Abstract Two-dimensional free-surface flow over a rectangular obstacle in the channel bottom is considered. Generalised hydraulic rise solutions (uniform supercritical flow upstream and a train of waves downstream) are examined using the forced Korteweg-de Vries model. A recently developed technique is expanded to consider all solutions in the infinite family of generalised hydraulic rises simultaneously. This new technique allows the effect of the height and length of the disturbance on the solution space to be understood in greater detail than previously possible. Using this method to examine the solutions with the largest waves shows the connection between the generalised hydraulic rise solutions and the supercritical solutions (uniform supercritical flow at both ends). By focussing on the smallest waves this method reveals parameter values where the special, waveless, hydraulic rise solutions can be obtained and other parameter values where the infinite family contains only generalised hydraulic rise solutions. All solution types are then mapped in the topographic parameter space. The behaviour of the solutions is then examined in the fully nonlinear potential flow model using established boundary integral methods.
Michalski et al. (Sun,) studied this question.