Internal waves in two-layer stratified flows

This paper deals with a problem of internal waves in a two-layer stratified fluid with a density that depends exponentially on the depth inside the layers and has a jump at the interface. The equation of second-order long-wave approximation, which describes solitary waves, is derived. The spectral properties of the equations of small perturbations of a horizontal piecewise constant flow are studied, and possible mechanisms for the shear instability of a stratified flow are characterized.