The Forced Korteweg–de Vries Equation as a Model for Waves Generated by Topography

Abstract

This is a brief survey article discussing simple yet very rich models for free surface flows over topographical features. We consider the most interesting case where the flow is near critical (the Froude number is near 1). We derive Kortewegde Vries and Burgers‘ equations, and consider both steady configurations and time-dependent numerical solutions. The topography is taken to be either a localized bump or hole or a more extended plateau or depression. The calculations involving extended topography are new and in some cases show surprisingly complex dynamics.