Depth-Averaged Model of Open-Channel Flows over an Arbitrary 3D Surface and Its Applications to Analysis of Water Surface Profile

A new set of depth-averaged equations is introduced to study the flow over an arbitrary three-dimensional (3D) surface. These equations are derived based on a generalized curvilinear coordinate system attached to the 3D bed surface, therefore it allows us to include the effect of centrifugal force due to the bottom curvature. These general equations make it possible to analyze flows over complex terrain without the limitation of mild slope assumption used in conventional depth-averaged models. This new model is then applied to calculate the water surface profiles of (1) flow over a cylindrical surface; (2) flow over a circular surface; and (3) flow with an air-core vortex at a vertical intake. A simple hydraulic experiment is conducted in the laboratory to observe the water surface profile of flow over a circular surface. The results obtained from the model are in good agreement with experimental measurements and calculation by an empirical formula. Consequently, it demonstrates the applicability of the model in cases of flow over a highly curved bottom.