a crosssection of E (Figure 11), simulated in the variable wind case, for periods of and days, corresponding to the maximum of the overflow volume rate in the easterly wind phase, and of and days, corresponding to the minimum of the overflow volume rate in the westerly wind phase (cf. Figure 9). In contrast to the no-wind case, when evolution of the coupled structure of meanders and eddies had a cyclic character with an approximately 25-day period, it now clearly follows the wind stress/overflow volume rate undulations. The easterly wind phase is characterized by a well-pronounced above-halocline cyclonic eddy and the right-hand flank alignment of the gravity current in the western part of SF, while in the eastern part the excursion/ meander of the current to the left-hand flank and its comeback at the SF outlet are observed, but the intrahalocline anticyclonic eddies are missing. During the westerly wind phase, the above-halocline cyclonic eddy is almost destroyed, the meandering begins earlier to the west, and the meander structure breaks up into two intrahalocline anticyclonic 12 of 17

13 Figure 10. Snapshots of current velocity at 40 m and 60 m depth simulated with variable wind-forcing. Moments of t =14.14 days and days correspond to the maximum of the overflow volume rate in the easterly wind phase; t =17.15 days and days correspond to the minimum of the overflow volume rate in the westerly wind phase. eddies. The salinity and along-channel velocity patterns in a cross-section of E demonstrate the above-halocline cyclonic eddy and the right-hand flank position of the gravity current accompanied with the downward-bending of density contours and establishing purely horizontal density gradients in BBL during the easterly wind phase, which are replaced by the intrahalocline anticyclonic eddy and the left-hand flank alignment of the gravity current during the westerly wind phase. The salinity pattern in Figure 11a displays a steep ascent of the interface in the right-hand flank, which could be considered a signature of the easterly wind phase. Note that there is a clear resemblance between the simulated salinity contours in Figure 11a and the observed ones in Figures 2a and 2b; inspection of the weather conditions during the field measurements showed that in both cases the 3-day period before the CTD profiling was characterized by fresh NE winds with speeds up to 12 m s 1. [49] The preferable formation of cyclonic eddies above gravity currents is a well-known phenomenon repeatedly observed in the field, laboratory and numerical experiments [see, e.g., Spall and Price, 1998; Lane-Serff and Baines, 2000; Cenedese et al., 2004; Zhurbas et al., 2003, 2004]. Cyclonic eddies are probably generated by a process in which the upper-layer columns get stretched, conserving potential vorticity and causing the dense fluid to break up into a series of domes [Lane-Serff and Baines, 2000; 13 of 17

14 Figure 11. (left) Salinity and (right) along-channel velocity in a cross-section of E simulated in the variable wind case for moments of and days, corresponding to the maximum and minimum of the overflow volume rate, respectively. The locations of the transects as lines superimposed on snapshots of current velocity are shown in Figure 10. Cenedese et al., 2004]. In accordance with laboratory experiments by Lane-Serff and Baines [2000], there are three main mechanisms for this: first, the downslope gravity current may take captured upper-layer fluid with it out into deeper water; second, adjustment of the current to geostrophic balance stretches the fluid column above the current; and, finally, continuous viscous draining from the current (and later from the domes) also causes stretching in the ambient fluid. One more mechanism of cyclonic eddy generation as the adjustment (by means of stretching) of the high potential vorticity (PV) outflow water column to a low potential vorticity environment (so-called PV outflow hypothesis) was suggested by Spall and Price [1998]) in their study of cyclogenesis in the Denmark Strait outflow/overflow. All these mechanisms of cyclonic eddies above gravity currents are common in that that the key process is vortex stretching under conservation of potential vorticity. Taking into account the fact that the modeled cyclonic eddies in SF have a highly uniform vertical distribution of the horizontal components of velocity, u and v, within the upper-layer column (recall that we are considering a winter-type stratification when the seasonal thermocline is missing), we suggest that the cyclonic rotation was acquired as a result of the uniform stretching of the upper-layer column from the undisturbed downstream thickness h 0 = 45 m in the Bornholm Basin to h 1 =60m (the undisturbed upper-layer thickness in SF see the numbers next to equation (7)). If the relative vorticity in the upper layer of the upstream basin is zero (V 0 = 0), and applying the potential vorticity conservation in the form d dt V þ f h ¼ 0; ð8þ where V v x u y is the relative vorticity (the subscripts x and y indicate partial derivatives), and h is the upper-layer thickness, one can obtain for the upper-layer relative vorticity in the downstream basin, V 1, V 1 ¼ f h 1 h 0 h 0 : ð9þ [50] Substitution of h 0 = 45 m and h 1 = 60 m into (9) yields V 1 /f = 1/3, which is a factor of 2.2 as small as the value of V/f = 0.73 in the center of the modeled cyclonic eddy (Figure 12a). Therefore, uniform stretching of the upper-layer column can explain no more than 50% of the relative vorticity of the cyclonic eddy. [51] Apart from the stretching of the upper-layer column, one can imagine other explanations for the above-halocline cyclonic eddies, for example, spin-up due to entrainment into the gravity current. In accordance with (8), the growth rate of the upper-layer relative vorticity due to entrainment, dv 1 /dt, is governed by a differential equation dv 1 dt ¼ V 1 þ f h 1 w e ; ð10þ where w e = EU is the entrainment velocity and E is the entrainment ratio. Integration of (10) with the initial condition V 1 =0att = 0 yields ln V 1 f þ 1 ¼ w e h 1 t: ð11þ [52] Arneborg et al. [2007] obtained E = for the Arkona Basin gravity current at Fr0.5, while in SF we have Fr0.3, which implies a much smaller value of 14 of 17

15 Figure 12. Normalized relative vorticity, V/f, andu-component of velocity in cross-channel sections passing though the center of (a) the above-halocline cyclonic eddy shown in Figures 5 and 7a at t = days, (b)the intrahalocline anticyclonic eddy shown in Figure 5 at t = days, and (c) the intrahalocline cyclonic eddy shown in Figures 5 and 7c at t = days. Estimates of V/f and u are the vertically averaged estimates in a layer of 0 40 m (Figure 12a) and m (Figures 12b and 12c). 15 of 17