Steady two-dimensional free-surface flow over semi-infinite and finite-length corrugations in an open channel

Free-surface flow past a semi-infinite or a finite-length corrugation in an otherwise flat and horizontal open channel is considered. Numerical solutions for the steady flow problem are computed using both a weakly nonlinear and fully nonlinear model. The new solutions are classified in terms of a depth-based Froude number and the four classical flow types (supercritical, subcritical, generalized hydraulic rise, and hydraulic rise) for flow over a small bump. While there is no hydraulic fall solution for semi-infinite topography, we provide strong numerical evidence that such a solution does exist in the case of a finite-length corrugation. Numerical solutions are also found for the other flow types for either semi-infinite or finite-length corrugation. For subcritical flow over a semi-infinite corrugation, the free-surface profile is found to be quasiperiodic downstream.