Modulational instability of two obliquely interacting interfacial waves in the presence of a basic current shear

Abstract

Evolution equations are derived for two obliquely interacting interfacial waves in the presence of a basic current shear. Using these equations modulational instability analysis is carried out for a pair of obliquely interacting uniform wave trains considering both unidirectional and bidirectional perturbations. It is found that the region of instability reduces in the presence of a basic current shear. Variations in the perturbed wavenumber at marginal stability due to changes in wave steepness and vorticities in the two mediums are displayed graphically. The maximum growth rate of instability for unidirectional perturbations increases with the increase in vorticity in the lower layer, but the reverse effect is observed when the vorticity in upper layer increases. The maximum growth rate of instability decreases with the increase in the angle of interaction of the two wave packets when the angle is acute, but the effect is opposite when the angle is obtuse.