Table of Contents
International Journal of Oceanography
Volume 2014, Article ID 597895, 9 pages
Research Article

Nonlinear Evolution Equations for Broader Bandwidth Wave Packets in Crossing Sea States

1Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700 009, India
2Department of Mathematics, Abhedananda Mahavidyalaya, Sainthia, Birbhum 731234, India

Received 14 February 2014; Accepted 2 May 2014; Published 9 June 2014

Academic Editor: Leonard Pietrafesa

Copyright © 2014 S. Debsarma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two coupled nonlinear equations are derived describing the evolution of two broader bandwidth surface gravity wave packets propagating in two different directions in deep water. The equations, being derived for broader bandwidth wave packets, are applicable to more realistic ocean wave spectra in crossing sea states. The two coupled evolution equations derived here have been used to investigate the instability of two uniform wave trains propagating in two different directions. We have shown in figures the behaviour of the growth rate of instability of these uniform wave trains for unidirectional as well as for bidirectional perturbations. The figures drawn here confirm the fact that modulational instability in crossing sea states with broader bandwidth wave packets can lead to the formation of freak waves.