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Double-diffusive instability in an inclined fluid layer Part 2. Stability analysis

Published online by Cambridge University Press:  19 April 2006

R. C. Paliwal  and
C. F. Chen
R. C. Paliwal
Affiliation:
Department of Mechanical, Industrial and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey 08903 Present address: Electronic Associates, Inc., West Long Branch, N.J. 07764.
C. F. Chen
Affiliation:
Department of Mechanical, Industrial and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey 08903
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Abstract

Linear stability analysis is applied to the problem of a density-stratified fluid contained in an inclined slot being subjected to a lateral temperature gradient. Stability equations are solved using the Galerkin technique with 12 terms in the truncated expansion series. Within the range of θ considered, |θ| < 75°, critical instability was found to be of the stationary type. Results of critical thermal Rayleigh numbers and wavenumbers at all inclination angles are in good agreement with the experimental results obtained earlier (Paliwal & Chen 1980). Contrary to intuition, these results show that the system is more stable when the lower wall is heated. This is shown to be the result of the increased vertical solute gradient in the steady state prior to the onset of instabilities when the heating is from below.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 4 , 26 June 1980 , pp. 769 - 785
Copyright
© 1980 Cambridge University Press

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