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Jeffery-Hamel boundary-layer flows over curved beds

Published online by Cambridge University Press:  21 April 2006

P. M. Eagles
P. M. Eagles
Affiliation:
Department of Mathematics, The City University, Northampton Square, London EC1V 0HB, UK
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Abstract

We find certain exact solutions of Jeffery-Hamel type for the boundary-layer equations for film flow over certain beds. If β is the angle of the bed with the horizontal and S is the arclength these beds have equation sin β = (const.)S−3, and allow a description of flows on concave and convex beds. The velocity profiles are markedly different from the semi-Poiseuille flow on a plane bed.

We also find a class of beds in which the Jeffery-Hamel flows appear as a first approximation throughout the flow field, which is infinite in streamwise extent. Since the parameter γ specifying the Jeffery-Hamel flow varies in the streamwise direction this allows a description of flows over curved beds which are slowly varying, as described in the theory, in such a way that the local approximation is that Jeffery-Hamel flow with the local value of γ. This allows the description of flows with separation and reattachment of the main stream in some cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 186 , January 1988 , pp. 583 - 597
Copyright
© 1988 Cambridge University Press

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