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Discontinuous velocity profiles for the Orr-Sommerfeld equation

Published online by Cambridge University Press:  28 March 2006

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

Simple ideas of dimensional analysis and of limiting cases are used to elucidate the stability characteristics of a steady basic parallel flow of a viscous incompressible fluid. The principal result is that the stability characteristics of a smoothly varying velocity profile for wave disturbances of small wave-number can be found by use of a discontinuous velocity profile. The boundary conditions for a disturbance at a discontinuity of the basic flow are derived, and are used to find the stability characteristics of broken-line representations of the hal-jet and jet. These findings are in agreement with previous ones.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 10 , Issue 4 , June 1961 , pp. 571 - 583
Copyright
© 1961 Cambridge University Press

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