On the accuracy of the stationary forced Korteweg-de Vries equation as a model equation for flows over a bump

Abstract

Considered are the stationary supercritical free-surface solitary waves and subcritical free-surface hydraulic falls in flows over a bump in a two-dimensional channel. The stationary forced Korteweg-de Vries equation (sfKdV) sometimes can be used to predict these solitary waves and hydraulic falls. This paper studies the deviation of the results deduced from the sfKdV from the exact solutions found by computations and experiments. The elucidation of this deviation (called the error) is by comparing the sfKdV results with the computational and experimental results since an analytic approach seems impossible. From the comparisons made in this paper and the previous studies in [6], we conclude that the sfKdV is a good model in the sense that the relative error is less than 10