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New similarity solutions of the unsteady incompressible boundary-layer equations


Ludlow, DK and Clarkson, PA and Bassom, AP, New similarity solutions of the unsteady incompressible boundary-layer equations, Quarterly Journal of Mechanics and Applied Mathematics, 53, (2) pp. 175-206. ISSN 0033-5614 (2000) [Refereed Article]

Copyright Statement

Copyright Oxford University Press 2000

DOI: doi:10.1093/qjmam/53.2.175


The 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.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107382
Year Published:2000
Web of Science® Times Cited:41
Deposited By:Mathematics and Physics
Deposited On:2016-03-11
Last Modified:2016-07-08

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