On long waves in shallow water with shear flow

Abstract

Various evolution equations for long interfacial waves with shear flow are derived with the assumptions that: (1) the wavelength of the interfacial waves is much larger than the total depth of the fluids, and (2) that the spanwise dependence is much weaker than the streamwise dependence. A particular case of interest occurs when the interfacial waves are at or near direct resonance. In this case the Boussinesq equation replaces the Korteweg-de Vries equation. Various special solutions in two dimensions are discussed.