Mikhail A Sokolovskiy - Academia.edu (original) (raw)

Papers by Mikhail A Sokolovskiy

Theoretical and Computational Fluid Dynamics, Aug 8, 2009

In a quasi-geostrophic model, we study the baroclinic instability of a two-layer vortex. The sing... more In a quasi-geostrophic model, we study the baroclinic instability of a two-layer vortex. The singular unstable modes for potential vorticity anomalies are compared with the classical normal modes. Shorttime singular modes are explosively unstable and, at short times, depend only on the baroclinic component of the flow. As time progresses, they evolve towards the normal modes and their sensitivity to flow parameters is explored. Asymptotic solutions are provided.

Springer eBooks, 2009

Using the method of contour surgery, we examine the evolution of an initially vertically aligned ... more Using the method of contour surgery, we examine the evolution of an initially vertically aligned elliptical heton. A classification of quasi-stable and unstable regimes for the case of two-layered vortex structure is suggested.

Springer eBooks, Dec 22, 2007

As a development of the work [2], we give a short analysis of regular and chaotic regimes in an i... more As a development of the work [2], we give a short analysis of regular and chaotic regimes in an idealized periodical current over a submerged obstacle of Gaussian shape.

Oceanology, 2021

In this study we explore the origin of the high stability of the Lofoten vortex, persistently obs... more In this study we explore the origin of the high stability of the Lofoten vortex, persistently observed in the central part of the Lofoten Basin of the Norwegian Sea. It is shown that the higher steepness of the southwestern bottom slopes and a small inclination of the bottom topography towards the region where the Norwegian Current splits into two branches increase the dynamic stability of the Lofoten vortex. The observed minor variations of bottom topography of the basin form the area with the small gradients of the background potential vorticity. When residing in this area, the Lofoten vortex can retain 60 to 90% of the core volume over two years, even without gaining energy from external sources. When the vortex deviates from its mean position in the center of the basin, or when the external conditions deviate from their characteristic values for the Lofoten basin, the rate of the Lofoten vortex deformation and decay typically increases. Thus, the topography of the Lofoten Basin together with the characteristics of the Norwegian Current in the study region form almost optimal conditions for the permanence of an anticyclonic vortex in the center of the basin.

Proceedings of the First International Conference on Ocean Thermohydromechanics-2017, 2017

The Ocean in Motion, 2018

Приводится обзор работ, посвященных изучению свойств вихревых движений в устойчиво стратифицирова... more Приводится обзор работ, посвященных изучению свойств вихревых движений в устойчиво стратифицированной быстро вращающейся жидкости и описываемых уравнением эволюции потенциального вихря в квазигеострофическом приближении. Основное внимание уделено вихрям с нулевой суммарной циркуляцией — так называемым хетонам. Рассматриваются задачи самодвижения дискретных хетонов, устойчивости единичного распределенного хетона, взаимодействия двух хетонов конечных размеров. Приводятся также новые решения задач о трех и более дискретных вихрях хетонной структуры. Даются примеры возникновения хаотических режимов. Обсуждаются область применимости хетонной теории и перспективыее возможных приложений, в частности, — для анализа динамической стадии развития глубокой конвекции в океане.

Intrathermocline lenses are vortex patches (anticyclonic or cyclonic) localized at intermediate h... more Intrathermocline lenses are vortex patches (anticyclonic or cyclonic) localized at intermediate horizons (600–1600 m) of ocean. They are observed everywhere in the World Ocean, but mainly in the North Atlantic. A typical situation is when anticyclonic and cyclonic lenes are located near each other and both are affected by a large-scale vortex [1]. In this paper, we study some mechanisms of interaction of a pair of intrathermoclinic lenses with a synoptic surface vortex. We use a three-layer quasi-geostrophic model with a density stratification in the form of a two-step piecewise constant function that approximates the mean multi-year vertical density distribution of the North Atlantic. Anticyclonic and cyclonic intrathermoclinic lenses are presented in the form of vortex patches with potential vorticities of negative and positive signs, respectively, and with horizontal scales of the order of the Rossby deformation radius. The surface cyclone, having a radius of 4 times larger, is r...

