Gravity currents play a crucial role in the formation of deep waters in the ocean, contributing to the vorticity and energy transfers towards the ocean interior. We present results from an experimental study on downslope intruding and rotating gravity currents into an initially two-layer stably stratified ambient at high buoyancy Reynolds numbers. A new turbulent process of downslope transport, intermittent and localized, is identified, taking the form of cascades. The lifetime of cascades presents a power law relationship, and the related transport does not exhibit any characteristic length scale, suggesting self-organized criticality. Cascades reveal to be the main contributor to the vorticity and turbulence in the ocean interior, with a dependence on the Coriolis parameter and the density anomaly to the surrounding ambient. Vorticity is produced both by the spreading of the cascade into the interior, and by the meandering and the break up of the deep boundary current (formed from downward Ekman transport). When the intrusion spreads at the pycnocline only, anticyclonic eddies are formed in the intrusion and top layers, whereas for intrusions spreading through the full bottom layer, vortices of both signs are generated due to bottom friction. The turbulence in the receiving ambient reveals to be horizontally isotropic, non-stationary and non-homogeneous. In the intrusion area close to the slope, the turbulence is forced by energy injection at the penetration length scale through the cascades. The central area far from the boundaries is characterized, instead, by freely evolving two-dimensional turbulence, forced at large scales.

The increasing amount of data in earth-observing systems allows us to move from considering low-order moments (means and variances) of fluctuating observations to their PDFs (Probability Density Functions). For two years of HFR (High Frequency Radar) sea surface current increments in the Gulf of Trieste (Northern Adriatic Sea) we found the analytical fat-tailed PDF form (a combination of a gaussian and a convolution of two exponentials) using superstatistics and the maximum entropy principle twice: on a short and on a longer time scale. The data observed under different wind regimes (Bora, Sirocco and low wind, from the WRF model local forecasts) follow the same analytical PDF, pointing towards a universal behaviour.We developed an idealised deterministic-stochastic model of the wind-driven sea surface currents in the Gulf of Trieste. The deterministic model consists of a time-dependent Ekman layer system, including the tidal signal, with a quadratic drag. It describes 57% of the variability, missing the fast fluctuations. The stochastic part accounts for the fast fluctuations, reproducing the superstatistical PDFs from the observations. The model, providing a huge amount of data, allows for studying the PDF of the mechanical power-input into the ocean and the associated extreme events.

Severe winters in the northern Adriatic potentially generate gravity currents flowing along the eastern flank of the Adriatic, filling and ventilating the deepest layer of the southern Adriatic Pit with high-density water. The pulses of gravity current observed by data at the moorings in the Canyon of Bari (BB site) and the shelf-slope observation site (FF) are followed by strong fluctuations in the thermohaline properties in the pit observed at the E2M3A site in 2012, 2017, 2018 and 2022. While temperature was the main driver of gravity flow in 2012, salinity played an equal or greater role in the following extreme gravity current events. Thermohaline data from these three moorings show an arrival from mid-February to June and the relaxation phase of the high frequency oscillations (few tens of hours) lasts about two months. During this phase, the gravity current water displaces and mixes with the surrounding water masses. The gravity currents lead to a restratification of the water column, while local convection processes in winter time erode the stratification. The effects of gravity currents in the southern Adriatic have a profound impact on the Eastern Mediterranean circulation, influencing its thermohaline properties and facilitating the ventilation of deep waters. The Adriatic dense water formation adds to and competes with the convection in the Gulf of Lion, forming the dense waters in the Mediterranean which outflow through the Strait of Gibraltar into the northern Atlantic. The European Multidisciplinary Seafloor and water column Observatory (EMSO) South Adriatic Regional Facility (E2M3A in the pit, BB and FF at the edge of the pit) has been providing hourly data on temperature, salinity, oxygen and currents along the water column for about 15 years. This makes it possible to study these high-frequency small-scale processes and their interaction with the surroundings over an extended period of time and to assess their role in a changing climate.

