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Resonant generation of finite‐amplitude waves by the uniform flow of a uniformly rotating fluid past an obstacle
Author(s) -
Grimshaw R.,
Yi Z.
Publication year - 1993
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s002557930001370x
Subject(s) - obstacle , amplitude , mathematics , rotational symmetry , flow (mathematics) , potential flow , mechanics , wave equation , standing wave , mathematical analysis , classical mechanics , physics , geometry , acoustics , optics , political science , law
In a previous paper (Grimshaw, 1990a) we showed that the resonant, or critical, flow of a rotating fluid past an axisymmetric obstacle placed on the axis of a cylindrical tube is described by a forced Korteweg‐de Vries equation for the amplitude of the dominant resonant mode. Here we show that in the anomalous but important case when the oncoming flow is uniform with uniform angular velocity a different theory is required which leads to an evolution equation describing finite‐amplitude waves. Some numerical solutions of this equation are described.