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Fixed-flux convection in a tilted slot

Published online by Cambridge University Press:  26 April 2006

Paola Cessi  and
W. R. Young
Paola Cessi
Affiliation:
Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093, USA Permanent address: Istituto FISBAT-CNR, Bologna. Italy.
W. R. Young
Affiliation:
Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093, USA
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Abstract

We study fixed-flux convection in a long, narrow slot which is inclined to the horizontal. (Gravity is in the vertical direction, and horizontal is perpendicular to this.) Because of the fixed-flux boundary conditions the convective modes have much larger lengthscales in the along-slot direction than in the transverse direction. In the case of a horizontal slot this disparity in scales has been previously exploited to obtain an amplitude equation for the single mode which first becomes unstable as the Rayleigh number is increased above critical. When the slot is tilted we show that there is a distinguished limit in which there are two active modes in the slightly supercritical regime. This new limit is when the horizontal wavenumber, the supercriticality, and the tilt of the slot away from vertical, are all small. A modification of the well-known expansion for fixed flux convection in a horizontal slot leads to a coupled system of partial differential equations for the amplitudes of the two modes.

Numerical solution of this system suggests that all initial conditions eventually evolve into one of the two states, both of which consist of a single, steady roll in the cavity. The states are distinguished by the direction of circulation of the roll, and by the buoyancy fields, which are quite different in the two cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 237 , April 1992 , pp. 57 - 71
Copyright
© 1992 Cambridge University Press

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