In the Gulf of Trieste, the sea surface currents were observed by high-frequency radar for almost 2 years (2021–2022) at a temporal resolution of 30 min. We developed a hierarchy of idealized models to simulate the observed sea surface currents, combining a deterministic and a stochastic approach, in order to reproduce the externally forced motion and the internal variability, which is characterized by fat-tailed statistics. The deterministic signal includes tidal and Ekman forcing and resolves the slowly varying part of the flow, while the stochastic signal represents the fast-varying small-scale dynamics, characterized by Gaussian or fat-tailed statistics, depending on the statistic used. This is done using Langevin equations and modified Langevin equations with a gamma-distributed variance parameter. The models were adapted to resolve the dynamics under nine tidal and wind forcing protocols in order to best fit the observed forced motion and internal variability probability density function (PDF). The stochastic signal requires 2 stochastic degrees of freedom when the average tidal forcing is adopted, while it needs 1/2 stochastic degree of freedom when the complete tidal forcing is used. Despite its idealization, the deterministic–stochastic model with stochastic fat-tailed statistics captures the essential dynamics and permits mimicking the observed PDF. Moreover, a fluctuation response relation is valid when the stochastic signal is perturbed, showing that the response to an external perturbation can be obtained by considering the fluctuations of the unperturbed system.

Hydrostatic models were and still are the workhorses for realistic simulations of ocean dynamics, especially for climate applications. Introducing a Fourier space projection method and using the Heisenberg–Gabor limit, a formalism is developed to systematically evaluate the role of flatness, stratification, rotation and friction for the fidelity of the hydrostatic approximation. The hydrostatic approximation is formally first order in γ=H/L, where H is the vertical and L the horizontal scale of the phenomenon considered. For linear (low-amplitude) and unforced stratified rotating flow, the dynamics can be separated into balanced flow and wave motion. It is shown that for the linear balanced motion the hydrostatic approximation is exact and for wave motion it is second order, obtaining the leading prefactors. The fidelity of the hydrostatic approximation therefore also relies on the ratio of the amplitude of wave motion to balanced motion. This ratio adds considerably to the quality of the hydrostatic approximation for larger-scale flows in the atmosphere and the ocean. Imposing the divergenceless condition is a linear projection of the dynamical variables into the subspace of divergenceless vector fields, for both the Navier–Stokes and the hydrostatic formalism. Both projections are local in Fourier space. The former is well known, while the latter, developed here, asks for an extension of the dynamical space to four dimensions. The projection is followed by a time-evolution operator, which differs in the wave frequencies only. Combining the projection and the linear evolution operators in both formalisms leads to the linear projection-evolution operator. Calculating the difference of the two projection-evolution operators, the expression of the error, scaling and prefactors done by the hydrostatic approximation is obtained. Analyzing the eigenspace of the projector-evolution operators, it is shown that for rotating buoyant vortical flow, the hydrostatic approximation is of third order for buoyant forcing, second order for horizontal and first order for vertical dynamical forcing. Balanced dynamics is in the kernel of the linear projection-evolution operator, and conservation of potential vorticity is expressed by the kernel of its adjoint. Using the Heisenberg–Gabor limit, it is shown that for large-scale ocean dynamics, the difference of the dynamics of the projection-evolution operator between the two formalisms is insignificant. It is shown that the hydrostatic approximation is appropriate for realistic ocean simulations with vertical viscosities larger than ≈10-2 m2 s−1. A special emphasis is on unveiling the physical interpretation of the calculations.

The renewal of bottom water masses in the deep South Adriatic Pit (SAP) is mainly determined by the arrival of very dense water that forms in the North Adriatic in winter (NAdDW) and which is transported into the SAP by gravity currents. To investigate the occurrence of these currents, we analyze high-frequency time series of thermohaline and velocity data at three moorings of the EMSO South Adriatic Sea regional facility, which consists of two observation areas: the SAP observatory (E2M3A) and the shelf and slope observatory (BB in the Bari Canyon and FF on the furrow area on the open slope), from 2012 to 2022, as well as reanalysis data from Copernicus over the same period. This analysis shows that gravity currents in the deep SAP (dSAP) only occurred in 2012, 2017, 2018, and 2022 (bottom ventilation years). The water masses were mixed differently after gravity current events, as 2012 was mainly driven by temperature, 2017 and 2022 by salinity, and 2018 by both. It was also found that in 2012 and 2018 the gravity current mainly passed through FF, while in 2017 it passed through BB. An analysis of the time scale showed that the average duration of the bursts of fluctuation triggered by the arrival of the gravity current in the dSAP was a few months (3 months on average). It was also revealed that the travel time from the formation of the NAdDW to BB was around 2 months on average, and that the travel time from BB (FF) to E2M3A was around 2 weeks. A comparison between the Copernicus reanalysis and the E2M3A time series also showed consistent differences in density, both in value and variability, resulting in the detection of gravity current events being unclear for the former.

