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Onset of cellular convection in a salinity gradient due to a lateral temperature gradient

Published online by Cambridge University Press:  29 March 2006

C. F. Chen
C. F. Chen
Affiliation:
Department of Mechanical, Industrial and Aerospace Engineering, Rutgers University, New Brunswick, New Jersey 08903
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Abstract

We consider the two-dimensional problem of a linearly stratified salt solution contained between two infinite vertical plates. The fluid and the plates are initially at the same temperature. At t = 0, one of the plates is given a step increase in temperature, while the other is maintained at the initial temperature. A time-dependent basic flow is thus generated. The stability of such a time-dependent flow is analysed using an initial value problem approach to the linear stability equations. The method consists of initially distributing small random disturbances of given vertical wavelength throughout the fluid. The disturbances may be in the vorticity, temperature or salinity. The linearized field equations are integrated numerically. The growth or decay of the kinetic energy of the perturbation delineates unstable and stable states. Results have been obtained for a wide range of gap widths. The critical wavelength and the critical Rayleigh number compare favourably with those obtained previously in both physical and numerical experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 63 , Issue 3 , 29 April 1974 , pp. 563 - 576
Copyright
© 1974 Cambridge University Press

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References

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