Implementation of a direct nonhydrostatic pressure gradient discretisation into a layered ocean model

Abstract

The increasing demand for the investigation of nonhydrostatic effects in ocean modelling requires crucial modifications to models applying the hydrostatic pressure assumption. Within many studies the capability of the pressure-correcting projection method for the inclusion of the missing nonhydrostatic pressure contribution into an existing hydrostatic model kernel was verified. It provides accurate results but also requires computational (and implementational) effort for solving a Poisson equation for the pressure correction.In contrast, some studies were based on an alternative approach that does not require the inversion of a Poisson equation. Within this alternative approach the nonhydrostatic pressure contribution is calculated by an explicit vertical integration of the additional nonhydrostatic terms in the balance of vertical momentum. Since ocean models are not intended to replace classical engineering tools and are usually applied to nearly hydrostatic flows, this straight-forward extension of the hydrostatic procedure is an interesting option. However, the feasibility of the alternative approach was not tested within a full 3D explicit mode-splitting model yet. Furthermore, the nonhydrostatic capability of the alternative approach has so far not been validated against well known nonhydrostatic benchmark test cases. In order to assess the potential of the alternative approach for future ocean modelling applications, in the present study these required but still missing investigations are carried out.To demonstrate the necessary modifications to an explicit mode-splitting hydrostatic model kernel, the extension of the General Estuarine Transport Model (GETM) is outlined. The simulation results of laboratory and idealised oceanic test cases are presented and compared to analytical theory, laboratory experiments and other numerical simulations. This validation indicates the nonhydrostatic capability of the extended GETM. However, stability issues limited the efficiency and the applicability of the straight-forward inclusion of nonhydrostatic dynamics.