M. A. Sokolovskiy

Finite-core hetons: stability and interactions

The dynamics of vertically compensated two-layer vortices (hetons) with nite cores are examined within the context of the quasi-geostrophic approximation on the f-plane. The two-layer version of the contour dynamics method is used, and complemented by the so-called contour surgery technique. Special attention is paid to two-heton interactions when the initial locations of the vortex patches are symmetrical. A classication of the dierent regimes observed is made according to external parameters, namely geometrical parameters and stratication. In this parameter space, novel quasi-stationary states resulting from collisions between two hetons may be observed: (i) formation of a conguration consisting of two-layer vortices moving in opposite directions and, as a special case, a conguration analogous to the ‘klapstoss’ billiard shot, (ii) absorption of one heton by the other and subsequent movement of a new dipole, (iii) formation of two-layer dipoles, larger than the original hetons, associated with rotating peripheral satellite eddies in their wakes. Some of these results may have implications for the analysis of mesoscale vortices in the ocean.

Baroclinic multipole formation from heton interaction

In a two-layer quasi-geostrophic model, the interaction between two oppositesigned hetons (baroclinic vortex pairs) is studied analytically and numerically, for singular and finite-area vortices. For point vortices, using trilinear coordinates, it is shown that the possible evolutions depend on the deformation radius Rd: for large Rd, the layers decouple, vortices pair in each layer and their trajectories are open; for medium Rd, the exchange of opposite-sign partners between layers becomes possible; for small Rd, two other regimes appear: one where hetons remain unaltered during their evolution but follow open trajectories, and one where hetons occupy only a bounded subdomain of space at all times. Conditions for invariant co-rotation of the heton pair are derived and analyzed. Then, the nonlinear evolutions of finite-area heton pairs, with piecewiseconstant vorticity, are computed with contour dynamics. When the central cyclonic vortex is initially aligned vertically, a transition occurs between three nonlinear regimes as layer coupling increases: for weak coupling, the vortices pair horizontally and drift away in opposite directions; for moderate layer coupling, the core vortex splits into two parts, one of which remains as a tilted columnar vortex at the center; for stronger layer coupling, each anticyclone pairs with part of the cyclone in each layer, thus forming an L-shaped dipole, a new coherent structure of two-layer flows. When the initial distance between the central and satellite vortices is increased, the velocity shear at the center decreases and the central vortex remains vertically aligned, thus forming a Z-shaped tripole, also a newly observed vortex compound. Such tripoles also compete with oscillating states, in which the core vortex periodically aligns and tilts, a regime observed when layer coupling is moderate and as vortices become closer in each layer. This Z-shaped tripole forms for various values of stratification and of initial distances between vortices, and is therefore a robust vortex compound in two-layer quasi-geostrophic flows.

Baroclinic multipole evolution in shear and strain

In a two-layer quasi-geostrophic model, the evolution of a symmetric baroclinic multipole, composed of a central vortex with strength μκ in the upper layer, and A satellites with strength κ in the lower layer, is studied. This multipole is imbedded in a center-symmetric shear/strain field, either steady or time-periodic. Special attention is given to the case of the tripole (A = 2). The stability of this tripole is assessed and its oscillations in the external field are analyzed. Conditions for resonance of these oscillations are derived and transition to chaos is described.

On the influence of an isolated submerged obstacle on a barotropic tidal flow

Abstract The influence of an isolated submerged obstacle on the dynamics of a material particle is studied within the limits of a barotropic, quasi-geostrophic model of oceanic f-plane flow, for cases in which the incident flow has both steady and tidal components of velocity. Two kinds of motion are shown to occur, namely (i) the particle performs quasi-periodic oscillations in the vicinity of the obstacle or (ii) the particle acquires an infinite character (i.e., the particle leaving the vicinity of the obstacle is irrevocably advected downstream by the background flow). Sufficient conditions are obtained for the existence of both classes of motion. Conditions for domain alternation of the finite and infinite solutions have been derived numerically for different external parameters (e.g., the kinematic characteristics of the flow field and the height of topography). Using the Contour Dynamics Method, results are presented to show how the predicted motions of individual particles can be extended to predi...

