A note on the potential flow past a lemniscate and a general method of Milne-Thomson

J. W. Miles, G. E. Backus
1968 Quarterly of Applied Mathematics  
Basset's (1885) solution for potential flow past a lemniscate is (a) disproved and (b) reproduced by a naive application of "a general method" of Milne-Thomson. The correct solution is also given. The result is of interest for Rayleigh scattering, as well as for potential theory. 1. Lemniscate in uniform flow. We seek the complex potential associated with uniform, plane, potential flow past a lemniscate. We follow Basset's [1], [2] terminology; Moon and Spencer [3] designate the generalized
more » ... the generalized lemniscate as a Cassini oval, and modern usage typically reserves lemniscate for the limiting figure (a = 0 below) of Bernoulli. Basset [1] introduces the coordinates £ and t? through the conformal mapping
doi:10.1090/qam/99844 fatcat:vpix7b7biffsvbcrx7a3fl6o4y