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On Green's functions for small disturbances of plane Couette flow

Published online by Cambridge University Press:  11 April 2006

Philip S. Marcus  and
William H. Press
Philip S. Marcus
Affiliation:
Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540
William H. Press
Affiliation:
Center for Astrophysics and Department of Physics, Harvard University, Cambridge, Massachusetts 02138
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Abstract

The linearized stability of plane Couette flow is investigated here, without using the Orr–Sommerfeld equation. Rather, an unusual symmetry of the problem is exploited to obtain a complete set of modes for perturbations of the unbounded (no walls) flow. An explicit Green's function is constructed from these modes. The unbounded flow is shown to be rigorously stable. The bounded case (with walls) is investigated by using a ‘method of images’ with the unbounded Green's function; the stability problem in this form reduces to an algebraic characteristic equation (not a differential-equation eigenvalue problem), involving transcendental functions defined by integral representations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 3 , 9 March 1977 , pp. 525 - 534
Copyright
© 1977 Cambridge University Press

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