Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-29T20:09:51.945Z Has data issue: false hasContentIssue false
  • English
  • Français

On resonant triad interactions of acoustic–gravity waves

Published online by Cambridge University Press:  22 December 2015

Usama Kadri  and
T. R. Akylas
Usama Kadri
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
T. R. Akylas*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: trakylas@mit.edu
Get access Rights & Permissions [Opens in a new window]

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.

JFM classification

Acoustics: Acoustics Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 788 , 10 February 2016 , R1
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bretherton, F. P. 1964 Resonant interactions between waves. The case of discrete oscillations. J. Fluid Mech. 20, 457–479.Google Scholar
Craik, A. D. D.1985 Wave Interactions and Fluid Flows, p. 322. Cambridge University Press.Google Scholar
Dalrymple, R. A. & Rogers, B. D. 2006 A note on wave celerities on a compressible fluid. In Proceedings of the 30th International Conference on Coastal Engineering, pp. 3–13.Google Scholar
Kadri, U. & Stiassnie, M. 2013 Generation of an acoustic–gravity wave by two gravity waves, and their subsequent mutual interaction. J. Fluid Mech. 735, R6.Google Scholar
Kedar, S., Longuet-Higgins, M. S., Webb, F., Graham, N., Clayton, R. & Jones, C. 2008 The origin of deep ocean microseisms in the North Atlantic Ocean. Proc. R. Soc. Lond. A 464, 777–793.Google Scholar
Longuet-Higgins, M. S. 1950 A theory of the origin of microseisms. Phil. Trans. R. Soc. Lond. A 243, 1–35.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9, 193–217.CrossRefGoogle Scholar
Phillips, O. M. 1981 Wave interactions – the evolution of an idea. J. Fluid Mech. 106, 215–227.Google Scholar