Impact of the dense water flow over the sloping bottom on the open-sea circulation: Laboratory experiments and the Ionian Sea (Mediterranean) example

The North Ionian Gyre (NIG) displays prominent inversions on decadal scales. We investigate the role of internal forcing, induced by changes of the horizontal pressure gradient due to the varying density of the Adriatic Deep Water (AdDW), that spreads into the deep layers of the Northern Ionian Sea. In turn, the AdDW density fluctuates according to the circulation of the NIG through a feedback mechanism named Bimodal Oscillating System. We set up laboratory experiments with a two-layer ambient fluid in a circular rotating tank, where densities of 1000/1015 kg m characterise the upper/lower layer, respectively. From 20 the potential vorticity evolution during the dense water outflow from a marginal sea, we analyse the response of the open-sea circulation to the along-slope dense water flow. In addition, we show some features of the cyclonic/anticyclonic eddies that form in the upper layer over the slope area. We illustrate the outcome of the experiments of varying density and varying discharge rates associated with the dense water injection. When the density is high, 1020 kg m, and the discharge is large, the kinetic energy of the mean flow is stronger than the eddy kinetic energy. On the other hand, when the density is smaller, 1010 kg m , and the 25 discharge is reduced, vortices are more energetic than the mean flow, that is, the eddy kinetic energy is larger than the kinetic energy of the mean flow. In general, over the slope, following the onset of the dense water injection, the cyclonic vorticity associated with a current shear develops in the upper layer. The vorticity behaves in a two-layer fashion, thus becoming anticyclonic in the lower layer of the slope area. Concurrently, over the deep flat-bottom portion of the basin, a large-scale anticyclonic gyre forms in the upper layer extending partly toward a sloping rim. Density record shows the rise of the pycnocline due to the dense 30 water sinking toward the flat-bottom portion of the tank. We show that the rate of increase of the anticyclonic potential vorticity is proportional to the rate of the rise of the interface, namely, to the rate of decrease of the upper layer thickness (i.e., the upper layer squeezing). The comparison of laboratory experiments with the Ionian Sea is made for a situation when the sudden switch from https://doi.org/10.5194/os-2020-122 Preprint. Discussion started: 8 January 2021 c © Author(s) 2021. CC BY 4.0 License.


