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

Two-dimensional free-surface flow past a submerged rectangular disturbance in an open channel is considered. The forced Korteweg–de Vries model of Binder et al. (Theor Comput Fluid Dyn 20:125–144, 2006) is modified to examine the effect of varying obstacle length and height on the response of the free-surface. For a given obstacle height and flow rate in the subcritical flow regime an analysis of the steady solutions in the phase plane of the problem determines a countably infinite set of discrete obstacle lengths for which there are no waves downstream of the obstacle. A rich structure of nonlinear behaviour is also found as the height of the obstacle approaches critical values in the steady problem. The stability of the steady solutions is investigated numerically in the time-dependent problem with a pseudospectral method.