Regular and Chaotic Dynamics, 2021

Physics of Fluids, 2020

We examine the motion of N symmetric hetons (oppositely signed vertical dipoles) in a two-layer q... more We examine the motion of N symmetric hetons (oppositely signed vertical dipoles) in a two-layer quasi-geostrophic model. We consider the special case of N-fold symmetry in which the original system of 4N ordinary differential equations reduces to just two equations for the so-called “equivalent” heton. We perform a qualitative analysis to classify the possible types of vortex motions for the case N = 2. We identify the regions of the parameter space corresponding to unbounded motion and to different types of bounded, or localized, motions. We focus on the properties of localized, in particular periodic, motion. We identify classes of absolute and relative “choreographies” first introduced by Simó [“New families of solutions to the N-body problems,” in Proceedings of the European 3rd Congress of Mathematics, Progress in Mathematics Vol. 201, edited by C. Casacuberta, R. M. Miró-Roig, J. Verdera, and S. Xambó-Descamps (Birkhäuser, Basel, Barcelona, 2000), pp. 101–115]. We also study t...

Mathematics, 2020

The theory of point vortices is used to explain the interaction of a surface vortex with subsurfa... more The theory of point vortices is used to explain the interaction of a surface vortex with subsurface vortices in the framework of a three-layer quasigeostrophic model. Theory and numerical experiments are used to calculate the interaction between one surface and one subsurface vortex. Then, the configuration with one surface vortex and two subsurface vortices of equal and opposite vorticities (a subsurface vortex dipole) is considered. Numerical experiments show that the self-propelling dipole can either be captured by the surface vortex, move in its vicinity, or finally be completely ejected on an unbounded trajectory. Asymmetric dipoles make loop-like motions and remain in the vicinity of the surface vortex. This model can help interpret the motions of Lagrangian floats at various depths in the ocean.

Physics of Fluids, 2018

A simple dynamical model of vortex interactions taking place near a curved boundary mimicking a c... more A simple dynamical model of vortex interactions taking place near a curved boundary mimicking a circular bay is formulated and examined. An initial configuration consisting of a point vortex in the bay and of an incident point vortex moving toward the bay along the straight part of the boundary is considered. Both vortices are of equal strengths. Typical stationary regimes of the bay-bound vortex when the incident vortex is far from the bay are obtained. When the incident vortex comes near the bay, its interaction with the bay-bound one may result in irregular motion of both vortices. Typical outcomes of the interaction are established to be (i) the incident vortex passes over the bay without forcing the bay-bound vortex to leave the bay; (ii) the incident vortex becomes entrapped within the bay, whereas the bay-bound vortex leaves it; (iii) both vortices leave the bay shortly after the interaction as separate vortices or as a bound leap-frogging pair; (iv) both vortices exhibit con...

Geoinformatics Research Papers, 2019

В данном отчете представлены результаты российских океанографов в 2015-2018 гг. Авторами исследов... more В данном отчете представлены результаты российских океанографов в 2015-2018 гг. Авторами исследований были подготовлены краткие обзоры. В подготовке данного отчета принимали участие представители следующих организаций: Институт океанологии им. П.П. Ширшова РАН (Москва) и его филиалы Санкт-Петербурге и Калининграде; Тихоокеанский океанологический институт им. В.И. Ильичева ДВО РАН (Владивосток); Институт прикладной физики РАН (Нижний Новгород); Институт гидродинамики им. М.А. Лаврентьева СО РАН (Новосибирск).

