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Some aspects of the initial-value problem for the inviscid motion of a contained, rotating, weakly-stratified fluid

Published online by Cambridge University Press:  29 March 2006

J. S. Allen
J. S. Allen
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University
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Abstract

The initial-value problem for the linear, inviscid motion of a contained, rotating stratified fluid is considered in the limit of weak stratification, that is, for small values of the stratification parameter S = N2/Ω2, where N is the Brunt–Väisälä frequency and Ω is the rotational frequency. The limiting flow is of interest because, although the initial-value problem has been studied, both for the case of a homogeneous, rotating fluid and for the case of a stratified, rotating fluid, the exact relationship of the two flows, in the limit of vanishing stratification, is not straightforward. For example, the method of determining, from the initial conditions, the steady geostrophic component of the flow of a rotating, stratified fluid does not in general give a motion that reduces, in the limit S → 0, to the steady component of the flow of a homogeneous fluid. By including a consideration of slow unsteady motions that vary on a time scale dependent on the stratification parameter, the relationship of the limiting flow to the flow of a homogeneous fluid is established.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 1 , 15 March 1971 , pp. 1 - 23
Copyright
© 1971 Cambridge University Press

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