Introduction
The effect of dense water outflow from marginal seas on the ocean circulation has attracted great attention because it represents an important component of the global thermohaline circulation (Jungclaus and Backhaus, 1994;Dickson, 1995). Numerical and 40 laboratory studies of this phenomenon have been inspired primarily by the observations of mesoscale eddies over the dense water outflow in the ocean (e.g., Denmark Strait, Gibraltar Strait) (Mory et al., 1987, Whitehead et al., 1990Lane-Serff and Baines, 1998;Lane-Serff and Baines, 2000;Etling et al., 2000). The coupling between the upper layer circulation and the dense water plume was also addressed by numerical modelling (see i.e., Spall and Price, 1998) which confirmed the formation of eddies in the upper layer. The eddies were predicted to travel along isobaths with a characteristic speed which depends on reduced gravity, 45 bottom slope, and Coriolis parameter (Nof, 1983). The early hypotheses stated that the cyclones form by the stretching of the high potential vorticity water column (Spall and Price, 1998). In addition to the formation of cyclonic eddies in the lighter upper part of the water column, according to Lane-Serff and Baines (2000) secondary anticyclonic motion occupying a major part of the tank develops. This is the only mention in the literature of this type of consequence of the dense water cascading off the slope.
The Ionian Sea, the deepest basin of the Mediterranean (maximum depth over 5000 m) together with its two adjacent basins, 50 the Adriatic and Aegean Seas, represents a key area for both the Eastern and Western Mediterranean. It is crossed by the main Mediterranean water masses (Levantine Intermediate Water -LIW, Atlantic Water -AW) and it comprises the site of the Eastern Mediterranean Deep Water (EMDW) formation, a process which takes place mainly in the Adriatic Sea. Adriatic Dense Water (AdDW) overflows the Otranto Sill, represents the main component of the EMDW and spreads along the western continental slope as a bottom-arrested current affecting the northern Ionian circulation. Only occasionally very dense water forms in the Aegean Sea 55 as it happened in the early 1990's during the Eastern Mediterranean Transient -EMT (Roether et al., 1996;Klein et al., 1999). It was shown that the Aegean dense water overflow affected the upper layer circulation increasing the cyclonic vorticity at the continental slope area (Menna et al., 2019).
Analysis of long-term altimetric data reveals that the sea surface circulation in the Ionian shows peculiar characteristics (Vigo et al., 2005): at decadal time scales it switches from a cyclonic basin-wide gyre occupying the entire northern area, to an 60 anticyclonic meandering. This fact contributes to determine the thermohaline properties of the interior Ionian basin, of the Adriatic Sea, and of the Levantine and even the Western Mediterranean basins (Gačić et al., 2013). During the cyclonic circulation mode, Ionian and Adriatic Seas are invaded by a highly saline Levantine water. On the other hand, during the anticyclonic circulation the two basins are affected by the low-salinity waters of Atlantic and Western Mediterranean origin (Brandt et al., 1999). For more than ten years the decadal inversions of the northern Ionian circulation have been the focus of Mediterranean scientists' attention 65 because the phenomenon is very prominent and involves a large part of the water column (about 2000 m deep). There has been a long discussion about the mechanism generating such inversions and some scientists suggested, mainly based on the numerical modelling studies, that the phenomenon is linked to the wind stress curl (see e.g., Pinardi et al., 2015;Nagy et al., 2019). Other studies, however, showed that the wind curl variations are not strong enough to generate such changes; these studies sustain that https://doi.org/10.5194/os-2020-122 Preprint. Discussion started: 8 January 2021 c Author(s) 2021. CC BY 4.0 License. the inversions are due to the interplay between the dense water flow (Adriatic or Aegean origin) and the Ionian horizontal 70 circulation (e.g., Gačić et al. 2010;2011;Theocharis et al., 2014;Velaoras et al., 2014). The long-term density variability of the bottom water associated with the salinity variations in the deep-water formation site induce reversals of the horizontal pressure gradient in the Ionian Sea and hence of the circulation pattern (Borzelli et al., 2009). The mechanism was named Adriatic-Ionian Bimodal Oscillating System (BiOS) and described for the first time by Gačić et al. (2010). It is the purpose of this paper to study in more detail the inversions of the open-ocean residual circulation generated by dense water flow over a sloping bottom, 75 and to understand whether this flow is strong enough to produce inversions in the upper-layer circulation like those observed in the Ionian Sea.
To address the impact of the dense water flow on the basin-wide open-sea circulation and on the formation of anticyclonic vorticity in the upper layer, we base our study on the analysis of the results of a series of rotating tank experiments with injection of the dense water at the slope area. Our attention is concentrated on a two-layer system, which approximates rather well the Ionian 80 Sea conditions. Then, we examine the response of the central abyssal plain of the idealized basin to the dense water sinking and to its along-slope flow and compare the findings with the observative studies. We also discuss mesoscale eddies and their specific features in function of the dense water outflow rate. The dense water flow is quite often a time-limited phenomenon with the duration of several months after the winter convection in a marginal sea; therefore, our experiments are designed to mimic this kind of conditions. More specifically, we address the response time of the residual current field at the open sea area to the dense 85 water flow of the limited duration over the continental slope. Hence, we discuss the effect of different discharge rates of the dense water at the slope on the surface circulation at the open sea attempting to reproduce the circulation inversions in the northern Ionian Sea. Rubino et al. (2020), by comparing the results of experiments in the rotating tank with those obtained by a numerical model and altimetry data, show qualitatively that the inversion of the circulation in the Ionian Sea can be solely explained in terms of the onset of the dense water injection over the slope area. Starting from this finding, the present work goals are 1) to study the evolution 90 of potential vorticity fields both in the slope and in the central area of the rotating tank, using the outputs of three different experiments, and 2) to compare them with vorticity obtained from altimetry (surface layer) and model derived (deep layer) flow in the 'real' Ionian.
We distinguish the slope and central deep (flat bottom) areas in the tank that are equivalent to the continental slope and deep zone of the northern Ionian basin, respectively. We compare the potential vorticity evolution in each area as related to the 95 dense water flow. The two areas are presumably controlled by different processes of the vorticity generation. In the central area (flat bottom) the upper layer squeezing, due to the downslope sinking of the dense water to the lower layer, generates the upper layer anticyclonic vorticity. In the slope area, the upper layer stretching due to the downslope water flow results in the generation of the cyclonic vorticity. The lower layer on the slope is subject to squeezing and anticyclonic vorticity generation as related to the formation of the dense water flow parallel to isobaths.

