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A criterion for nonlinear wave stability

  • K. Hasselmann (a1)

Abstract

Nonlinear resonant wave triads composed of one finite and two infinitesimal components are unstable for sum interactions and neutrally stable for difference interactions. A similar criterion holds for tertiary interactions.

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References

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Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. 27, 41730. Part 2. Experiments. J. Fluid Mech. (to appear).
Davis, R. E. & Acrivos, A. 1967 The stability of oscillatory internal waves. J. Fluid Mech. 30, 723.
Hasselmann, K. 1966 Feynman diagrams and interaction rules of wave—wave scattering processes. Rev. Geophys. 4, 132.
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Kelly, R. E. 1967 On the stability of an inviscid shear layer which is periodic in space and time. J. Fluid Mech. 27, 65789.
Longuet-Higgins, M. S. & Phillips, O. M. 1962 Phase velocity effects in tertiary wave interactions. J. Fluid Mech. 12, 333336.
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Whitham, G. B. 1967 Variational methods and applications to water waves. Proc. Roy. Soc. A 299, 625.
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A criterion for nonlinear wave stability

  • K. Hasselmann (a1)

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