Evaluation of a simplified approach for simulating gravity currents over slopes of varying angles

Using high resolution numerical simulations of the two-dimensional Navier–Stokes equations, we evaluate a conceptually simple approach to modeling gravity currents traveling over a bottom boundary of varying slope. We consider a rectangular computational domain, which allows for simple and efficient implementation of the equations and boundary conditions. Rather than implementing a complete coordinate transformation, the varying slope is modeled through the introduction of a spatially varying gravity vector. Our methodology is validated through studies of mass and energy conservation. The propagation velocity of the current and qualitative features of the flow are also found to be consistent with experimental observations of gravity currents traveling down constant or varying slopes.