The effect of an isolated submarine obstacle on the motion of fluid particles in a periodic external flow is studied within the framework of the barotropic, quasi-geostrophic approximation on f-plane. The concept of background currents advanced by Kozlov [1995. Background currents in geophysical hydrodynamics. Izvestia, Atmos. Oceanic Phys. 31 (2), 245–250] is used to construct a dynamically consistent stream function satisfying the potential vorticity conservation law. It is shown that a system of two topographic vortices revolving about a rotation center can form in a circular external flow. Unsteady periodic perturbations, associated with either variations in the background current or deviations of the external flow from circulation, are analyzed. Unsteadiness in the external flow essentially complicates the pattern of the motion of fluid particles. Vortex-type quasi-periodic structures, identified with nonlinear resonances that form in Lagrangian equations of fluid particle advection, are examined. They either surround the stationary configuration by a vortex chain—a ringlet-like structure [Kennelly, M.A., Evans, R.H., Joyce, T.M., 1985. Small-scale cyclones on the periphery of Gulf Stream warm-core rings. J. Geophys. Res. 90(5), 8845–8857], or they form a complex-structure multivortex domain. Asymptotic estimates and numerical modeling are used to study the distribution and widths of the nonlinear resonance domains that appear under unsteady perturbations of different types. The onset of chaotic regimes owing to the overlapping of nonlinear resonance domains is analyzed. Transport fluxes determined by chaotic advection and barriers for transport (KAM-tori) and the conditions of their existence are studied. The relation of the rotation frequency of fluid particles on their initial position (when the dependence is calculated in the undisturbed system) is shown to completely determine the main features of the pattern of Lagrangian trajectories and chaotization effects. Because of nonlinear effects, the domain involved in quasi-periodic and chaotic motions can be much larger than the domain occupied by steady topographic vortices. The results of study by Sokolovskiy et al. [1988. On the influence of an isolated submerged obstacle on a barotropic tidal flow. Geophys. Astrophys. Fluid Dyn. 88(1), 1–30] concerning the due regard on the irrotational background component as the necessary factor for the transportation of fluid particles from the vortex domain to infinity are confirmed.

Persian Gulf Water and Red Sea Water are salty and dense waters flowing at intermediate depths in the Gulf of Oman and the Gulf of Aden, respectively. Their spreading pathways are influence by mesoscale eddies that dominate the surface flow in both semi-enclosed basins. In situ measurements combined with altimetry indicate that Persian Gulf Water is stirred in the form of filaments and submesoscale structures by mesoscale eddies. In this paper, we study the formation and the life cycle of intense submesoscale vortices and their potential impact on the spreading of Persian Gulf Water and Red Sea Water. We use a primitive-equation three-dimensional hydrostatic model at a submesoscale-resolving resolution to study the evolution of submesoscale vortices. Our configuration idealistically mimics the dynamics in the Gulf of Oman and the Gulf of 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. First, intense vorticity filaments are generated over the continental slope due to frictional interactions of the background flow with the sloping topography. These filaments are shed into the ocean interior and undergo horizontal shear instability that leads to the formation of submesoscale coherent vortices. The second mechanism is inviscid and features baroclinic instabilities arising at depth due to the weak stratification. Submesoscale vortices subsequently drift away, merge and form larger vortices. They can also pair with opposite-signed vortices and travel across the domain. They eventually dissipate their energy via several mechanisms, in particular fusion into the larger eddies or erosion on the topography. Since no submesoscale flow clearly associated with the fragments of Persian Gulf Water was observed in situ, we modeled Persian Gulf Water as Lagrangian particles. 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, without 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 potentially important role of submesoscale eddies in spreading Persian Gulf Water and Red Sea Water.

The chaotization of a vortical flow caused by a nonstationary incident flow is studied by the examples of several dynamically consistent models. It is shown that for relatively small values of excitation amplitude, the chaotization of such flows and, correspondingly, chaotic transport of passive scalars is determined by a small number of nonlinear resonances with frequencies close to the excitation frequency. Hence, the analysis of locations and overlaps of these resonances in the considered models makes it possible to derive fairly good estimates of excitation frequencies that are optimal for the chaotic transport.

Quasi-geostrophic dynamics of an ellipsoidal vortex embedded in a nonuniform flow is studied in the approximation of the infinitely deep rotating ocean with a constant buoyancy frequency. The vortex core is an ellipsoid with a constant vorticity different from the background vorticity value. The core is shown to move along with the flow and to deform under the effect of it. Regimes of the core's behavior depend on the flow characteristics and the initial values of the vortex parameters (the shape and the orientation relative to the flow). These regimes are (i) rotation (along with the eccentricity oscillation), (ii) oscillation about one of the two specific directions (along with the eccentricity oscillation), and (iii) infinite horizontal elongation of the core. The localized regimes (rotation and oscillation) of the core motion are analyzed. It is shown, that zones of the water mass capturing can appear in the induced velocity field. The mechanisms of fluid particle trajectory chaotization are revealed; in particular, it is shown that, owing to the double periodicity of the core motion, all the nonlinear resonances appear as pairs of two resonance islands with the same winding number.

By employing an analytical model for a constant-vorticity distributed vortex, namely, the ellipsoidal vortex embedded in a constant buoyancy frequency shear flow, the problem of the passive scalar transport through the vortex's boundary is addressed. Since the model's governing equations do not allow such transition to occur, we implement a low-scale diffusion process into the vortex model. Taking into consideration the diffusion term, we study the passive scalar transport in a steady state (the boundary of the ellipsoidal vortex does not change in time) and in a perturbed state (the boundary of the ellipsoidal vortex changes in time periodically) within the time scope corresponding to the characteristic life cycle of a mesoscale oceanic eddy. An increase of the passive scalar transport through the boundary in the perturbed state in comparison with the steady state due to the irregular dynamics of the surrounding flow is shown. The applicability scopes of the investigation for studying oceanic eddies in nature are discussed.