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The free surface on a liquid filling a trench heated from its side

Published online by Cambridge University Press:  29 March 2006

Daniel D. Joseph  and
Leroy Sturges
Daniel D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis
Leroy Sturges
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis
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Abstract

In this paper we compute the motion and the shape of the free surface on a liquid in a trench heated from its side. The analysis is based on Joseph's Lagrangian theory of domain perturbations, which is developed in general and through simple examples, chosen so as to make the comparison of the Lagrangian method with Stokes's Eulerian theory very clear. The perturbation problems are resolved analytically by application of biorthogonality conditions to a powerful set of biharmonic eigenfunctions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 3 , 10 June 1975 , pp. 565 - 589
Copyright
© 1975 Cambridge University Press

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