Reflection of intrathermocline eddies on the ocean surface

In the northeastern portion of the Atlantic Ocean, at depths of 500–1500 m, there are regular intrathermocline eddies that are characterized by high temperature and salinity. As these eddies interact with the ambient medium, they can transmit a dynamic signal to the ocean surface. These eddies are clearly identifiable on altimetric maps showing variations in the ocean’s surface level obtained by satellites. Such observations allow recording not only the complex interaction pattern of surface cyclonic and anticyclonic eddies, but also the processes of merging and separation of intrathermocline eddies.

Evolution of intrathermocline eddies moving over a submarine hill

Anticyclonic and cyclonic mediterranean eddies are formed on continental slopes of the Iberian Peninsula. Cyclonic eddies commonly live for 0.5–1 year at most. Anticyclonic eddies (meddies) live for 4–5 years, on average, but there are eddies of 7–8 years in age drifting at the distance of up to 6000 km from the region of its formation. According to the results of observations, in some regions of the Atlantic Ocean, the meddies are destructed partially or completely after contact with submarine mountains. However, it is impossible to trace evolution of the lens moving over the submarine obstacle by the field data. We studied the modeled influence of variable-height submarine hills on movement of cyclonic and anticyclonic intrathermocline eddies by the contour dynamics method. The evolution of lenses appeared to be quite sensitive to variations in hill height. Cyclonic and anticyclonic lenses interact with the hill in different ways. The data of unique field observations of Mediterranean lenses in the North Atlantic are confirmed by the results of our model experiments. Hence, it is possible to predict basic, similar to real, scenarios of interaction of intrathermocline eddies under conditions of complex bottom relief in the context of the three-layered ocean model.

Dynamics of Intrathermocline Lenses

The Mediterranean water outflowing with the bot� tom current from the Strait of Gibraltar occupies intermediate depths in the eastern part of the North Atlantic at depths from 800 to 1500 m (1). Anticy� clonic intrathermocline eddies (lenses) are regularly found in the water column of this water mass over the entire region of its spread. They are also filled with the Mediterranean water and are clearly distinguished by their high values of temperature and salinity. This dis� tinguishing property from the surrounding waters in the core of the lens can vary from 1 to 4 °C by the tem� perature and from 0.3 to 1.0 psu by the salinity depending on the distance of the lens from the region of its formation (1). At the same time, the influence of lenses on the density field is strongly mutually com� pensated, and the lens core is characterized by homo� geneous water density. The absolute values of water density σ0 in the cores of the lenses vary from 27.5 to 28.2, while the cores can be located at depths from 800 to 1400 m (2). The available catalogue of the main characteristics

Interaction of a two-layer vortex pair with a submerged cylindrical obstacle in a two layer rotating fluid

We consider the dynamics of a two-layer compensated vortex pair (heton) interacting with a submerged cylindrical obstacle of small height located in the lower layer of a two-layer fluid in the f-plane. The pair consists of two counter-rotating vortices of equal strengths each located in different layers of the two-layer rotating fluid. We make use of two approaches. The first one considers a model of point vortices, and the second one assumes the vortices as finite-core vorticity patches analyzed by means of contour dynamics techniques. The point vortex model features two regimes of the pair’s motion: an unbounded motion as the pair advances to infinity after being deflected by the cylindrical obstacle and an oscillatory motion inside a bounded region near the cylindrical obstacle. The oscillations, in turn, are of two types. The first corresponds to a finite yet unpredictable number of vortex revolutions near the cylinder, and the second results in an infinite number of revolutions. By exploiting contour...

Vortex merger in surface quasi-geostrophy

The merger of two identical surface temperature vortices is studied in the surface quasi-geostrophic 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.

Geostrophic tripolar vortices in a two-layer fluid: Linear stability and nonlinear evolution of equilibria

We investigate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can co-exist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabout...