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The suppression of short waves by a train of long waves

Published online by Cambridge University Press:  26 April 2006

A. M. Balk
A. M. Balk
Affiliation:
Applied Mathematics 217-50, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

It is shown that a train of long waves can suppress a short-wave field due to four-wave resonance interactions. These interactions lead to the diffusion (in Fourier space) of the wave action of the short-wave field, so that the wave action is transported to the regions of higher wavenumbers, where it dissipates more effectively. The diffusion equation is derived.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 315 , 25 May 1996 , pp. 139 - 150
Copyright
© 1996 Cambridge University Press

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References

Balk, A. M., Nazarenko, S. V. & Zakharov, V. E. 1990 On the nonlocal turbulence of drift type waves. Phys. Lett. A 146, 217–221.Google Scholar
Balk, A. M., Zakharov, V. E. & Nazarenko, S. V. 1990 Nonlocal turbulence of drift waves. Sov. Phys. JETP 71, 249–260.Google Scholar
Banner, M. L. 1973 An investigation of the role of short waves and wind drift in the interaction between wind and long gravity waves. PhD dissertation, The Johns Hopkins University.
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. J. Fluid Mech. 27, 417–430.Google Scholar
Crawford, D. R., Saffman, P. G. & Yuen, H. C. 1980 Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves. Wave Motion 2, 1–16.Google Scholar
Hasselmann, K. 1962 On the nonlinear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech. 12, 481–500.Google Scholar
Kolmogorov, A. N. 1941 Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 299–303.Google Scholar
Mitsuyasu, H. 1966 Interactions between water waves and wind. Rep. Res. Inst. Appl. Mech., Kyushu University 14, 67–88.Google Scholar
Phillips, O. M. & Banner, M. L. 1974 Wave breaking in the presence of wind drift and swell. J. Fluid Mech. 66, 625–640.Google Scholar
Yuen, H. G. 1988 Some recent experimental results on the effects of long waves on short waves under wind. In Nonlinear Topics in Ocean Physics. (ed. A. R. Osborne), pp. 915–922. North-Holland.
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2, 190–194.Google Scholar
Zakharov, V. E. 1992 Inverse and direct cascade in the wind-driven surface wave turbulence and wave breaking. In Breaking Waves: IUTAM Symposium (ed. M. L. Banner & R. H. Grimshaw) pp. 69–91. Springer.
Zakharov, V. E. & Filonenko, N. N. 1966 The energy spectrum for stochastic oscillations of a fluid's surface. Sov. Phys.-Dokl. 11, 881–883.Google Scholar
Zakharov, V. E., Musher, S. L. & Rubenchik, A. M. 1985 Hamiltonian approach to the description of nonlinear plasma phenomena. Phys. Reports 129, 285–366.Google Scholar