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The symmetric state of a rotating fluid differentially heated in the horizonal

Published online by Cambridge University Press:  28 March 2006

Allan R. Robinson
Allan R. Robinson
Affiliation:
Pierce Hall, Harvard University
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Abstract

The motion of a fluid inside a rotating annulus of square cross-section, whose dimensions are small compared with the distance from the axis of rotation, is considered. The rigid side walls are held at different constant temperatures and the fluid motions that occur are strongly influenced by Coriolis accelerations. A detailed study is made of the azimuthally independent state, a Hadley cell, in the limit of small thermal Rossby number. It is convenient to employ a boundary layer type analysis, essentially with respect to the Taylor number and all the imposed boundary conditions are rigorously satisfied.

An entirely geostrophic thermal wind is found to obtain over the main body of the fluid. The circulation in the plane of the annular cross-section is entirely confined within narrow boundary layers and consists of a superposition of three cellular motions: a cell occupying the cross-section and two additional cells confined to the side-wall boundary layers. These motions are intimately related to the rotational constraint. The temperature distribution and its relation to the conductive and convective processes are determined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 6 , Issue 4 , November 1959 , pp. 599 - 620
Copyright
© 1959 Cambridge University Press

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