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Abstract

Studies of the properties of vortex motions in a stably stratified and fast rotating fluid that can be described by the equation for the evolution of a potential vortex in the quasi-geostrophic approximation are reviewed. Special attention is paid to the vortices with zero total intensity (the so-called hetons). The problems considered include self-motion of discrete hetons, the stability of a solitary distributed heton, and the interaction between two finite-core hetons. New solutions to the problems of three or more discrete vortices with a heton structure are proposed. The existence of chaotic regimes is revealed. The range of applications of the heton theory and the prospects for its future application, particularly in respect, to the analysis of the dynamic stage in the development of deep ocean convection, are discussed.

Vortex Interactions Subjected to Deformation Flows: A Review

“…All these assumptions lead to the quasi-geostrophic approximation, which can be formulated in terms of the potential vorticity conservation law for quasi-two-dimensional fluids [79]. The review deals with such fluids, considering mesoscale vortices in barotropic and layered configurations [1,9,36,37,42,43,79].…”

“…The simplest vortex model is the singular (point-) vortex model [1,9,36,37,42,43,49,77,96,97,[100][101][102][103][104].…”

“…The system eq. (6), (10) can be regularly inverted to give explicit forms for the stream-functions [9,37,43,79]. Since the system is linear, all the contributions from each vortex and external flows can be considered separately, while the resulting stream-functions combine them all.…”

“…The first one is the classic model of singular vortices, which, more than 150 years after its introduction [28,29], is still widely used in a variety of applications ranging from nano-scale in superfluids [30][31][32] to cosmological scales in astrophysics [33]. The singular vortex model is also 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 also allows a simple formulation of multipolar vortex systems that are instrumental in studying stationary vortex configurations [49][50][51][52][53].…”

Vortex Interactions Subjected to Deformation Flows: A Review

“…The first one is the classic model of singular vortices, which, more than 150 years after its introduction [28,29], is still widely used in a variety of applications ranging from nano-scale in superfluids [30][31][32] to cosmological scales in astrophysics [33]. The singular vortex model is also 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 also allows a simple formulation of multipolar vortex systems that are instrumental in studying stationary vortex configurations [49][50][51][52][53].…”