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The linear barotropic vorticity equation for an f-plane approximation as derived from Lee-Lueng et al. (1995) in radial coordinates for the surface layer without wind-stress forcing is: The paper is organized as follows: in section 2 we present experimental setup, an overview of the selected experiments and data analysis methods. In section 3 measurements and results are described, while section 4 is dedicated to the comparison of the 110 laboratory results and Ionian Sea example. Finally, section 5 presents a summary and conclusions of the paper.   The slope area was realized using an axisymmetric conical-shaped boundary descending toward the centre of the tank with a constant slope which was determined by keeping dynamical similarity between the phenomenon to be simulated in the rotating tank and that occurring in the Ionian Sea. The similarity results from the ratio between the gravitational (g's) and Coriolis 130 accelerations (fu) being of the same order of magnitude for the two basins. Here g' = gΔρ/ρ is the reduced gravity, Δρ is the density difference between the injected water and the ambient water densities, f is the Coriolis parameter and u is the velocity component tangential to isobaths. We introduce typical values for g', f and u for the Ionian Sea (g' = 1.5 x 10 -3 m s -2 , f = 10 -4 s -1 , u = 10 -2 m s -1 ) and take the value 5 x 10 -2 for the western Ionian continental slope from the literature (Ceramicola et al., 2014). To get the similarity between the laboratory experiments and the Ionian Sea we set the slope s in the tank to 0.1, g' to 0.1 m s -2 ; for f we take 135 0.1 s -1 , corresponding to one rotation day (1 revolution) lasting 120 s, while for a typical speed we chose 10 -2 m s -1 . In this way the rotating tank slope angle is equal to 5.7 0 and the ratios of the two acceleration terms are of the same order of magnitude for both basins. Hence, the slope area, with a total width of 4 m, gradually descends from the tank edge, where its height is 40 cm, down to the tank bottom. The central deep area with constant depth has a diameter of 5 m.

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From the eastward and northward current components, we calculated radial and tangential velocities (in the right-hand side coordinate system); a radial one (v) is defined positive toward the tank edge.
The horizontal spatial resolution, for all velocity components, as well as for other derived fields, like vorticity, at each of the 12 vertical levels, is 5 x 5 cm.
For each vertical profile of density measured in the central deep area (by means of a probe Cp3, Fig. 1 For what concerns the terms of the quasi-geostrophic linear vorticity equation (Eq. 1), the surface is defined as the mean of 165 levels 2 to 5, and the bottom as the mean of levels 10 and 11. Level 1 is discarded because in the central deep area it is too close to the free surface and is therefore noisy. In the computation of the derivative of the curl, both the vorticity time series and its derivative are smoothed with moving average on 7 points.
In the calculation of the time-lag cross correlation of vorticity over the tank slope area, we averaged vorticity values over the levels 1 to 4 in each of three arbitrarily chosen zones. In the slope area, the levels 1-4 are well inside the upper layer of the 15°-21°E), separating the centre of the northern Ionian (bins located on depths larger than 2200 m) from the slope (bins located on depths smaller than 2200 m). Time series of these spatially averaged parameters are normalized (dividing by the Coriolis parameter) and filtered using a 61-day moving average.

Density in the central deep area
The dense fluid sinks from the source toward the central portion of the tank within the distance on the order of one radius of deformation and then it turns and flows along-slope (Smith, 1975;Juncklaus and Backhaus, 1994;Lane-Serff and Baines, 1998).
Due to the sinking of the dense fluid, the interface, intended as the upper boundary of the pycnocline layer, in the central deep area of the tank rises. The rate of the interface rise is proportional to the volume discharge rate assuming that this water is distributed 195 evenly over the entire basin: where ( ) = 0 + ( ℎ ) is the radius of the cylinder filled by the discharge and R0 is the radius of the interface between the upper and lower layers at t = 0.
This estimate in our case can be compared with the experimental data, i.e., the vertical density profiling near the centre of as follows from Eq. (2), directly proportional to the discharge rate and inversely proportional to the square of the radius of the volume of the tank occupied by the injected water.