Gravity currents are ubiquitous in polar regions and marginal seas and play a crucial role in the formation of deep waters in the ocean. They contribute to the vorticity and energy transfers towards the ocean interior. We present results from an experimental study on downslope intruding gravity currents into an initially two-layer stably stratified ambient on a rotating platform at high buoyancy Reynolds numbers. We identify a turbulent process for the downslope transport, intermittent and localized, which takes the form of cascading. This process is intrinsic to rotating gravity currents, i.e., it arises without any external tuning, and the related transport does not exhibit any characteristic length scale, suggesting self-organized criticality. The cascading intrusion mechanism reveal to be the main contributor to the vorticity and turbulence in the ambient interior, with a dependence on the Coriolis parameter f and the density anomaly to the surrounding ambient. Two mechanisms for vorticity production are recognized: first, the spreading of the intrusion from cascading into the interior and, second, the meandering and breakup of the deep boundary current (formed from downward Ekman transport) induced by intrusion from cascading. When the intrusion spreads at the pycnocline only, anticyclonic eddies are formed in the intrusion and top layers, whereas for intrusions spreading through the full bottom layer, vortices of both signs are generated due to bottom friction. The turbulence in the receiving ambient reveals to be horizontally isotropic, nonstationary, and nonhomogeneous. Energy is injected through the intrusion issued by cascading at the penetration length scale L p and forces the turbulence in the intrusion area close to the slope. The central area far from the boundaries is characterised, instead, by freely evolving two-dimensional turbulence, forced at large scales. These results suggest a complementary way to interpret oceanic observations of gravity currents spreading in the ocean interior.

In double-diffusive mixing, whenever salinity and temperature decrease with depth, the water column is either unstable or predisposed to a state called salt fingering (SF), which exhibits increased vertical mixing. Analysis of a high-frequency time series of thermohaline data measured at the EMSO-E2M3A regional facility in the southern Adriatic Pit (SAP) from 2014 to 2019 reveals that in the south Adriatic, SF is the dominant regime. The same time series shows the presence of a very saline core of the Levantine Intermediate Water that penetrated with unprecedented strength during the winter of 2016/17 at around 550 dbar and even higher-salinity water above. The effect of strong heat loss at the surface during that winter allowed deep convection to transport this high-salinity water from the intermediate to the deep layers within the pit. This resulted in an increased predisposition to SF throughout the water column. In the subsurface layer (350 to 550 dbar) the increase is from 27 % to 72 % of observations. We observe an alteration of vertical stratification throughout the water column during the winter of 2016/17 from a stratified water column to an almost homogeneous water column down to 700 dbar, with no return in the following years.

Understanding the dynamics and structures in the deep ocean is one of the remaining challenges in oceanography and climate sciences. We present results from large-scale laboratory experiments of rotating down-slope gravity currents intruding into a two-layer stratified ambient, performed in the largest rotating tank in the world, the Coriolis Rotating Platform in Grenoble. By means of velocity and density measurements, we show that no mixing occurs once the current has detached from the boundary. The shape of the vertical density profile in the stratified receiving ambient enables to identify two distinct regimes: the first issued by laminar transport through Ekman dynamics, the second by turbulent transport due to intermittent dense water cascading. Vertical density gradients reveal a piece-wise linear dependence on the density anomaly for the turbulent transport, suggesting an advection-diffusion process. For the turbulent regime, the scale height is deduced and an analytical model based on the critical Froude number is proposed to predict its value. Results show that the total thickness of the intruding current is on average 2.5 times the scale height. For laminar intrusions the scale height diverges whereas the thickness of the intrusion is a few times the Ekman layer thickness. Comparing the intrusion scale height with its measured vertical extension has led to a criteria to distinguish between laminar and turbulent regimes, which is corroborated by two additional independent criteria, one based on the sign of the local vorticity and the other based on the local maxima of the vertical density gradient. The model allows us to connect laboratory experiments to deep sea observations, gravity currents and Meddies and emphasizes the importance of laboratory experiments in understanding climate dynamics.