Ocean Dynamics, 2018

Within the framework of the quasi-geostrophic approximation, the interactions of two identical in... more Within the framework of the quasi-geostrophic approximation, the interactions of two identical initially circular vortex patches are studied using the contour dynamics/surgery method. The cases of barotropic vortices and of vortices in the upper layer of a two-layer fluid are considered. Diagrams showing the end states of vortex interactions and, in particular, the new regime of vortex triplet formation are constructed for a wide range of external parameters. This paper shows that, in the nonlinear evolution of two such (like-signed) vortices, the filaments and vorticity fragments surrounding the merged vortex often collapse into satellite vortices. Therefore, the conditions for the formation and the quasi-steady motions of a new type of triplet-shaped vortex structure are obtained.

Ocean Science Discussions, 2019

The Persian Gulf Water and Red Sea Water are salty and dense waters recirculating at subsurface i... more The Persian Gulf Water and Red Sea Water are salty and dense waters recirculating at subsurface in the Gulf of Oman and the Gulf of Aden respectively, under the influence of mesoscale eddies which dominate the surface flow in both semi-enclosed basins. In situ measurements combined with altimetry indicate that the Persian Gulf Water is driven by mesoscale eddies in the form of filaments and submesoscale structures. In this paper, we study the formation and the life cycle of intense submesoscale vortices and their impact on the spread of Persian Gulf Water and Red Sea Water. We use a three-dimensional hydrostatic model with submesoscale-resolving resolution to study the evolution of submesoscale vortices. Our configuration is an idealized version of the Gulf of Oman and Aden: a zonal row of mesoscale vortices interacting with north and south topographic slopes. Intense submesoscale vortices are generated in the simulations along the continental slopes due to two different mechanisms. The first mechanism is due to frictional generation of vorticity in the bottom boundary layer, which detaches from the topography, forms an unstable vorticity filament, and undergoes horizontal shear instability that leads to the formation of submesoscale coherent vortices. The second mechanism is inviscid and implies arrested topographic Rossby waves breaking and forming submesoscale coherent vortices where a mesoscale anticyclone interacts with the topographic slope. Submesoscale vortices subsequently drift away, merge and form larger vortices. They can also pair with opposite signed vortices and travel across the domain. They can weaken or disappear via several mechanisms, in particular fusion into the larger eddies or erosion on the topography. Particle patches are advected and sheared by vortices and are entrained into filaments. Their size first grows as the square root of time, a signature of the merging processes, then it increases linearly with time, corresponding to their ballistic advection by submesoscale eddies. On the contrary, witout intense submesoscale eddies, particles are mainly advected by mesoscale eddies; this implies a weaker dispersion of particles than in the previous case. This shows the important role of submesoscale eddies in spreading Persian Gulf Water and Red Sea Water.

Deep Sea Research Part I: Oceanographic Research Papers, 2017

The Lofoten Vortex (LV), a quasi-permanent anticyclonic eddy in the Lofoten Basin of the Norwegia... more The Lofoten Vortex (LV), a quasi-permanent anticyclonic eddy in the Lofoten Basin of the Norwegian Sea, is investigated with an eddy-permitting primitive equation model nested into the ECCO2 ocean state estimate. The LV, as simulated by the model, extends from the sea surface to the ocean bottom at about 3000 m and has the subsurface core between 50 m and 1100 m depths. Above and below the vortex core the relative vorticity signal decreases in amplitude while the radius increases by as much as 25-30% relative to the values in the core. Analyzing the model run, we show that the vertical structure of the LV can be casted into four standard configurations, each of which forms a distinct cluster in the parameter space of potential vorticity anomalies in and above the LV core. The stability of the LV for each of the configurations is then studied with three-layer and a two-layer (in winter) quasi-geostrophic (QG) models over a flat bottom as well as over a realistic topography. The QG results show a number of common features with those of the primitive equation model. Thus, among the azimuthal modes dominating the LV instability, both the QG model and the primitive equation model show a major role the 2nd and 3rd modes. In the QG model simulations the LV is the subject of a rather strong dynamic instability, penetrating deep into the core. The results predict 50-95% volume loss from the vortex within 4-5 months. Such a drastic effect is not observed in the primitive equation model, where, for the same intensity of perturbations, only 10-30% volume loss during the same period is detected. Taking into account the gently sloping topography of the central part of the Lofoten basin and the mean flow in the QG model, brings the rate of development of instability close to that in the primitive equation model. Some remaining differences in the two models are discussed. Overall, the LV decay rate obtained in the models is slow enough for eddy mergers and convection to restore the thermodynamic properties of the LV, primarily rebuilding its potential energy anomaly. This justifies the quasi-permanent presence of the LV in the Lofoten Basin. (about 2000 m deep) and the northwestern flank of the Voring plateau (Fig. 1). Warm and salty Atlantic Water (AW) occupies the upper 800-1000 m of the Lofoten Basin. The AW overlies denser waters of both lower temperatures and salinities (Blindheim and Rey, 2004; Nilsen and Nilsen, 2007). In the AW layer, temperature and salinity both increase towards the center of the basin (Boyer et al., 2005), while

