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Some mathematical problems in the theory of the stability of parallel flows

Published online by Cambridge University Press:  28 March 2006

C. C. Lin
C. C. Lin
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology
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Abstract

By applying the method of initial values to the theory of stability of shear flows, Case has recently found certain results which are in apparent conflict with those obtained by the theory of normal modes. It is shown how these differences may be reconciled. Some new features in the theory of normal modes are also brought out. The relative merits of the two theories are compared.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 10 , Issue 3 , May 1961 , pp. 430 - 438
Copyright
© 1961 Cambridge University Press

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References

Case, K. M. 1960 Stability of inviscid plane Couette flow. Phys. Fluids 3, 143.Google Scholar
Case, K. M. 1961 Hydrodynamic stability and the inviscid limit. J. Fluid Mech 10, 420.Google Scholar
Friedrichs, K. O. 1941 Fluid Dynamics (Brown University Lecture Notes), p. 209.
Langer, R. E. 1940 Butt. Amer. Math. Soc. 46, 257.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Lin, C. C. & Rabenstein, A. L. 1960 Asymptotic solutions of a class of differential equations of the fourth order. Trans. Amer. Math. Soc. 94, 24.Google Scholar