Effect of uniform wind flow on modulational instability of two crossing waves over finite depth water

Sumana Kundu, Suma Debsarma, K. P. Das

Abstract


The effect of uniform wind flow on modulational instability of two crossing waves is
studied here. This is an extension of an earlier work to the case of a finite-depth water
body. Evolution equations are obtained as a set of three coupled nonlinear equations
correct up to third order in wave steepness. Figures presented in this paper display the
variation in the growth rate of instability of a pair of obliquely interacting uniform wave
trains with respect to the changes in the air-flow velocity, depth of water medium and
the angle between the directions of propagation of the two wave packets. We observe
that the growth rate of instability increases with the increase in the wind velocity and the
depth of water medium. It also increases with the decrease in the angle of interaction of
the two wave systems.


doi:10.1017/S1446181118000172

Keywords


crossing seas, evolution equation, gravity waves, instability, wind effect.



DOI: http://dx.doi.org/10.21914/anziamj.v60i0.12375



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.