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Instabilities of dynamic thermocapillary liquid layers. Part 2. Surface-wave instabilities

Published online by Cambridge University Press:  20 April 2006

Marc K. Smith  and
Stephen H. Davis
Marc K. Smith
Affiliation:
Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201 Present address: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston, Illinois 60201
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Abstract

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to surface-wave instabilities that couple the interfacial deflection to the underlying shear flow. These instabilities are found to be directly related to the two-dimensional waves on an isothermal layer subject to wind shear as described by Miles and by Smith & Davis. Hence the surface-tension gradients are important only in that they drive the basic shear flow. The surface-wave stability characteristics for liquid layers with and without return-flow profiles are presented, and special attention is paid to long-wave instabilities. Comparisons are made with available experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 145 - 162
Copyright
© 1983 Cambridge University Press

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References

Benjamin, T. B. 1957 J. Fluid Mech. 2, 554.
Miles, J. W. 1960 J. Fluid Mech. 8, 593.
Scott, M. R. & Watts, H. A. 1975 Sandia Labs. Rep., SAND75-0198, Albuquerque.
Scott, M. R. & Watts, H. A. 1977 SIAM J. Num. Anal. 14, 40.
Sen, A. K. & Davis, S. H. 1982 J. Fluid Mech. 121, 163.
Smith, M. K. 1982 Ph.D. dissertation, Northwestern University.
Smith, M. K. & Davis, S. H. 1982 J. Fluid Mech. 121, 187.
Smith, M. K. & Davis, S. H. 1983 J. Fluid Mech. 132, 119.
Yih, C. S. 1963 Phys. Fluids 61, 321.