A three-dimensional unstructured mesh finite element shallow-water model, with application to the flows around an island and in a wind-driven, elongated basin

Abstract

We present a new three-dimensional, unstructured mesh finite element shallow-water model. The current configuration is suitable for studying unstratified flows and the evolution of passive tracers. The model has a free surface and is hydrostatic. The mesh is unstructured in the horizontal and extruded towards the seabed in the direction parallel to the local gravity vector to generate a mesh made up of prisms. The mesh moves in the vertical and accommodates the free-surface motions. We describe the numerical treatment of the hydrodynamical equations with the finite element method. A discontinuous representation is used in the vertical for all velocity components. The horizontal velocity components are non-conforming in the horizontal, which is particularly appropriate for advection-dominated flows. The model is validated against a realistic tidal flow around a shallow-water island for which field measurements are available and is shown to operate successfully. The three-dimensional character of the flow is emphasized by use of a passive tracer. We also assess the model’s ability to represent the vertical structure of the horizontal flow field by applying it to a wind-driven flow experiment in an elongated rectangular basin.