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The excitation of resonant triads by single internal waves

Published online by Cambridge University Press:  29 March 2006

By Seelye Martin ,
William Simmons  and
Carl Wunsch
By Seelye Martin
Affiliation:
University of Washington, Seattle
William Simmons
Affiliation:
Woods Hole Oceanographic Institution
Carl Wunsch
Affiliation:
Massachusetts Institute of Technology
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Abstract

The stability of progressive internal waves of modes 1 and 3, propagating down a long tank filled with a linearly stratified salt water solution, is studied theoretically and experimentally. Examination of the spectra of the waves shows when a1 > 10−2, where a is the wave amplitude and l is the vertical wavenumber, that single internal waves excite waves of several resonant triads, where the excited waves belong to that set of triads with the largest theoretical growth rates. For example, a wave of mode 3 with a non-dimensional frequency around 0.66 excites waves of the following triads: (5,8,3), (6,9,3), (8,11,3), (9,12,3) and (10,13,3), where the integers are mode numbers. The spontaneous appearance of these naturally excited triads greatly complicates attempts to isolate and study preselected wave interactions. In one case, when waves of mode 1 and 3 with al > 10−2 were generated simultaneously while tuned to the (1,3,4,7) multiple resonance, the fastest growing wave was neither a wave of mode 4 located at the difference frequency nor a wave of mode 7 at the sum frequency, but rather a wave of mode 9 located at a frequency slightly above that of the 4-wave.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 1 , 9 May 1972 , pp. 17 - 44
Copyright
© 1972 Cambridge University Press

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