Models for strongly-nonlinear evolution of long internal waves in a two-layer stratification

Models describing the evolution of long internal waves are proposed that are based on different polynomial approximations of the exact expression for the phase speed of uni-directional, fully-nonlinear, infinitely-long waves in the two-layer model of a density stratified environment. It is argued that a quartic KdV model, one that employs a cubic polynomial fit of the separately-derived, nonlinear relation for the phase speed, is capable of describing the evolution of strongly-nonlinear waves with a high degree of fidelity. The marginal gains obtained by generating higher-order, weakly-nonlinear extensions to describe strongly-nonlinear evolution are clearly demonstrated, and the limitations of the quite widely-used quadratic-cubic KdV evolution model obtained via a second-order, weakly-nonlinear analysis are assessed. Data are presented allowing a discriminating comparison of evolution characteristics as a function of wave amplitude and environmental parameters for several evolution models.