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

Miles, J. W.; Backus, G. E.

doi:10.1090/qam/99844

Authors: J. W. Miles and G. E. Backus
Journal: Quart. Appl. Math. 26 (1968), 441-442
DOI: https://doi.org/10.1090/qam/99844
MathSciNet review: QAM99844
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Abstract | References | Additional Information

Abstract: 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.

A. Basset, On the motion of a liquid in and about certain quartic and other cylinders, Quart. J. Pure Appl. Math. 20, 234-250 (1885)

A. B. Basset, A treatise on hydrodynamics with numerous examples, Dover Publications, Inc., New York, 1961. MR 0134559
P. Moon and D. E. Spencer, Field theory handbook, 2nd ed., Springer-Verlag, Berlin, 1988. Including coordinate systems, differential equations and their solutions. MR 947546
Horace Lamb, Hydrodynamics, 6th ed., Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1993. With a foreword by R. A. Caflisch [Russel E. Caflisch]. MR 1317348

Lord Rayleigh, On the incidence of aerial and electric waves on small obstacles. . ., Phil. Mag. 44, 28-52 (1897); Scientific papers, vol. 4, pp. 305-326

L. M. Milne-Thomson, Theoretical hydrodynamics, The Macmillan Co., New York, 1960. 4th ed. MR 0112435