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Uniformly valid solution of the Orr-Sommerfeld equation by a modified Heisenberg method

Published online by Cambridge University Press:  20 April 2006

Shunichi Tsugé  and
Hiroshi Sakai
Shunichi Tsugé
Affiliation:
Institute of Engineering Mechanics, University of Tsukuba, Sakura. Ibaraki 305. Japan
Hiroshi Sakai
Affiliation:
Institute of Engineering Mechanics, University of Tsukuba, Sakura. Ibaraki 305. Japan
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Abstract

The classical Heisenberg method of solving the Orr–Sommerfeld equation is modified in such a way that inner and outer expansions are replaced by a uniformly valid successive approximation in which no data on the second derivative of the parallel shear profile are needed. It is shown that this feature enables us to calculate stability characteristics for wider classes of flows with improved accuracy. As a preliminary check for validity of the method, stability of the Blasius flow is calculated and compared with existing methods. It turns out that the method works for high Reynolds numbers, up to about 105, and that the expressions for the eigenfunctions and the eigenvalue condition are much simpler than those found by existing methods.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 153 , April 1985 , pp. 167 - 183
Copyright
© 1985 Cambridge University Press

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