Two years (2021–2022) of high-frequency-radar (HFR) sea surface current data in the Gulf of Trieste (northern Adriatic Sea) are analysed. Two different timescales are extracted using a superstatistical formalism: a relaxation time and a larger timescale over which the system is Gaussian. We propose obtaining an ocean current probability density function (PDF) combining (i) a Gaussian PDF for the fast fluctuations and (ii) a convolution of exponential PDFs for the slowly evolving variance of the Gaussian function rather than for the thermodynamic β=1/σ2 in a system with a few degrees of freedom, as the latter has divergent moments. The Gaussian PDF reflects the entropy maximization for real-valued variables with a given variance. On the other hand, if a positive variable, as a variance, has a specified mean, the maximum-entropy solution is an exponential PDF. In our case the system has 2 degrees of freedom, and therefore the PDF of the variance is the convolution of two exponentials. In the Gulf of Trieste there are three distinct main wind forcing regimes: bora, sirocco, and low wind, leading to a succession of different sea current dynamics on different timescales. The universality class PDF successfully fits the observed data over the 2 observation years and also for each wind regime separately with a different variance of the variance PDF, which is the only free parameter in all the fits.

<div>In this study, two years (2021-2022) of High Frequency Radar (HFR) sea surface current data (30 min time resolution) and modelled near-bottom wind data (1 h time resolution) in the Gulf of Trieste (Northern Adriatic Sea) are analysed through a superstatistical (a superposition of different statistics) approach.</div> <div> </div> <div>Three distinct main wind forcing regimes are present in the Gulf of Trieste: Bora, Sirocco and low wind. Bora and Sirocco are strong winds whose characteristics are different: the Bora is a cold wind that blows in gusts from the East-North-East with a short fetch, the Sirocco is a warm wind that blows from the South with a fetch along the entire Adriatic.</div> <div> </div> <div>The currents in the Gulf of Trieste are forced and highly dependent on such variable wind conditions. It results in a succession of different sea current dynamics on different time scales, asking for a superstatistical analysis of the sea surface current data. From the oceanic signal it is possible to extract two different time scales: a relaxation time <em>τ</em>, the time the system spends to reach the local equilibrium and a larger timescale <em>T</em>, the time for which the signal is locally gaussian. This permits extracting a slowly varying <em>β(t)</em> strictly connected to the original time series’ local variance <em>σ<sup>2</sup>=β<sup>-1</sup></em>. Neither <em>β</em> nor <em>σ<sup>2</sup></em> show well known PDFs and have algebraic tails. Contrary to what one might expect, they show a universal behaviour with respect to the different wind regimes blowing over the Gulf of Trieste.</div>

We present experimental results from large-scale laboratory experiments of rotating downslope gravity currents intruding into a two-layer stratified ambient performed in the Coriolis Rotating Platform in Grenoble. By means of PIV velocity and conductivity data for the density measurement, we show that mixing occurs mostly on the slope area during the descent rather than once the current has penetrated the stratified ambient, where the Richardson number remains above the stability threshold of 1/4. Looking at the time evolution of the vertical density profile in the stratified receiving ambient, two distinct mixing regimes can be identified, the first issued by laminar transport through Ekman dynamics, the second by turbulent transport due to intermittent cascading events. Vertical density gradients reveal a linear piece-wise dependence on the density anomaly, highlighting an advection-diffusion process as proposed by the theoretical model of Munk & Wunsch (1998). If the gravity current flow is laminar on the slope, the structure shows a linear variation of the density with depth ; For the turbulent transport regime characterized by intermittent cascades, an exponential shape is rather observed. The shape of the density structure allows to estimate bulk mixing coefficients and entrainment velocities at the top and the bottom of the intruding gravity current, which can be further compared to oceanographic observational data.

