Hamiltonian formulation of the problem of a single vortex evolution on a beta-plane
G.K. Korotaev
Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, Russian Federation
e-mail: korotaevgren@mail.ru
Abstract
Evolution of a single intense vortex on the ß-plane is studied based on the “elliptical approach” which was introduced by Legras and Dritschel for description of the eddies with uniform vorticity. A vortex is represented by two round patches of uniform vorticity – one inside another. One of them constitutes the vortex core and another – the trap zone. Radiation of the Rossby waves is not considered in this study. Application of the “elliptical approach” permits to generalize the earlier-proposed theory of intense vortex evolution on the ß-plane. Besides the Rossby and Zhukovsky–Kutta forces, it includes the inertia force in the equations describing the vortex motion. It is shown that the deduced system of equations is written down using non-canonical variables; and it can be represented in the generalized Hamiltonian form in case the vortex motion equations are supplemented with the equation of absolute vorticity conservation. Being analyzed, the deduced equations’ solutions show that they both provide new interpretation of the vortex self-propagation on the ß-plane and permit to characterize high-frequency oscillations of the vortex center position. Thus the represented theory permits to explain similar oscillations sometimes arising in the numerical experiments.
Keywords
intensive vortex, ß-plane, Hamiltonian formalism
For citation
Korotaev, G.K., 2016. Hamiltonian formulation of the problem of a single vortex evolution on a beta-plane. Physical Oceanography, (6), pp. 15-23. doi:10.22449/1573-160X-2016-6-15-23
DOI
10.22449/1573-160X-2016-6-15-23
References
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