Modulational instability of two crossing waves in the presence of wind flow

In this study, we investigate modulational instability in the presence of wind flow in a situation where sea states crossed over water with a finite depth. It is assumed that the wind flows in a specific direction to produce angles with two directions of propagation by two wave systems with the same carrier wave number and same frequency. The evolution equations considered in this study represent a balance among the effects of wind forcing, dispersion, and nonlinearity at the lowest order. These evolution equations are used to study the stability of the uniform wave solution in crossing seas. We show that in the presence of wind flow, the uniform waves grow super-exponentially. We also demonstrate that the region of asymptotic instability in the perturbed wave number plane is larger than that in the absence of wind flow.