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Doubly symmetric finite-core heton equilibria

Published online by Cambridge University Press:  15 August 2012

V. G. Makarov,
M. A. Sokolovskiy and
Z. Kizner
V. G. Makarov
Affiliation:
Interdisciplinary Center of Marine Sciences of the National Polytechnic Institute, La Paz, Baja California Sur 23096, Mexico
M. A. Sokolovskiy
Affiliation:
Water Problems Institute of the Russian Academy of Sciences, 3 Gubkina Str. 119333, Moscow, Russia
Z. Kizner*
Affiliation:
Departments of Physics and Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
*
†Email address for correspondence: Ziv.Kizner@biu.ac.il
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Abstract

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A finite-core heton is a baroclinic $f$-plane modon of a special type: it is composed of two patches of uniform quasi-geostrophic potential vorticity (PV) residing in different layers of a two-layer rotating fluid. This paper focuses on numerical construction of steadily translating, doubly symmetric, finite-core hetons and testing their stability. Such a heton, which possesses symmetry about the translation axis and the transverse axis, is a stationary solution to the equations of PV conservation in each of the layers when considered in a comoving frame of reference. When constructing the heton solutions and examining their bifurcations, we identify a heton by a pair of independent non-dimensional parameters, the half-length (in the translation direction) of a PV patch and the distance of the front point of the upper patch from the translation axis. The advantage of this method over other tried approaches is that it allows one to obtain solutions of new, previously unknown types. The results of testing the heton stability are presented on the plane made by a mean radius of a PV patch and the (horizontal) separation between the centroids of the patches. Two kinds of stability are tested separately, the stability to arbitrary perturbations that do not preserve the symmetry of the initial state and the stability to so-called symmetric perturbations that do not violate the initial symmetry. The hetons comparable in size with the Rossby radius, and smaller, are always stable in both senses. However, when some critical size is exceeded, the heton stability becomes dependent on the separation, and the larger the heton, the higher the separation required for stability. The separation guaranteeing the stability to symmetric perturbations is smaller than that required for the stability to arbitrary perturbations. Interrelations between instabilities and bifurcations are briefly discussed.

JFM classification

Vortex Flows: Contour dynamicsGeophysical and Geological Flows: Rotating flowsVortex Flows: Vortex instability

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 708 , 10 October 2012, pp. 397 - 417
Copyright
Copyright © Cambridge University Press 2012

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