A sigma-coordinate non-hydrostatic discontinuous finite element coastal ocean model

Abstract

A𝜎-coordinate non-hydrostatic coastal ocean model is developed using the discontinuous Galerkin fi-nite element method. With the selection of the low-order piecewise-constant PDG0and piecewise-linearPDG1discretisations in the vertical for the velocity and pressure fields, respectively, the proposed𝜎-coordinatemodel can naturally retain the wave dispersion characteristics of the widely-adopted multi-layer approach ofZijlema 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 whichcan reduce the number of vertical layers required for the accurate representation of wave dispersion. Themodel is verified and validated through comparisons against a series of test cases with analytical solutions orexperimental measurements. All the comparisons demonstrate good agreement, indicating that the proposedmodel can accurately represent dispersive barotropic surface waves with as few as one vertical layer, and cansimulate baroclinic internal waves with reasonable accuracy using relatively coarse mesh resolution. It is alsodemonstrated that consistency in the coupling of barotropic and baroclinic flows can be properly ensured.