Nonhydrostatic Effects in Long Term Shallow Fluid Flow

Darryl D. Holm¹, Len G. Margolin², and Balu T. Nadiga<sup>2,3

1</sup>Theoretical Division and Center for Nonlinear Studies, MS-B284
Los Alamos National Lab., NM 87545
²Institute for Geophysics and Planetary Physics, MS-C305
Los Alamos National Lab., NM 87545
³Corresponding Author

Submitted to Physica D

Abstract:

We investigate the importance of nonhydrostatic effects in numerical simulations of the wind-driven, double-gyre system of the mid-latitude oceans integrated over climate time scales. In particular, we compare results from three different shallow fluid approximations based on the presence or the absence of dispersion due to nonhydrostasy. This dispersion represents the horizontal effect of the vertical acceleration after the three-dimensional governing equations are averaged across the thin dimension. Although scaling arguments suggest that these nonhydrostatic terms are small in magnitude, we show that nonhydrostatic effects can lead to significant changes in the low-frequency variability of the system. We further demonstrate that the magnitude of the changes due to nonhydrostatic effects are comparable to those due to large variations in parameters controlling other subgrid scale processes like eddy-viscous dissipation and interfacial friction. The results of the present study indicate that it may be necessary to appropriately parametrize the nonhydrostatic effects in large-scale ocean models when the scales on which they occur cannot be fully resolved.