On resonant triad interactions of acoustic–gravity waves
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Kadri_Akylas_JFM_FINAL.pdf
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Author(s)
Kadri, Usama
Akylas, Triantaphyllos R.
Date Issued
December 2015
Journal
Journal of Fluid Mechanics
Publisher
Cambridge University Press
Citation
Kadri, Usama, and T. R. Akylas. “On Resonant Triad Interactions of Acoustic–gravity Waves.” Journal of Fluid Mechanics 788 (December 22, 2015).
Version
Author's final manuscript
Abstract
The propagation of wave disturbances in water of uniform depth is discussed, accounting for both gravity and compressibility effects. In the linear theory, free-surface (gravity) waves are virtually decoupled from acoustic (compression) waves, because the speed of sound in water far exceeds the maximum phase speed of gravity waves. However, these two types of wave motion could exchange energy via resonant triad nonlinear interactions. This scenario is analysed for triads comprising a long-crested acoustic mode and two oppositely propagating subharmonic gravity waves. Owing to the disparity of the gravity and acoustic length scales, the interaction time scale is longer than that of a standard resonant triad, and the appropriate amplitude evolution equations, apart from the usual quadratic interaction terms, also involve certain cubic terms. Nevertheless, it is still possible for monochromatic wavetrains to form finely tuned triads, such that nearly all the energy initially in the gravity waves is transferred to the acoustic mode. This coupling mechanism, however, is far less effective for locally confined wavepackets.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1017/jfm.2015.721
