Benjamin-Ono dynamics of internal waves with currents

Abstract

Internal water waves arise when there is a change in density stratification in a fluid, which may occur in an oceanographical context due to variations in temperature, salinity, or other fluctuations in the equations of state. We present a derivation of nonlinear integrable models for the propagation of interfacial internal waves arising between two fluid layers of different densities (at the so called pycnocline). We examine the integrable Benjamin-Ono (BO) equation as an internal wave model, incorporating underlying currents by permitting a sheared current in both fluid layers. The BO equation arises for a specific small-amplitude asymptotic regime. We show that the BO soliton characteristics are strongly affected by the shear current parameters.