Eddy Fluxes and Second-Order Moment Balances for Nonhomogeneous Quasigeostrophic Turbulence in Wind-Driven Zonal Flows

Abstract

The balances of momentum and second-order moments (potential enstrophy, energies, and potential vorticity flux) of wind-driven zonal flow, using a suite of numerical eddy resolving experiments in a two-layer channel, governed by quasigeostrophic dynamics, are investigated. The flow regime in these experiments does not satisfy the usual scaling of quasigeostrophic large-scale dynamics: relative vorticity is a significant contribution to the quasigeostrophic potential vorticity (QPV) in the deep layer and the lateral Reynolds stress divergence is comparable to the interfacial form stress in the top layer. The balances of second-order moments confirm that the eddy-induced fluxes of QPV and layer thickness are downgradient but significant contributions of triple moments occur. Existing parameterizations and scaling laws of the eddy fluxes of QPV and layer thickness are tested against data from the numerical experiments and it is shown that the usual downgradient forms of parameterization with diffusivities chosen from theories of baroclinic instability or homogeneous ?-plane turbulence fail in the present flow regime. The authors suggest that the discrepancy is a manifestation of the strong constraint of the fluxes by the balance of momentum in the steady state. A consistent parameterization for the eddy-induced flux of QPV is derived from the balance of this moment. The flux is produced by a gradient term, whereas the ageostrophic pressure?QPV covariance is the major destruction, with small but significant contributions from a triple moment divergence. The approximated balance of the QPV flux, shows that the QPV flux is not completely diffusive (i.e., downgradient the mean potential vorticity) but that there is an additional transport that relates to the eddy flux of the flux of QPV itself. A parameterization of this triple term by the mean relative vorticity is proposed and the resulting new parameterization of the QPV flux is tested in a simple coarse model of the zonal flow.