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The slowest decrease of the upper layer thickness, i.e., a MLD decrease, is evident during the experiment 26, which is characterized by the lowest dense water discharge rate. In that case, the rise (descent) of the upper (lower) boundaries of the pycnocline layer probably depends both on the dense water sinking and the vertical mixing, which provokes the thickening of the https://doi.org/10.5194/os-2020-122 Preprint. Discussion started: 8 January 2021 c Author(s) 2021. CC BY 4.0 License.
pycnocline layer. The temporal evolution of the MLD for the other two experiments is mainly due to the dense water sinking, while the vertical mixing and turbulent diffusion probably play a minor role. This is evident from the rise of the interface (that is, the 230 upper boundary of the pycnocline) being larger than the deepening of the lower boundary. Indeed, as already pointed out, the rise of the interface is directly proportional to the discharge rate and inversely proportional to the area of the base of the volume occupied by the discharged water (Eq. 2). We limit our study to cases in which the filling up of the lower layer with the dense water is to a larger extent responsible for the interface rise, i.e., to experiments 24 and 27.
We compare the MLD temporal evolution with variations of the lower layer thickness from the theoretical relationship (Eq.

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3). The interface rise as a function of the dense water injection rate (Fig. 3) is a good approximation of the interface depth variations in the central deep area. In fact, the inclination of the curves is remarkably close to each other. The offset between the theoretical curve and the experimental data is present probably because the interface is not a plane but a layer of the finite thickness due to the vertical diffusion.
or from Eq.
(2) we have: The temporal evolution of the vorticity in the two presented experiments (Fig. 4) indeed confirms the above considerations.
In the case of the experiment 24, when the dense water discharge rate was set constant to 0.  To summarize, at the slope area the vorticity behaves in a two-layer fashion. In the case of experiment 24 in the lower layer it becomes anticyclonic a few days after the beginning of the experiment, while in the upper layer (Fig. 4 left) it becomes cyclonic with about ten days phase-lag with respect to the underneath part of the water column. In the case of the experiment 27 the 280 generation of the anticyclonic vorticity takes place only after the onset of the dense water injection with a high discharge rate (1.6 10 -3 m 3 s -1 , phase II), while in the phase I we set up very low discharge rate which did not virtually affect the vorticity field. Again, https://doi.org/10.5194/os-2020-122 Preprint. shows the occurrence of a strong anticyclonic motion in the upper layer, while in the lower layer there is no well-defined behaviour of the vorticity. The two-layer distribution of the vorticity at the slope area can be explained in terms of a small vertical-to-lateral 285 friction ratio, whereas the single-layer circulation occurring occasionally in the center of the tank is supported by a relatively large vertical-to-lateral friction ratio (Orlić and Lazar, 2009). This also suggests that we cannot neglect the frictional influence especially at the slope.
Equation (5) (Table 3) are negative and statistically significant at the 95% confidence level. Therefore, in the flat-bottom area the 300 quasi-geostrophic potential vorticity equation approximates rather well the upper layer vorticity evolution. In addition, it is evident that curves of the rate of change of the potential vorticity and the upper layer depth for the experiment 24 are noisier than for the experiment 27, which is probably due to the more prominent mesoscale activity in the former experiment than in the latter, as it will be shown later.
In the slope area we must consider also the topographic β-term (Eq. 1). Thus, we compare the rate of the vorticity change 305 with the sum of the rate of change of the lower layer thickness and the topographic β-term for the two experiments (Fig. 6). We calculate the average radial velocity, which is negative for the downslope flow. We take the average lower layer radial velocity over the entire slope area since the downslope dense-water flow generates stretching of the water column in the surface layer and cyclonic vorticity. In fact, for a major part of the experiments the topographic β-term is negative (graph not shown) suggesting that the cyclonic vorticity generation takes place due to the cross-isobath, downslope dense water flow. Generally, the correlation 310 coefficients for the slope area are smaller than for the central deep area. This confirms that at the continental slope the quasigeostrophic vorticity equation does not describe the vorticity variations as successfully as in the flat-bottom area. This can probably be explained by the fact that the bottom viscous draining at the slope area is not included in the quasi-geostrophic vorticity equation.
This fact is also supported by a two-layer vorticity behaviour.

