The effect of obstacle length and height in supercritical free-surface flow

Two-dimensional open channel flow past a rectangular disturbance in the channel bottom is considered in the case of supercritical flow, where the dimensionless flow rate is greater than unity. The response of the free surface to the height and length of a rectangular disturbance is investigated using the forced Korteweg-de Vries model of Michalski et al. (Theor Comput Fluid Dyn 38:511 - 530, 2024). A rich and complex structure of solutions is found as the length of the disturbance increases, especially in the case of a negative disturbance. As the length of the disturbance is decreased, some solutions approach those of the well-studied point forcing approximation, but there are other solutions, for a negative disturbance, that are not predicted by the point forcing model. The stability of steady solutions is then considered numerically with established pseudospectral methods.