Abstract
Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.
Highlights
Coherent vortex structures are ubiquitous in the ocean
It is worth noting that the dynamics of oceanic mesoscale features may be affected by the beta-effect, that is the change of the Coriolis frequency with the latitude, if the size and strength of the vortices do not comply with the f -plane approximation, p that is βL/ f ≈ O(1) and U/( βL2 ) ≈ O(1)
This review aims at presenting a short account of the dynamical phenomena attributed to the impact of deformation flows on vortices either with singular or distributed vorticity
Summary
Coherent vortex structures are ubiquitous in the ocean. Their horizontal scales range from kilometres to thousands of kilometres (as in large-scale ocean gyres) [1,2,3,4]. The singular vortex model is very useful in getting qualitative insights into the motion of coherent vortical structures in the ocean [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] It allows a simple formulation of multipolar vortex systems that are instrumental in studying stationary vortex configurations [49,50,51,52,53]. In the case of singular vortex systems, the nonstationarity originates from the vortex motion itself, whereas, in the case of an elliptic vortex, changing the vortex shape produces nonstationarity in the velocity field
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