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A perturbation theory for the solitary-drift-vortex solutions of the Hasegawa-Mima equation

Published online by Cambridge University Press:  13 March 2009

Gordon E. Swaters
Gordon E. Swaters
Affiliation:
Applied Mathematics Institute, Department of Mathematics, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1
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Abstract

A multiple-scales adiabatic perturbation theory is presented describing the adiabatic dissipation of the solitary vortex-pair solutions of the Hasegawa-Mima equation. The vortex parameter transport equations are derived as solvability conditions for the asymptotic expansion and are identical with the transport equations previously derived by Aburdzhaniya et al. (1987) using an energy- and enstrophy-conservation balance procedure. The theoretical results are compared with high-resolution numerical simulations. Global properties such as the decay in the enstrophy and energy are accurately reproduced. Local properties such as the position of the centre of the vortex pair, decay of the extrema in the vorticity and stream-function fields, and the dilation of the vortex dipole are also in good agreement. In addition, time series of vorticity–stream-function scatter diagrams for the numerical simulations are presented to verify the adiabatic ansatz.

Type
Research Article
Information
Journal of Plasma Physics , Volume 41 , Issue 3 , June 1989 , pp. 523 - 539
Copyright
Copyright © Cambridge University Press 1989

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