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On rotating thermal convection driven by non-uniform heating from below

Published online by Cambridge University Press:  20 April 2006

Phillip Hignett ,
Alan Ibbetson  and
Peter D. Killworth
Phillip Hignett
Affiliation:
Meteorological Office, Bracknell, Berkshire
Alan Ibbetson
Affiliation:
Department of Meteorology, University of Reading
Peter D. Killworth
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

Experiments are described in which a radial temperature gradient is maintained along the lower horizontal boundary of a rotating annulus containing a thermally convecting fluid; the vertical side walls and upper horizontal boundary are nominally insulating. Comparison is made with the non-rotating experiments of Rossby (1965) and the same general asymmetric circulation is observed, i.e. that of a weakly stratified interior of slowly descending fluid occupying most of the annular gap, overlying a thin thermal layer of large vertical temperature gradients, stable over the cold part of the base and statically unstable over the warmer part; the circulation is completed by a narrow region of rising motion at the warm end of the base.

A boundary-layer scaling analysis demonstrates the existence of six flow regimes, depending on the magnitude of a quantity Q defined such that Q is the square of the ratio of the (non-rotating) thermal-layer scale to the Ekman-layer scale. For small Q the flow is only weakly modified by rotation but as Q increases past unity rotation tends to thicken the thermal layer. Also presented are some numerical similarity solutions for the special case of a quadratic temperature distribution on the lower boundary and partially covering the range of Q achieved in the experiments, which is zero to ten. Above a certain critical value of Q (for the geometry used here Qc = 3·4) a baroclinic wave regime exists but is not examined in detail here although a brief discussion of an instability problem is given. Throughout comparisons are drawn between the experimental results and theoretical aspects of the problem.

It is thought that the essential features of a system thermally driven in this way have their counterparts in natural systems such as the large-scale thermally induced ocean circulation driven by the latitudinal variation of incoming solar radiation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 161 - 187
Copyright
© 1981 Cambridge University Press

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