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The effect of mainflow transverse velocities in linear stability theory

Published online by Cambridge University Press:  29 March 2006

T. S. Chen ,
E. M. Sparrow  and
F. K. Tsou
T. S. Chen
Affiliation:
University of Missouri-Rolla, Rolla, Missouri
E. M. Sparrow
Affiliation:
University of Minnesota, Minneapolis, Minnesota
F. K. Tsou
Affiliation:
Drexel University, Philadelphia, Pennsylvania
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Abstract

In studying the stability of the boundary layer with surface mass injection, a generalized version of the Orr–Sommerfeld equation was derived which takes account of the transverse velocity component in the mainflow. The new terms in the generalized Orr–Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem was solved numerically for a wide range of values of the mass injection intensity. It was found that the critical Reynolds number (based on the distance from the leading edge) decreases with increasing mass injection. The deviations between the critical Reynolds numbers from the generalized and conventional Orr–Sommerfeld equations have a different sign at low injection intensities from that at high injection intensities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 4 , 29 December 1971 , pp. 741 - 750
Copyright
© 1971 Cambridge University Press

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