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The Quarterly Journal of Mechanics and Applied Mathematics 1995 48(1):135-156; doi:10.1093/qjmam/48.1.135
© 1995 by Oxford University Press
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PLANE IRROTATIONAL FLOW AGAINST A POROUS PLATE

I. D. HOWELLS and R. T. WAECHTER

( St Leo's College, University of Queensland St Lucia, Queensland 4067, Australia
Department of Mathematics and Statistics, James Cook University Cairns, Queensland 4870, Australia )

The standard hodograph approach to irrotational flow with a free surface, past a solid obstacle, was extended by Cumberbatch (Q. Jl Mech. appt. Math. 35 (1982)) to the case of a porous plate, or mesh. He introduced a sink distribution at the mesh, satisfying an integral equation of the second airfoil type. Explicit solutions can then be given by quadratures. The present paper shows how the solution to the above case, and also to the case of jet flow against a mesh, can be expressed much more simply, and even in closed form for suitable values of one parameter. Motivation comes from the attempt to model the motion of spray droplets being blown over a row of vines or trees.


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