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Double-diffusive instabilities at a sloping boundary

Published online by Cambridge University Press:  26 April 2006

O. S. Kerr
O. S. Kerr
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
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Abstract

When a body of fluid with a vertical salinity and temperature gradient is bounded by a sloping boundary, convective instabilities are often observed. These can occur if the fluid is subjected to heating or the addition of solute at the boundary, or if the boundary is an insulator. These instabilities often take the form of long thin convection cells that are almost horizontal. We present a linear stability analysis of the background states associated with these different boundary conditions and derive criteria for their stability in terms of one non-dimensional parameter, Q. This parameter is related to the Rayleigh number and is a generalization of the similar parameter found by Kerr (1989) in his study of heating a salinity gradient from a vertical boundary. This analysis uses a quasi-static assumption that is valid when the vertical lengthscales of the instabilities are less than the horizontal lengthscales.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 225 , April 1991 , pp. 333 - 354
Copyright
© 1991 Cambridge University Press

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