The influence of wind on the evolution of two random wavetrains on deep water

We have studied the effect of randomness on the stability of interfacial gravity waves on deep water in the presence of uniform wind flow. The fourth-order nonlinear evolution equations for two Stokes wavetrains are used here to obtain the wave-kinetic equations for narrow-band of gravity wavetrains. Employing these kinetic equations we have then made the stability analysis of two initially homogeneous Lorentz form of wave spectra subject to infinitesimal perturbations. The effect of randomness is observed to reduce the growth rate and the extent of the instability region. The key result of the present analysis is that the fourth-order terms in the evolution equations significantly modify the modulational instability properties and produce a decrease on the growth rate. It is found that the growth rate of instability increases due to the effect of wind velocity.