A simple closure model for gradually varied open channel flow

In this work we propose a 2D model for open channel flows. By using the Reynolds equations with a suitable modified mixing length closure model, we derive a mathematical formulation. A factorized explicit numerical scheme was used to find numerical solutions. In order to validate the model several tests were performed. These tests can be divided into three groups. In the first one, analytical solution of the model was derived for uniform motion and compared to the experimental log-law. In the second one, comparisons were performed with results obtained with the shallow water approximation. In the third group comparisons were made between experimental and numerical results in the case of unsteady motion. All these tests confirm the global validity of the methodological approach followed and its suitably as a tool in modelling 2D open channel flow