On the steady two-dimensional open channel flow

This note concerns the open channel flow problem. The flow is assumed to be steady (with constant discharge), two-dimensional (with non-hydrostatic pressure distribution), without both wave breaking and sediment transport. The flow problem consists in finding the location of the free surface, and the velocity and pressure fields. The problem solution is obtained by a hybrid model which incorporates the dissipation in potential flows. In order to set up the model, this note proposes a new Picard iteration for the potential velocity field. By coupling approximate expressions for the velocity field to dynamic equations, the flow problem is reduced to one of solving a nonlinear ordinary differential equation. To illustrate the model validation, numerical simulations are performed for open channel flow over curved bottom, and the free overfall problem. In terms of free surface location and bottom pressure profile, the obtained results are in good agreement with data in literature.