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On stability of parallel flow of an incompressible fluid of variable density and viscosity

Published online by Cambridge University Press:  24 October 2008

P. G. Drazin
P. G. Drazin
Affiliation:
Department of Mathematics, University of Bristol
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Abstract

Some aspects of generation of water waves by wind and of turbulence in a heterogeneous fluid may be described by the theory of hydrodynamic stability. The technical difficulties of these problems of instability have led to obscurities in the literature, some of which are elucidated in this paper. The stability equation for a basic steady parallel horizontal flow under the influence of gravity is derived carefully, the undisturbed fluid having vertical variations of density and viscosity. Methods of solution of the equation for large Reynolds numbers and for long-wave disturbances are described. These methods are applied to simple models of wind blowing over water and of fresh water flowing over salt water.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 4 , October 1962 , pp. 646 - 661
Copyright
Copyright © Cambridge Philosophical Society 1962

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