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Generation of an acoustic-gravity wave by two gravity waves, and their subsequent mutual interaction

Published online by Cambridge University Press:  29 October 2013

Usama Kadri  and
Michael Stiassnie
Usama Kadri*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Michael Stiassnie
Affiliation:
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria
*
†Email address for correspondence: usama.kadri@gmail.com
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Abstract

The nonlinear triad interaction of two opposing gravity waves with almost identical frequencies and one much longer acoustic-gravity wave is studied for non-resonance, as well as for exact resonance conditions. For non-resonance conditions the previously known results for a ‘bound’ acoustic-gravity wave are recovered. For resonance, or near-resonance conditions, where all three waves are ‘free waves’, the interaction is recurrent and the amplitude of the free acoustic-gravity wave turns out to be much larger than that known for the bound wave. The results for the recurrent evolution are given analytically, in terms of Jacobian elliptic functions and elliptic integrals.

JFM classification

Acoustics: Acoustics Compressible Flows: Compressible Flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 735 , 25 November 2013 , R6
Copyright
©2013 Cambridge University Press 

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Footnotes

‡

Permanent address: Faculty of Civil and Environmental Engineering, Technion, Haifa 32000, Israel

References

Ardhuin, F. & Herbers, T. H. C. 2013 Noise generation in the solid Earth, oceans, and atmosphere, from nonlinear interacting surface gravity waves in finite depth. J. Fluid Mech. 716, 316–348.CrossRefGoogle Scholar
Byrd, P. F. & Friedman, M. D. 1971 Handbook of Elliptic Integrals for Engineers and Scientists. Springer.CrossRefGoogle Scholar
Dalrymple, R. A. & Rogers, B. D. 2006 A note on wave celerities on a compressible fluid. In Proc. 30th Int. Conference on Coastal Engineering (ICCE) 2006, 2007, pp. 3–13.Google Scholar
Hasselmann, K. 1962 On the nonlinear energy transfer in a gravity wave spectrum. Part 1. General theory. J. Fluid Mech. 12, 481–501.CrossRefGoogle Scholar
Kartashova, E. 2010 Nonlinear Resonance Analysis, Theory, Computation, Applications. Cambridge University Press.CrossRefGoogle Scholar
Kibblewhite, A. C. & Wu, C. Y. 1991 The theoretical description of wave–wave interactions as a noise source in the ocean. J. Acoust. Soc. Am. 89, 2241–2252.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1950 A theory of the origin of microseisms. Philos. Trans. R. Soc. Lond. A 243, 1–35.Google Scholar
Shemer, L. & Stiassnie, M. 1985 Initial instability and long-time evolution of Stokes waves. In The Ocean Surface: Wave Breaking, Turbulent Mixing and Radio Probing (ed. Toba, Y. & Mitsuyasu, H.), pp. 51–57. D. Reidel.CrossRefGoogle Scholar