Analytical Solution of a Four-cusped Wake

Abstract

In his letter in Nature of May 10, Dr. R. V. Southwell discusses the question of finite wakes in the two-dimensional motion of an inviscid fluid. Solutions exhibiting a wake of cuspidal form had been obtained by Miss Vaisey using relaxation methods; and Sir Geoffrey Taylor had remarked that these methods (since they employ a finite mesh) could not rigorously establish the existence of such forms, in that they can never dispose of the possibility that a ‘splash’ occurs at what has been assumed to be a cuspidal junction. The size of the mesh used in the relaxation process can be made very small, but it must always remain finite, and within that finite interval some disturbance may remain undetected. Dr. Southwell expressed his hope of finding some exact analytical solution exemplifying a closed wake with a cuspidal junction.