The EMSO-E2M3A South Adriatic Regional Facility provides high-frequency (every hour) temperature and salinity data from 2006 to 2019 along the water column from 150 dbar to the seafloor. Their study reveals processes on different temporal scales, i.e. daily, seasonal, intra-annual and inter-annual, as well as their recurrence (seasonal or not) and climatic trends. The area is characterized by cyclonic circulation, which preconditions deep convection processes that involve both atmospheric and ocean dynamics, forming new, dense and oxygen-rich waters. There are intermittent influxes of high salinity water from the Ionian Sea, that favor salt fingering, and dense overflows from the northern Adriatic. The region is also subject to strong surface cooling. Data collected by the E2M3A observatory allows monitoring of variability on short scales related to convection and submesoscale processes. On an intermediate time scale, changes in basin circulation are monitored, and on a larger time scale, climate variability in the area is monitored. The various processes interact in a nonlinear manner, highlighting the importance of high-frequency measurements of rapid processes and their interaction with and correction of slowly varying properties on a longer time scale.From ADCP data, the signature of zooplankton migration at the surface/intermediate layer is determined to be enhanced by convection-induced mixing. On the monthly scale, thermohaline variability increases substantially due to oscillations triggered by a combination of factors that include salinity intrusion into the intermediate layer, strong heat loss at the surface, and variability in vorticity during the winter months. The lower layer of the pit has been characterized by a slightly positive trend in temperature and salinity over the last decade, interrupted only by the inflow of dense water from the northern Adriatic Sea cascading through the Canyon of Bari.

Using a set of direct numerical simulations (DNS) we investigate the circulation of a buoyancy driven experiment in a circular rotating tank. The initial density structure is a two-layer stable-stratification. The water is densified at 32 points at the upslope side of a circular incline and flows downward as a gravity current before it intrudes to the interior along the interface between the two layers. The water above recirculates to the densification points.When the buoyancy production is lower than the maximal Ekman transport, the gravity current proceeds in the laminar Ekman layer. In the opposite case, the water cascades down the incline in a no-stationary dynamics, turbulent transport becomes important and the boundary layer is thickened. The thermal wind relation applied to the tangential velocity averaged-along-the-slope predicts the density structure averaged-along-the-slope in the domain.When the densified water arrives at the interface it flows along the slope in the cyclonic direction, in a geostrophically adjusted deep boundary current. The distance of the boundary current from the slope is given by inertial overshoot of the Ekman current due to the self advection by the inertia. When this distance is small the boundary current is close to the slope and subject to boundary friction. In the opposite case the boundary current evolves detached from the boundary. The intrusion along the interface, in the (negative) radial direction, is slow, as the intruding distance is proportional to the square-root of time.The recirculation in the upper layer is close to a geostrophic equilibrium. Its quasi-geostrophic evolution is due to the compression of the water column, caused by the gravity and intruding currents, below. This leads to a large-scale anti-cyclonic circulation in the upper layer. When the associated geostrophic surface pressure gradient exceeds the pressured gradient due to the dense water on the slope, the Ekman transport is upslope.A special emphasis is put on the interactions of the three phases of the circulation: gravity-current, intrusion and recirculation. The circulation and the mixing of density and momentum in the gravity current determine the water-mass properties in the deep boundary current. Both determine the recirculation. The recirculation leads to an increasing anti-cyclonic circulation above the gravity current which, through the corresponding surface pressure gradient, reduces and finally blocs the downslope movement in the Ekman layer.

We show that the most prominent of the work theorems, the Jarzynski equality and the Crooks relation, can be applied to the momentum transfer at the air–sea interface using a hierarchy of local models. In the more idealized models, with and without a Coriolis force, the variability is provided from Gaussian white noise which modifies the shear between the atmosphere and the ocean. The dynamics is Gaussian, and the Jarzynski equality and Crooks relation can be obtained analytically solving stochastic differential equations. The more involved model consists of interacting atmospheric and oceanic boundary layers, where only the dependence on the vertical direction is resolved, the turbulence is modeled through standard turbulent models and the stochasticity comes from a randomized drag coefficient. It is integrated numerically and can give rise to a non-Gaussian dynamics. Also in this case the Jarzynski equality allows for calculating a dynamic beta βD of the turbulent fluctuations (the equivalent of the thermodynamic beta β=(kBT)-1 in thermal fluctuations). The Crooks relation gives the βD as a function of the magnitude of the work fluctuations. It is well defined (constant) in the Gaussian models and can show a slight variation in the more involved models. This demonstrates that recent concepts of stochastic thermodynamics used to study micro-systems subject to thermal fluctuations can further the understanding of geophysical fluid dynamics with turbulent fluctuations.

