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On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 2. The development of a solution for plane Poiseuille flow and for plane Couette flow

Published online by Cambridge University Press:  28 March 2006

J. Watson
J. Watson
Affiliation:
National Physical Laboratory, Teddington, Middlesex
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Abstract

In Part 1 by Stuart (1960), a study was made of the growth of an unstable infinitesimal disturbance, or the decay of a finite disturbance through a stable infinitesimal disturbance to zero, in plane Poiseuille flow, and that paper gave the most important terms in a solution of the equations of motion. The greater part of the present paper is concerned with a re-formulation of this problem which readily yields the complete solution. By the same method a solution for Couette flow is obtained. This solution is only a formal one for the present because the conditions imposed in deriving the solution may not be valid for Couette flow; this flow is believed to be stable to infinitesimal disturbances of the type considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 9 , Issue 3 , November 1960 , pp. 371 - 389
Copyright
© 1960 Cambridge University Press

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References

Stuart, J. T. 1956a J. Aero. Sci. 23, 86.
Stuart, J. T. 1956b Z. angew. Math. Mech., Sonderheft, p. S.32.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353.
Watson, J. 1959 Aero. Res. Counc., Lond., Rep. no. 21, 189.