Stability of interfacial waves between two bounded fluids

Abstract

Two-dimensional periodic gravity waves at the interface between two bounded fuids of di#erent densities are considered. Based on the Hamiltonian structure of the problem, the relation between wave frequency and wave amplitude is obtained through a weakly nonlinear analysis. All classeso f time- and spaceperiodic waves are studied: traveling and standing waves as well as a degenerate class of mixed waves. As opposedt o water waves,m ixed interfacia] wavese xist even in the absenceo f capillality. The stability of traveling and standing waves with respect to three-dimensional modulationo i8 then studied. By using the method of multiple scales, Davey-Stewartson-type equations are obtained. A detailed stability analysis i8 performed and reveals that while for longitudinal and oblique modulations standing and traveling waves have the same stability behavior, for transverse modulations standing waves are less stable than traveling waves.