A [formula omitted]-coordinate non-hydrostatic discontinuous finite element coastal ocean model

Abstract

A σ-coordinate non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin finite element method. With the selection of the low-order piecewise-constant P0DGand piecewise-linear P1DGdiscretisations in the vertical for the velocity and pressure fields, respectively, the proposed σ-coordinate model can naturally retain the wave dispersion characteristics of the widely-adopted multi-layer approach of Zijlema and Stelling (2005), which is demonstrated through both mathematical derivation and numerical tests. Under the finite element approach, higher-order vertical discretisation choices can also be readily made which can reduce the number of vertical layers required for the accurate representation of wave dispersion. The model is verified and validated through comparisons against a series of test cases with analytical solutions or experimental measurements. All the comparisons demonstrate good agreement, indicating that the proposed model can accurately represent dispersive barotropic surface waves with as few as one vertical layer, and can simulate baroclinic internal waves with reasonable accuracy using relatively coarse mesh resolution. It is also demonstrated that consistency in the coupling of barotropic and baroclinic flows can be properly ensured.