Modulational instability of two obliquely interacting waves in two-layer fluid domain

Abstract

This research report is concerned with the derivation of two evolution equations of two obliquely interacting wave packets in a two-layer fluid domain in which the lower fluid is of infinite depth. These two evolution equations are then employed to perform stability analysis of two obliquely interacting uniform wave trains. Results of the stability analysis are shown graphically. It is observed that the growth rate of instability increases as the thickness of the upper lighter fluid increases. If the angle of interaction between the two waves is acute then the growth rate of instability decreases with the increase in the angle; but the result is reversed if the angle of interaction is obtuse. Also, the growth rate of instability of one wave train increases with the increase in the amplitude of the other wave train.