Internal wave evolution in a space-time varying field

An extended Korteweg-de Vries (KdV) equation is derived that describes the evolution and propagation of long interfacial gravity waves in the presence of a strong, space-time varying background. Provision is made in the deriv ation for a spatially varying lower depth so that some topographic effects can also be included. The extended KdV model is applied to some simple scen arios in basins of constant and varying depths, using approximate expressio ns for the variable coefficients derived for the case when the background f ield is composed of a moderate-amplitude ultra-long wave. The model shows t hat energy can be transferred either to or from the evolving wave packet de pending on the relative phases of the evolving waves and the background var iation. Comparison of the model with laboratory experiments confirms its ap plicability and usefulness in examining the evolution of weakly nonlinear w aves in natural systems where the background state is rarely uniform or ste ady.