Steady transcritical flow over a hole: Parametric map of solutions of the forced Korteweg-de Vries equation

Transcritical flow of a stratified fluid over an obstacle, or through a contraction, can be modeled by the forced Korteweg-de Vries equation, which describes a balance among weak nonlinearity, weak dispersion, and small forcing effects. Here we seek steady solutions with constant but different amplitudes upstream and downstream of the forcing region. Our interest is in the case when the forcing has negative polarity, which represents a hole. The effects of the width of the hole and the amplitude of the hole on these steady solutions are investigated. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3430607]