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New similarity solutions of the unsteady incompressible boundary-layer equations
journal contribution
posted on 2023-05-18, 17:49 authored by Ludlow, DK, Clarkson, PA, Andrew BassomAndrew BassomThe standard boundary-layer equations play a central role in many aspects of fluid mechanics as they describe the motion of a slightly viscous fluid close to a surface. A number of exact solutions of these equations have been found and here we extend the class of known solutions by implementing the Clarkson-Kruskal direct method (1) for finding similarity reductions. We demonstrate the existence of reductions which take the boundary-layer forms to lower-order partial differential systems and others which simplify them to the solution of ordinary differential equations. It is shown how not only do we recover many of the previously known exact solutions but also find some completely new forms.
History
Publication title
Quarterly Journal of Mechanics and Applied MathematicsVolume
53Pagination
175-206ISSN
0033-5614Department/School
School of Natural SciencesPublisher
Oxford Univ PressPlace of publication
Great Clarendon St, Oxford, England, Ox2 6DpRights statement
Copyright Oxford University Press 2000Repository Status
- Restricted