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

Abstract EN

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.