Hydrostatic, quasi‐hydrostatic, and nonhydrostatic ocean modeling

Abstract

Abstract. Ocean models based on consistent hydrostatic, quasi-hydrostatic, and nonhydrostatic equation sets are formulated and discussed. The quasi-hydrostatic and nonhydrostatic sets are more accurate than the widely used hydrostatic primitive equations. Quasi-hydrostatic models relax the precise balance between gravity and pressure gradient forces by including in a consistent manner cosine-of-latitude Coriolis terms which are neglected in primitive equation models. Nonhydrostatic models employ the full incompressible Navier Stokes equations; they are required in the study of smallscale phenomena in the ocean which are not in hydrostatic balance. We outline a solution strategy for the Navier Stokes model on the sphere that performs efficiently across the whole range of scales in the ocean, from the convective scale to the global scale, and so leads to a model of great versatility. In the hydrostatic limit the Navier Stokes model involves no more computational effort than those models which assume strict hydrostatic balance on all scales. The strategy is illustrated in simulations of laboratory experiments in rotating convection on scales of a few centimeters, simulations of convective and baroclinic instability of the mixed layer on the 1-to 10-km scale, and simulations of the global circulation of the ocean.

A Greenland Sea Perspective on the Dynamics of Postconvective Eddies*

“…This is consistent with the schematic provided in Fig. 2 and with laboratory and numerical experiments (Narimousa 1998;Marshall and Schott 1999). The cyclone mostly contains water from outside the initial mixed patch.…”

“…For this reason, mixed-patch release experiments were carried out in a simple channel setting as well as in basin experiments more closely representing the Greenland Sea. All experiments were carried out with the Massachusetts Institute of Technology general circulation model (MITgcm; Marshall et al 1997) on an f plane ( f ϭ 1.5 ϫ 10 Ϫ4 s Ϫ1 ). The vertical resolution of the 40 levels decreased from 11 m at the surface to 147 m at the bottom (3750 m), and a very high horizontal resolution of 500 m ϫ 500 m was applied in order to resolve postconvective vortices.…”

“…2). Hetons are baroclinic dipoles that experiments in laboratory tanks and numerical models suggest are produced by deep convection (Marshall and Schott 1999) or by topographic interactions (Dewar 2002a). (For clarity, in this study we only use the expression "SCV" when discussing observations, and otherwise refer to hetons and their cyclonic and anticyclonic components.)…”

A nonhydrostatic version of FVCOM: 1. Validation experiments

“…The same experiment was also conducted using the Massachusetts Institute of Technology general circulation model (MITgcm) and the Bergen Ocean Model (BOM) by Berntsen et al [2006]. MITgcm is a z coordinate structured grid nonhydrostatic finite volume model that uses a shaved cell approach to treat near-bottom flow over sloping-bottomed topography [Marshall et al, 1997a[Marshall et al, , 1997b, and BOM is a sigma coordinate nonhydrostatic finite difference model [Berntsen, 2000]. Berntsen et al [2006] found that the shoaling and breaking process predicted by MITgcm in the case without bottom friction looked like BOM's results with bottom friction.…”

“…FVCOM was developed originally with the hydrostatic approximation in which the rate of change, advection, and diffusion of the vertical velocity are ignored and the pressure gradient in the vertical is balanced by gravity. According to scaling analysis, the hydrostatic balance is valid for large-scale motions in regional scale and larger-scale ocean waters, where the horizontal motion is dominant [Mahadevan et al, 1996a;Marshall et al, 1997a]. In coastal and estuarine waters, particularly over shallow banks and the shelfbreak where internal waves can be energetic, and in inlets or narrow river passages, where the motion's horizontal scale can be comparable to the local depth, the flow is influenced by nonhydrostatic dynamics.…”