Eddies over the slope area
The time evolution of the flow field reveals that the two chosen experiments do exhibit the eddy formation on the slope but not of 325 the same intensity. Animated maps of the horizontal flow at level 1 for the entire experiment duration (animations S1 and S2 in the Supplementary Material) support this difference. Here we illustrate the eddy formation by showing the two selected snapshots from each of the three phases of the experiments (Fig. 7). Although eddies are not of our primary interest, we will shortly address their characteristics for experiments 24 and 27 since, as stressed by Whitehead at al. (1990), "Isolated eddies are some of the most beautiful structures in fluid mechanics". Qualitatively speaking, experiment 24 shows stronger eddy activity than the experiment 330 27. To explain differences between the two experiments in terms of the eddy formation, we calculated the relative vortex stretching and the relative importance of the viscous draining following the approach by Lane-Serff and Baines (2000). With a reference to   The ratio between the eddy kinetic energy per unit mass (EKE) and the kinetic energy of the mean flow per unit mass (MKE) measures the relative importance of eddies with respect to the mean flow. Thus, we calculate the average EKE and MKE for both experiments for the three phases over the entire slope area, as well as the ratio between the two (Fig. 8). It is evident that in the phase I for the experiment 24 EKE > MKE, i.e., eddies are more energetic than the mean flow (MKE), as already pointed 360 out from the relationship between the relative stretching and the relative importance of the viscous draining. For both experiments MKE is larger than EKE in the phase II, as it also follows from the fact that the two experiments fall within the overlapping region where eddies are less likely to be formed. Finally, in the phase III both experiments have MKE larger than EKE, although they fall within the eddy region. This can be due to the rather high remaining energy of the mean flow from the phase II being larger than the energy of the newly formed eddies.

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During the phase II, when the dense water discharge is stronger for the experiment 27 than for the experiment 24, toward the end of the phase the flow field shows strong clockwise basin wide circulation more spatially coherent for the experiment 27 than for the experiment 24. Eddy activity as a residual of the phase I is still prominent in the experiment 24. The phase III with the same dense-water flow rate for both experiments shows the slowdown of the basin wide anticyclonic circulation and the relative increase of the mesoscale activity.

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To study in more detail the evolution of the vorticity field in the upper layer of the slope area, we calculate average vorticities for three chosen zones at the slope of the tank (Fig. 9a) and the lagged cross-correlation between them, to estimate eddy propagation direction and speed. As an example, we present here the results for experiment 24, which has a prominent eddy activity at the slope area as shown earlier. The cross-correlation between zones 1 and 2 (Fig. 9b)

Comparison between the laboratory experiment and the Ionian Sea
We compare the laboratory experiments, which simulate the effects of the dense water overflow into the real ocean with an event occurred in the northern Ionian Sea characterized by the sudden change of the circulation as a consequence of the very dense water flow from the Adriatic Sea following harsh winter (Mihanović et al., 2012;Bensi et al., 2013;Raicich et al., 2013;Gačić et al., 415 2014;Querin et al., 2016). This discharge event, which took place in 2012, generated an abrupt and temporary inversion of the upper-layer Ionian circulation from cyclonic to anticyclonic. Gačić et al. (2014) were able to determine accurately the start and the cessation of the dense water flow thanks to an ample availability of in situ data mainly from floats. They estimated that the sudden inversion of the horizontal circulation from cyclonic to anticyclonic took place in June 2012 and subsequent return to cyclonic in maximum cyclonic and anticyclonic motion, respectively, in October/early November (Fig. 11), when the dense water outflow from the Adriatic seemingly ceased, as suggested by Gačić et al. (2014). At the 1000 m depth in the continental slope area the vorticity curve varied out of phase with respect to the upper layer. This suggests the presence of the two-layer structure of the vorticity field at the continental slope area similarly to what was observed in the rotating tank experiments. In the deeper central area, as in the rotating tank experiments, no clear two-layer structure occurred in the vorticity field; solely the surface layer was characterized by the circulation inversion from cyclonic to anticyclonic motion. The 1000 m vorticity values are one order of magnitude smaller than those at the surface since the depth of 1000 m is below the velocity zero-crossing level but close to it.
According to some estimates from the thermal wind relationship (Giuseppe Civitarese, personal communication) the zero-crossing is situated at the depth of around 800 m. Consequently, velocities are smaller than those at the surface having as a result the smaller vorticity values, even for one order of magnitude.

