**Darryl D. Holm ^{1}, Len G. Margolin^{2}, and Balu T. Nadiga^{2,3}
**

^{1}Theoretical Division and Center for Nonlinear Studies, MS-B284

Los Alamos National Lab., NM 87545

^{2}Institute for Geophysics and Planetary Physics, MS-C305

Los Alamos National Lab., NM 87545

^{3}Corresponding Author

*Submitted to Physica D*

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.

- Introduction
- The governing equations
- The Instantaneous Fields
- Spectral Estimation
- Comparison of the variabilities
- Dependence on Initial Conditions
- Bootstrap Analysis
- Singular Spectrum Analysis (SSA) of the Low Frequency Variability
- Summary and Discussion
- Acknowledgments
- The Green-Naghdi (GN) Model
- Numerical Model of the Nonhydrostatic Equations
- References
- Figure Captions
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