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Two-layer geostrophic vortex dynamics. Part 1. Upper-layer V-states and merger

Published online by Cambridge University Press:  26 April 2006

L. M. Polvani ,
N. J. Zabusky  and
G. R. Flierl
L. M. Polvani
Affiliation:
Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Present address: Department of Mathematics, Room 2–339, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
N. J. Zabusky
Affiliation:
Institute for Computational Mathematics and Applications, Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA
G. R. Flierl
Affiliation:
Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

We generalize the methods of two-dimensional contour dynamics to study a two-layer rotating fluid that obeys the quasi-geostrophic equations. We consider here only the case of a constant-potential-vorticity lower layer. We derive equilibrium solutions for monopolar (rotating) and dipolar (translating) geostrophic vortices in the upper layer, and compare them with the Euler case. We show that the equivalent barotropic (infinite lower layer) case is a singular limit of the two-layer system. We also investigate the effect of a finite lower layer on the merger of two regions of equal-sign potential vorticity in the upper layer. We discuss our results in the light of the recent laboratory experiments of Griffiths & Hopfinger (1986). The process of filamentation is found to be greatly suppressed for equivalent barotropic dynamics on scales larger than the radius of deformation. We show that the variation of the critical initial distance for merger as a function of the radius of deformation and the ratio of the layers at rest is closely related to the existence of vortex-pair equilibria and their geometrical properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 205 , August 1989 , pp. 215 - 242
Copyright
© 1989 Cambridge University Press

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