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The Quarterly Journal of Mechanics and Applied Mathematics 1949 2(1):64-71; doi:10.1093/qjmam/2.1.64
© 1949 by Oxford University Press
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THE FORMATION OF CLOSED WAKES IN FLUID MOTIONS

D. N. DE G. ALLEN

( Imperial College London )

Southwell and Vaisey (1) (1946) have applied relaxation methods to obtain a variety of solutions to problems of two-dimensional (steady) motion in an inviscid fluid. These are concerned with the determination of ‘free’ streamlines, and include one type of solution which is believed to be new, in that examples have been found of a flow which exhibits a junction of two ‘free’ streamlines. At such a junction the wake boundary must be cuspidal, and a remark of Sir Geoffrey Taylor about the existence of such cusps has stimulated this investigation. It was undertaken with the aim of finding a solution of cuspidal type by orthodox mathematical analysis, i.e. by an extension of the classical method (using conformal transformation) which was employed by Helmholtz, Kirchhoff, and Rayleigh.


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