Geophysical & Astrophysical Fluid Dynamics, 2016

This study focuses on the interaction between mid depth vortices and surface jets and fronts in a... more This study focuses on the interaction between mid depth vortices and surface jets and fronts in a three-layer quasi-geostrophic model. Such vortices may be regarded as an idealisation of meddies, eddies of Mediterranean Water in the Northeastern Atlantic Ocean, interacting with the Azores j t and front. Successively, a single vortex, a vortex doublet and a vortex pair (in the middle layer) are studied. When a single vortex is considered, the jet has a critical effect of its motion, temporarily slowing down its zonal drift and accelerating it meridionally as the vortex crosses the front. On the contrary, if the vortex does not cross the front, it can drift fairly rapidly along it. The merger of a vortex doublet (two like-signed vortices) below a surface jet is possible whatever the relative position of this doublet with respect to the jet axis. Nevertheless, doublets initially located below the front, will undergo stronger shear and merger efficiency will be diminished. The merged vortex will be circled at the surface by a large meander of the jet. Finally, eastward jet-dipole interaction experiments are performed with various orientations of the vortex dipoles. Eastward propagating dipoles below the jet follow it without deformation. Southeastward drifting dipoles finally join the previous evolution. Southward and southwestward directed dipoles cross the surface jet southeastward. The presence of meanders initially on the jet does not prevent its crossing by a single vortex. Characteristics of the surface jet meanders are also described for a possible remote detection of this process.

Geophysical & Astrophysical Fluid Dynamics, 2015

The merger of two identical surface temperature vortices is studied in the surface quasigeostroph... more The merger of two identical surface temperature vortices is studied in the surface quasigeostrophic model. The motivation for this study is the observation of the merger of submesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incompressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and symmetric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vortex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.

Oceanology, 2015

In the northeastern Atlantic Ocean, intrathermocline lenses (ITL) occur at depths of 600-1600 m. ... more In the northeastern Atlantic Ocean, intrathermocline lenses (ITL) occur at depths of 600-1600 m. These ITLs are localized vortex patches (anticyclonic and cyclonic), generally of an elliptical shape with hor izontal axes from 40 to 100 km, vertical axes from 0.4 to 1 km, and volumes of 1000-3500 km 3. According to observations, the coexistence of several lenses is a rather common phenomenon in certain ocean areas. Thus, the problem of their interaction, and, in particular, the influence of lenses on larger vortices, is especially important. The aim of the present work is to study, using a three layer quasi geostrophic model, the interaction between intrathermocline lenses and synoptic gyres existing in few layers. Simulations show that synoptic gyres change significantly their shape under the effect of ITLs. The authors propose a tentative mechanism of ITLs' deceleration because of the interaction with synoptic gyres, located at different layers. It is obvious that turbu lent exchanges at mid ocean depths intensify when vortices collapse.

Regular & Chaotic Dynamics, 2003