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Perturbation methods in boundary-layer theory

Published online by Cambridge University Press:  29 March 2006

W. H. H. Banks  and
P. G. Drazin
W. H. H. Banks
Affiliation:
Department of Mathematics, University of Bristol
P. G. Drazin
Affiliation:
Department of Mathematics, University of Bristol
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Abstract

To solve a mathematical problem involving a small parameter, it is customary to expand the solution in powers of that parameter. In singular cases the resultant linearized problem may be insoluble, and in some such cases it is appropriate to expand the solution in powers of the square-root of the small parameter. These cases are associated with bifurcation of the solution. The method is illustrated by applying it to the Falkner-Skan equation and to a problem in hydrodynamic instability. In particular, Hartree's conjecture, that near separation the skin friction vanes like the square-root of the appropriate parameter of the Falkner-Skan equation, is substantiated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 58 , Issue 4 , 22 May 1973 , pp. 763 - 775
Copyright
© 1973 Cambridge University Press

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