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Permanent Wave Structures on an Open Two Layer Fluid
Author(s) -
Bryant P. J.
Publication year - 1977
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1977573225
Subject(s) - harmonics , surface wave , free surface , envelope (radar) , surface (topology) , physics , nonlinear system , phase velocity , classical mechanics , mechanics , mathematics , optics , geometry , engineering , quantum mechanics , telecommunications , radar , voltage
There is a significant nonlinear interaction between fast free surface waves and slow interface waves when the group velocity of the free surface waves is the same as the phase velocity of the interface waves. This interaction leads to permanent wave structures consisting of a wave group of permanent envelope on the free surface and a wave of permanent shape on the interface. A theory is developed for periodic permanent wave structures of this type, from which solutions are found numerically. The theory includes all significant quadratic nonlinear interactions between free surface harmonics and interface harmonics, as well as between the interface harmonics themselves. It is found that there is a sequence of forms of differing free surface group structure.