(0)1. 0 The wind-driven double gyre cirulation of the surface layer in the midlatitude oceans and the accompanying Western Boundary Currents (WBCs) have been studied extensively during the last 50 years. Both altimetric and hydrographic observations of this system show significant variability over a wide range of time scales. For example, see Warren and Wunsch [1] for seasonal variablities; Auer [2] and Brown and Evans [3] for interannual variability of the mean position of the Gulf Stream; Levitus [4] for interpentadal variability of the steric sea level and geopotential thickness of the North Atlantic; Qiu et al.[5] for variability of the Kuroshio; Olson et al.[6] for variability of the separation latitude of the Brazil-Malvinas currents, etc.... While the naturally occuring double gyre circulation systems are complicated by an enormous number of physical processes, simple fluid mechanical models of the double gyre using only steady wind forcing have revealed equally high levels of variability, emphasizing the importance of the internal variability of ocean systems. Such simple modeling of the double gyre system has consisted mainly of using the quasi-geostrophic (QG) or primitive equations (PE) either for the reduced barotropic mode or for multiple layers or levels (various works from Veronis [7], to Holland and Lin [8], to Chassignet and Bleck [9]). While a symmetric wind forcing is used in models based on the PEs, the wind forcing must be asymmetric in the QG models for eddy activity to occur. Implicit in all these models however is the assumption of hydrostatic balance.
In the reduced barotropic-mode models (also called the layer models) that are used in the study of the double gyre system, the thermocline forms the lower boundary of the surface layer. With the assumption of a dynamically passive deep lower layer, the thermocline moves exactly out of phase with the upper free surface. In a flow corresponding to realistic midlatitude oceans, the variations in the depth of the upper layer are comparable to the depth of the undisturbed layer itself, and in keeping with the dynamically passive lower layer assumption, most of this variation results from the deformation of the thermocline. These large movements of the bottom boundary (thermocline) give rise to nonhydrostatic pressure terms, which in the vertically-integrated shallow-water models show up as dispersive terms involving higher-order derivatives [10,11,12,13]. Such higher-order (singular perturbation) terms are known to result sometimes in qualitatively different solution forms [13]. Nonetheless, they are neglected in imposing the usual hydrostatic approximation. The size of these terms is estimated by dimensional analysis to be small in the basin scale double gyre problem, as well. However, in this paper, we show that the effect of these small singular terms (involving higher-order derivatives) on the low frequency variability of the double gyre system is significant. Specifically, we compare simulations of the double gyre system in the presence and absence of the nonhydrostatic terms using three different systems: 1) the classic SW system, where the sole source of dispersion is the vertical component of the Earth's rotation, 2) system 1 with the additional effects of leading order nonhydrostatic terms but neglecting the horizontal component of the Earth's rotation (also called the GN system) and 3) system 2, including the leading order effects of vertical Coriolis force due to the horizontal rotation component (also called the GNH system).