On the sub-harmonic instabilities of three-dimensional interfacial gravity–capillary waves in infinite depths

Abstract

In order to analyze the stability of gravity–capillary short-crested waves propagating at the interface of two fluids of infinite depths, a numerical procedure has been developed using a collocation method. The three-dimensional wave is generated by an oblique reflection of a uniform wave train arriving at a vertical wall at some angle of incidence θ measured from the perpendicular to the wall. Fixing the reflection at angle θ=45°, and wave steepness at h=0.25, we studied the influence of the density ratio μ and the inverse Bond number δ on the unstable area and the growth rate. It was observed that the unstable regions and the maximum growth rate decrease when μ and δ increase. Also, we found that the dominant instability belongs to the Class Ib as in the case of free-surface gravity waves in deep water.