Abstract
In this chapter, we consider the stability of an isolated finite-core (or distributed) two-layer vortex with respect to relatively small and finite perturbations. An analogy between a distributed heton and A-symmetrical structure of discrete hetons is demonstrated. The specific features of the nonlinear stage of evolution of unstable vortices, and the interaction between two distributed hetons or antihetons are considered. The model is shown to be promising for the description of deep-convection processes,water mass mixing in the ocean, and the formation of new quasistationary vortex structures. We study the effect of external flow and of an isolated hill on heton motion. The results obtained for a three-layer, quasigeostrophic model are given; in particular, specific features of the dynamics of meddies are studied. The role of baroclinicity in the formation of the kinematic and thermohaline structure of the ocean is analyzed.
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- 1.
The values of stratification parameters in most calculations considered here was chosen for qualitative comparison of this figure (and those similar to it, where perturbations of contours were determined by a set of random amplitudes) with the results of laboratory experiments in the work [395], assuming γ = 14.
- 2.
Note that we used variables of the type R = γ r as space variables in the problems of the theory of discrete vortices. Thus, an increase or a decrease in the distance can be interpreted as an appropriate change in the stratification parameter γ, which, in its turn, is responsible for the state of stability of a distributed two-layer vortex.
- 3.
Most part of this Section and, in particular, Figs. 3.23–3.29, adapted from [562] by permission of Cambridge University Press
- 4.
Legras and Dritschel [530], who compared the results of calculations by the pseudospectral method and with the use of CDM, note their qualitative agreement. However, the authors of [530] note that CDM is more convenient in studying the formation of vortex threads and the merging and separation of vortices.
- 5.
At the second stage of motion, the vortex structures in the left and right parts of this figure are analogs of interactions of the type {1a} for discrete vortices (Fig. 2.23).
- 6.
The role of filamentation in the merger of anticyclonic lenses is investigated in detail by Cushman-Roisin [193].
- 7.
- 8.
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Sokolovskiy, M.A., Verron, J. (2014). Dynamics of Finite-Core Vortices. In: Dynamics of Vortex Structures in a Stratified Rotating Fluid. Atmospheric and Oceanographic Sciences Library, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-00789-2_3
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