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The Quarterly Journal of Mechanics and Applied Mathematics 2005 58(3):481-501; doi:10.1093/qjmam/hbi024
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Q. Jl Mech. Appl. Math, Vol. 58. No. 3 © The Author 2005. Published by Oxford University Press 2005; all rights reserved. For Permissions, please email: journals.permissions@oupjournals.org

An analysis of a three-dimensional interactive boundary layer developing on a curved surface (criss-cross interaction)

K. N. Vonatsos**

( School of Accounting and Finance, The University of Manchester, Oxford Road, Manchester M13 9PL )

** konstantinos.vonatsos{at}manchester.ac.uk

This paper analyses a three-dimensional interactive boundary layer developing on a curved surface. The specific problem has no counterpart in two dimensions and a distinguishing characteristic is that the pressure gradient in the normal direction across the boundary layer is retained in the interactive problem. Initially, we demonstrate that the problem admits a double similarity solution which allows for the analytical derivation of the eigensolutions, providing important insight into the physical mechanism of upstream influence due to curvature. Next, the problem is also shown to admit a single similarity solution corresponding to a special geometry. For both cases (double and single similarity solutions) numerical methodologies are developed which solve the respective nonlinear interactive problems.

Received 6 August 2004. Revise 11 May 2005.


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