We present experimental results of rotating downslope gravity currents performed at the Coriolis Platform in Grenoble, France. A novel experimental design to produce the downslope gravity flow has been employed using an axisymmetric configuration and a uniform flow injection that enabled the study of the long-term evolution of surface baroclinic vortices and of the gravity current, monitoring at the same time the evolution of the global circulation and the vorticity produced in the central deep area. The structure of the current, its relevant scales, and the characteristics of the generated surface vortices fairly agree with previous results in the literature in smaller scale installations. Discrepancies are attributable to the influence of both topographic Rossby waves and viscous effects that are much reduced in the Coriolis platform. Rotating intrusive gravity currents in a two-layer stratified ambient behave very differently from dense currents following the bottom slope. Substantial differences appear for the induced global circulation, which depend on the nature of the intrusion, with a strong influence of the rotation rate. In particular, intruding gravity currents give rise to a strong turbulent environment at intermediate and bottom depths in the central area, with submesoscale vortices (i.e., with a typical size smaller than the Rossby deformation radius) and a large variety of scales. In contrast, when the dense current follows the bottom slope, no significant vorticity production in the bottom and intermediate layers is reported. This clearly suggests that bottom boundary layers detaching from the boundary and propagating toward the ambient interior as in intrusive currents give an important contribution to the turbulence dynamics.

Ocean dynamics is predominantly driven by the shear stress between the atmospheric winds and ocean currents. The mechanical power input to the ocean is fluctuating in space and time and the atmospheric wind sometimes decelerates the ocean currents. Building on 24 years of global satellite observations, the input of mechanical power to the ocean is analysed. A fluctuation theorem (FT) holds when the logarithm of the ratio between the occurrence of positive and negative events, of a certain magnitude of the power input, is a linear function of this magnitude and the averaging period. The flux of mechanical power to the ocean shows evidence of a FT for regions within the recirculation area of the subtropical gyre but not over extensions of western boundary currents. A FT puts a strong constraint on the temporal distribution of fluctuations of power input, connects variables obtained with different lengths of temporal averaging, guides the temporal down- and up-scaling and constrains the episodes of improbable events.

The input of mechanical power to the ocean due to the surface wind stress, in regions which correspond to different regimes of ocean dynamics, is considered using data from satellites observations. Its dependence on the coarse-graining range of the atmospheric and oceanic velocity in space from 0.5 to 10∘ and time from 6 h to 40 days is determined. In the area of the Gulf Stream and the Kuroshio extensions, the dependence of the power input on space-time coarse-graining varies over tenfold for the coarse-graining considered. It decreases over twofold for the Gulf Stream extension and threefold for the Kuroshio extension, when the coarse-graining length scale passes from a few degrees to 0.5∘ at a temporal coarse-graining scale of a few days. It increases over threefold in the Gulf Stream and the Kuroshio extensions when the coarse-graining passes from several days to 6 h at a spatial coarse-graining of a few degrees. The power input is found to increase monotonically with shorter coarse-graining in time. Its variation with coarse-graining in space has no definite sign. Results show that including the dynamics at scales below a few degrees reduces considerably the power input by air-sea interaction in regions of strongly nonlinear ocean currents. When the ocean velocities are not considered in the shear calculation, the power input is considerably (up to threefold) increased. The dependence of the power input on coarse-graining in space and time is close to being multiplicatively separable in all regions and for most of the coarse-graining domain considered.

Abstract. The ocean dynamics is predominantly driven by the shear between the atmospheric winds and ocean currents. The ocean mostly receives energy, but it can also lose energy. Building on 24-years of global satellite observations, the input of mechanical power to the ocean is analysed. A Fluctuation Theorem (FT) holds when the logarithm of the ratio between the occurrence of positive and negative events, of a certain magnitude of the power input, is a linear function of this magnitude and the averaging period. The input of mechanical power into the ocean shows evidence of a FT, for regions within the recirculation area of the subtropical gyre, but not over extensions of Western Boundary Currents. A FT puts a strong constraint on the temporal distribution of fluctuations of power input, connects variables obtained with different length of temporal averaging and guides the temporal down- and up-scaling and constrains the occurrence of extreme events.