Boussinesq Modeling of Transcritical Flows over Steep Topography

Nonlinear shallow water equations effectively work for various fluvial hydraulic problems. However, the underlying assumption of hydrostatic pressure is violated by flows with significant vertical acceleration around steep landforms or manmade structures. Hence, unless the hydrostatic assumption is relaxed, refining the grid to resolve finer-scale topography does not guarantee enhancement in the accuracy of flow models. A potential solution to this issue is to employ the Boussinesq-type equations (BTE), which are suitable when the vertical flow scale is approaching the horizontal one. However, the classical BTE have been known to yield excessive undulations under certain conditions, which can lead to model robustness and stability issues. This study aims to develop a BTE model based on modified BTE free from erroneous undulations for fluvial applications. The model incorporates a free parameter responsible for controlling wave dispersion properties, which is optimized to ensure accurate results in flow simulations over steep beds. With the aid of artificial dissipation, the parameter-optimized BTE model successfully simulates transcritical flows, generating surface undulations within an appropriate range of flow conditions.