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Similarity between the Ionian and the rotating tank can also be quantified by comparing the respective vorticity rate of change, i.e., . It is inversely proportional to the residence time of the upper layer (see Eq. 5). Hence the ratio of the inclination of the vorticity curve for the Ionian and the rotating tank, is inversely proportional to the ratio of their residence times associated with the dense water flow rate. Calculating the receiving volume of the Ionian Sea and the tank and knowing the dense water flow 475 rate in the tank for the experiment 27 (1.6 10 -3 m 3 s -1 ) and the dense water outflow from the Adriatic (on average 3 10 5 m 3 s -1 according to Lascaratos, 1993), we estimate the ratio between the residence times. On the other hand, we estimate from vorticity curves both for the rotating tank and the Ionian (see Figs. 4 and 11) and the ratio of the vorticity rate of change of the two basins.
Our results indeed show that the ratio between residence times of the Ionian Sea and the rotating tank is of the same order of magnitude as the ratio of the vorticity rate of change in the rotating tank and in the Ionian Sea. This confirms the dynamical 480 similarities of the dense water flow in the two basins.

Summary and conclusions
The decadal inversions of the horizontal circulation, peculiar phenomena in the Ionian Sea, according to the BiOS theory (see e.g., Rubino et al., 2020 and papers cited therein) are not wind-induced but are due to inversions of the internal density gradients.
Observations reveal that a reversal can occur very rapidly, i.e., even at time scales on the order of a month (see Gačić et al., 2014).

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Here we simulate this type of situation in the rotating tank and compare it with observational data gathered in the Ionian basin during the 2012 exceptional dense water overflow. This remarkable phenomenon occurred when, due to the harsh 2012 winter the https://doi.org/10.5194/os-2020-122 Preprint. Discussion started: 8 January 2021 c Author(s) 2021. CC BY 4.0 License.
BiOS cyclonic mode which started in 2011, was suddenly interrupted and reversed to the anticyclonic flow. To carry out the comparison between such reversal and the tank experiments, we focus on two laboratory experiments where different dense water discharge rates created the similar dynamics to that observed in the real ocean. For the two experiments analysed in detail the 490 ambient fluid consists in two layers: the upper one is made of freshwater while the lower layer has a density of 1015 kg m -3 . In the first part of the experiments, water of 1010 kg m -3 was discharged for a period of 45 rotational days (1 day = 120 sec) after which a high-density water of 1020 kg m -3 was released until the 90 th day. We vary the dense water flow rates of the two experiments and observe the evolution of the current field. The formation of the large basin-wide anticyclonic gyre in the surface layer of the central flat-bottom area of the tank initiates after the dense water flow starts. Concurrently, over the slope area in the upper layer the 495 cyclonic vorticity manifests itself as a series of counter-clockwise travelling mesoscale cyclones (leaving the shallow water on their right) or in the form of a cyclonic basin-wide shear. We show that the mesoscale eddy activity depends on the dense water discharge rate. Also, the mesoscale eddies propagate anticlockwise from the dense water source, until the onset of the basin-wide anticyclonic circulation. Then, the vortices are advected by the mean basin-wide flow in the opposite direction. In the lower layer of the slope area, instead, an anticyclonic vorticity is generated and therefore in that portion of the tank the current field behaves 500 in a two-layer fashion from the point of view of the vorticity pattern. The vorticity in the Ionian Sea shows a vertical structure both in the continental slope and in the central deep area like in the rotating tank. We show that the evolution of the flow field in the Ionian following the dense water outflow from the Adriatic is dynamically similar to the flow field in the rotating tank following the dense water injection. The similarity is shown for the experiment with the dense water discharge rate of 1.6 10 -3 m 3 s -1 when the ratio between the vorticity rate of change in the Ionian and in the tank is of the same order of magnitude as the inverse of the 505 ratio of the residence times. This laboratory experiment confirms that the internal forcing, the only forcing applied in the rotating tank, is sufficient to create inversions of the basin-wide cyclonic circulation to the anticyclonic one in the Ionian Sea as already hypothesized by the BiOS theory.

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All used data sets can be made available by request to the first and corresponding author.

Supplement
Link to S1&S2.zip