The equations of complete depth-averaged turbulence model in general orthogonal coordinates

For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account. The depth-averaged equations of k- turbulence model are also obtained. Because it accounts for the three-dimensional effect, this model is named as the complete depthaveraged model.The boundaries of natural water bodies are usually curved. In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems.