Modulational instability of two obliquely interacting waves with different carrier frequencies

Abstract

The paper investigates the crossing sea state situation characterized by two obliquely interacting water wave systems having different carrier frequencies in finite depth domain. Nonlinear evolution equations are derived to study the instability properties of two obliquely interacting uniform wave trains for both unidirectional and bidirectional perturbations. It is found that the growth rate of modulational instability increases with the decrease in angle of interaction of the two wave systems and also with the increase in the ratio of the carrier wave numbers of the two wave systems. The growth rate of instability decreases with the increase in water depth, while it increases with the increase in wave steepness of the second wave system.