Modulational instability of obliquely interacting capillary-gravity waves over infinite depth

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Authors

  • S. Manna Department of Mathematics, Indian Institute of Engineering Science and Technology, India
  • A.K. Dhar Department of Mathematics, Indian Institute of Engineering Science and Technology, India

Abstract

Two coupled time-dependent two dimensional nonlinear Schrödinger equations have been derived using multiscale expansion for two nonlinearly interacting capillary-gravity waves over an infinite depth of water. These equations are then utilised to discuss the modulational (Benjamin-Feir) instability of two Stokes wavetrains due to unidirectional and bidirectional perturbations. It is found from the graphs and the three-dimensional contour plots that the rate of growth of instability for two wave packets interacting obliquely is higher than the instance of modulation of one wave packet. We have likewise examined the influence of capillarity on modulational instability.

Keywords:

nonlinear Schrödinger equation, crossing sea states, capillary-gravity waves, modulational instability