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The generalized Lagrangian-mean equations and hydrodynamic stability

Published online by Cambridge University Press:  20 April 2006

A. D. D. Craik
A. D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland
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Abstract

The generalized Lagrangian-mean (GLM) formulation of Andrews & McIntyre (1978a, b) offers alternative physical concepts and possible saving of effort in calculation, as compared with the more conventional Eulerian-mean approach. Though most existing applications of this theory concern waves on weakly sheared mean flows, it is also suitable for study of waves in strong shear flows. The hydrodynamic stability of parallel shear flows is examined from this point of view. An appreciation is gained of the roles of Stokes drift, pseudomomentum, energy and pseudoenergy in this context, such understanding being a necessary prerequisite for future developments. Several known results of linear stability theory, including the inflexion-point and semicircle theorems, are concisely rederived from the GLM conservation laws.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 27 - 35
Copyright
© 1982 Cambridge University Press

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References

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