A Novel Computational Approach for Wind-Driven Flows over Deformable Topography

Single-layer shallow water models have been widely used for simulating shallow water waves over both fixed and movable beds. However, these models can not capture some hydraulic features such as small eddy currents and flow recirculations. This study presents a novel numerical approach for coupling multi-layer shallow water models with elastic deformations to accurately capture complex recirculation patterns in wind-driven flows. This class of multi-layer equations avoids the computationally demanding methods needed to solve the three-dimensional Navier-Stokes equations for free-surface flows while it provides stratified flow velocities since the pressure distribution is still assumed to be hydrostatic. In the current study, the free-surface flow problem is approximated as a layered system made of multiple shallow water equations of different water heights but coupled through mass-exchange terms between the embedded layers. Deformations in the topography are accounted for using linear elastostatic systems for which an internal force is applied. Transfer conditions at the interface between the water surface and the topography are also developed using frictional forces and hydrostatic pressures. For the computational solver, we implement a fast and accurate hybrid finite element/finite volume method solving the linear deformations on unstructured meshes and the nonlinear flows using well-balanced discretizations. Numerical results are presented for various problems and the computed solutions demonstrate the ability of the proposed model in accurately resolving wind-driven flows over deformable topography.