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Permanent Wave Structures and Resonant Triads in a Layered Fluid
Author(s) -
Bryant P. J.,
Laing A. K.
Publication year - 1978
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/sapm1978593223
Subject(s) - triad (sociology) , wavenumber , harmonics , mode (computer interface) , physics , harmonic , nonlinear system , wave equation , wave propagation , classical mechanics , mechanics , mathematical analysis , acoustics , optics , mathematics , quantum mechanics , psychology , voltage , computer science , psychoanalysis , operating system
A closed three layer fluid with small density differences between the layers has two closely related modes of gravity wave propagation. The nonlinear interactions between the wave modes are investigated, particularly the nearly resonant or significant interactions. Permanent wave solutions are calculated, and it is shown that a permanent wave of the slower mode can generate resonantly a wave harmonic of the faster mode. The equations governing resonant triads of the two modes are derived, and solutions having a permanent structure are calculated from them. It is found that some resonant triad solutions vanish when the triad is embedded in the set of all harmonics with wavenumbers in its neighborhood