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A note on the wave action density of a a viscous instability mode on a laminar free-shear flow

Published online by Cambridge University Press:  26 April 2006

Thomas F. Balsa
Thomas F. Balsa
Affiliation:
Departement of Acrospace and Mechanical Engineering University Arizona, Tucson AZ, 85721, USA
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Abstract

Using the assumptions of an incompressible and viscous flow at large Reynolds number, we derive the evolution equation for the wave action density of an instability wave travelling on top of a laminar free-shear flow. The instability is considered to be viscous; the purpose of the present work is to include the cumulative effect of the (locally) small viscous correction to the wave, over length and time scales on which the underlying base flow appears inhomogeneous owing to its viscous diffusion. As such, we generalize our previous work for inviscid waves. This generalization appears as an additional (but usually non-negligible) term in the equation for the wave action. The basic structure of the equation remains unaltered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 302 , 10 November 1995 , pp. 141 - 148
Copyright
© 1995 Cambridge University Press

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References

Balsa, T. F. 1989 Ampitude equations for wave packets in slightly inhomogeneous unstable flows. J. Fluid. Mech. 204, 433–455.(referred to herein as (B).Google Scholar
Betchov, R. & Szewczyk, A. 1963 Stability of a shear layer between parallel streams.. Phys. Fluids 6, 1391–1396Google Scholar
Hayes, W. D. 1970 Conservation of action and modal wave action. Proc. R. soc. Lond. A. 320, 187–208.Google Scholar
Ho, C.-M. & Huerrf, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid. Mech. 16, 365–424.Google Scholar
Hultgren, L. S. 1992 Nonlinear equilibration of an externally excited instability wave in a free shear layer.. J. Fluid. Mech. 236 635–664.Google Scholar
Michalke, A. 1974 Liner and Nonlinear waves. Wiley.