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The dissipative quasigeostrophic equations

Part of: Turbulence Rotating fluids

Published online by Cambridge University Press:  26 February 2010

A. F. Bennett  and
P. E. Kloeden
A. F. Bennett
Affiliation:
Mathematics Department, Monash University, Clayton 3168, Australia.
P. E. Kloeden
Affiliation:
Mathematics Department, Monash University, Clayton 3168, Australia.
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Abstract

Existence and uniqueness of classical solutions are established for the dissipative quasigeostrophic equations of geophysical fluid dynamics, using a priori estimates and a Schauder fixed point theorem. The flow is periodic in both horizontal directions and is bounded above and below by rigid flat surfaces. The Reynolds analogy of unit turbulent Prandtl number is assumed. Existence is proved for an arbitrary finite time, if it is further assumed that the surface temperatures vanish. Without this additional assumption existence is guaranteed only for a certain finite time, which is inversely proportional to the norms of the sources and initial conditions.

MSC classification

Secondary: 76F99: None of the above, but in this section 76U05: Rotating fluids
Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 265 - 285
Copyright
Copyright © University College London 1981

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