The Influence of Negative Viscosity on Wind-Driven, Barotropic Ocean Circulation in a Subtropical Basin

Abstract

In this paper, a new barotropic wind-driven circulation model is proposed to explain the enhanced transport of the western boundary current and the establishment of the recirculation gyre. In this model the harmonic Laplacian viscosity including the second-order term (the negative viscosity term) in the Prandtl mixing length theory is regarded as a tentative subgrid-scale parameterization of the boundary layer near the wall. First, for the linear Munk model with weak negative viscosity its analytical solution can be obtained with the help of a perturbation expansion method. It can be shown that the negative viscosity can result in the intensification of the western boundary current. Second, the fully nonlinear model is solved numerically in some parameter space. It is found that for the finite Reynolds numbers the negative viscosity can strengthen both the western boundary current and the recirculation gyre in the northwest corner of the basin. The drastic increase of the mean and eddy kinetic energies can be observed in this case. In addition, the analysis of the time-mean potential vorticity indicates that the negative relative vorticity advection, the negative planetary vorticity advection, and the negative viscosity term become rather important in the western boundary layer in the presence of the negative viscosity. Further, the influence of the resolution and the negative viscosity intensity on the solutions are also examined.