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The Galerkin method applied to convective instability problems

Published online by Cambridge University Press:  28 March 2006

Bruce A. Finlayson
Bruce A. Finlayson
Affiliation:
Department of Chemical Engineering, University of Washington, Seattle, Washington 98105
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Abstract

The Galerkin method is applied in a new way to problems of stationary and oscillatory convective instability. By retaining the time derivatives in the equations rather than assuming an exponential time-dependence, the exact solution is approximated by the solution to a set of ordinary differential equations in time. Computations are simplified because the stability of this set of equations can be determined without finding the detailed solution. Furthermore, both stationary and oscillatory instability can be studied by means of the same trial functions. Previous studies which have treated only stationary instability by the Galerkin method can now be extended easily to include oscillatory instability. The method is illustrated for convective instability of a rotating fluid layer transferring heat.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 1 , 12 July 1968 , pp. 201 - 208
Copyright
© 1968 Cambridge University Press

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