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The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(1):65-72; doi:10.1093/qjmam/hbm001
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Q. Jl Mech. Appl. Math, Vol. 60. No. 1 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Steady vortical flow around a finite plate

ER Johnson and NR McDonald{dagger}

( Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK )

{dagger} robb{at}math.ucl.ac.uk

Received 12 November 2006. Revise 21 December 2006. Accepted 22 December 2006.


  Abstract

An explicit solution for a layer of fluid with constant vorticity surrounding a thin plate of finite length is obtained using elementary conformal mapping methods. In the limit of large plate length the behaviour of the solution near the ends of the plate tends to that of the previously known solution for a semi-infinite plate. Contour dynamics is used to investigate the stability of the steady solutions.


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