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

Sumana Kundu; Suma Debsarma; K. P. Das

doi:10.21914/anziamj.v60i0.12375

Authors

Sumana Kundu Salkia Mrigendra Dutta Smriti Balika Vidyapith (High)
Suma Debsarma Department of Applied Mathematics, University of Calcutta
K. P. Das Department of Applied Mathematics, University of Calcutta.

DOI:

https://doi.org/10.21914/anziamj.v60i0.12375

Keywords:

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

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

Author Biographies

Sumana Kundu, Salkia Mrigendra Dutta Smriti Balika Vidyapith (High)

Salkia Mrigendra Dutta Smriti Balika Vidyapith (High), Salkia, Howrah-711106.

Suma Debsarma, Department of Applied Mathematics, University of Calcutta

Professor, Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata 700009.

K. P. Das, Department of Applied Mathematics, University of Calcutta.

Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata 700009.