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Spin-up of a strongly stratified fluid in a sphere

Published online by Cambridge University Press:  29 March 2006

Alfred Clark ,
Patricia A. Clark ,
John H. Thomas  and
Nien-Hon Lee
Alfred Clark
Affiliation:
Department of Mechanical and Aerospace Sciences University of Rochester, Rochester, New York
Patricia A. Clark
Affiliation:
Department of Mechanical and Aerospace Sciences University of Rochester, Rochester, New York
John H. Thomas
Affiliation:
Department of Mechanical and Aerospace Sciences University of Rochester, Rochester, New York
Nien-Hon Lee
Affiliation:
Department of Mechanical and Aerospace Sciences University of Rochester, Rochester, New York
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Abstract

A linear theory is developed for the spin-up of a compressible fluid, stratified by a spherical gravity field. Numerical results are obtained for the case of strong stratification (BruntVisl frequency N much greater than the rotation frequency 0). The interior flow is solved in terms of a set of angular eigenfunctions which have been obtained numerically. The principal result is that the spin-up is limited to a layer adjacent to the spherical boundary, the thickness of the layer being of the order of L(0/N), where L is the radius of the boundary. The solution is qualitatively similar to that found by Holton (1965), Walin (1969), and Sakurai (1969a, b) for a stratified fluid in a cylinder. The thickness of the spin-up layer diminishes with latitude , the variation being described roughly by the formula L0| sin |/N. For the case of slow continuous spin-up, the Ekman suction velocity has been calculated, and the results show that || = 24 is the dividing angle between suction (|| > 24) and blowing (|| < 24).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 45 , Issue 1 , 15 January 1971 , pp. 131 - 149
Copyright
Copyright © Cambridge University Press 1971

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