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Nonlinear response of a rotating fluid to differential heating from below

Published online by Cambridge University Press:  21 April 2006

Charles Quon
Charles Quon
Affiliation:
Atlantic Oceanographic Laboratory, Department of Fisheries and Oceans, Bedford Institute of Oceanography, Dartmouth, N.S., Canada B2Y 4A2 and National Center for Atmospheric Research, Boulder, CO 80303, USA
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Abstract

This paper studies numerically the instabilities and quasi-steady states of thermal convection in a Boussinesq fluid within a unit square which is bounded rigidly on all sides, differentially heated on the bottom, insulated above, and rotating about a vertical axis. The flows for five ascending values of the thermal Rossby number β are studied for constant Prandtl number σ and infinitesimal Ekman number E. For small values of β, either transient or stationary spatial oscillations occur. The results agree with Daniels’ (1976) and Daniels & Stewartson's (1977, 1978) linear and weakly nonlinear theories in principle if not in detail. For large values of β. the flows are highly nonlinear. They undergo two distinct stages of instability and eventually settle down to steady states. It is shown that a viscous non-diffusive boundary layer can exist at steady state for large β. For the maximum value of β under investigation, only quasi-steady states have been reached in the interior. Inertial gravity waves are observed emanating from the unstable corner of the fluid. These numerical solutions establish that the initial instability is an exchange instability rather than a catastrophic one. The question of bifurcation has not been resolved.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 233 - 263
Copyright
© 1987 Cambridge University Press

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