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Spin down problem of rotating stratified fluid in thermally insulated circular cylinders

Published online by Cambridge University Press:  29 March 2006

Takeo Sakurai
Takeo Sakurai
Affiliation:
Department of Aeronautical Engineering, Kyoto University, Japan
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Abstract

A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing thermally insulated circular cylinder under the existence of stable distribution of the temperature is investigated within the framework of the Boussinesq approximation for a time duration of the order of the homogeneous-fluid spin down time in order to resolve the Holton-Pedlosky controversy. The explicit expression of the solution is obtained by the standard method and Holton's conclusion is confirmed. The secondary meridional current induced by the Ekman layers spins the fluid down to a quasi-steady state within the present time scale. However, unlike the homogeneous case, the quasi-steady state is not one of solid body rotation. The final approach to the state of rigid rotation is achieved via the viscous diffusion in the time scale of the usual diffusion time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 4 , 28 July 1969 , pp. 689 - 699
Copyright
© 1969 Cambridge University Press

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