Transcritical flow over obstacles and holes: Forced extended Korteweg–de Vries framework

Abstract

A forced extended Korteweg-de Vries equation is used to simulate the transcritical flow of a density stratified fluid over localized topography. The extension of the usual Korteweg-de Vries equation is by the addition of a cubic nonlinear term as well as the usual quadratic nonlinear term, which is motivated by certain density stratifications, such as a two-layer fluid model. The case of negative forcing corresponds to a near-surface sharp pycnocline over an obstacle.