Upgradient and Downgradient Potential Vorticity Fluxes Produced by Forced Rossby Waves. Part I: Basic Experiments

The mean flow and potential vorticity (PV) flux produced by Rossby waves are examined, particularly by focusing on the effects of stratification and nonlinearity on upgradient and downgradient PV fluxes. Rossby waves are excited by an external forcing confined near the surface and produce a northward (upgradient) PV flux in the surface layer. While the meridional PV flux is considerably weak in the deep layer in the weakly nonlinear case, the southward (downgradient) PV flux is produced as nonlinearity increases. In both the surface and deep layers, the distribution of the PV flux and mean flow is qualitatively similar to that in recirculation gyres obtained in an eddy-resolving model of the wind-driven circulation. A perturbation analysis shows that the primary and harmonic waves are excited by external forcing and wave-wave interaction between the primary waves, respectively. The meridional PV fluxes in the surface and deep layers are mostly produced by the primary and harmonic waves, respectively. The southward PV flux in the deep layer is produced by the interaction between the barotropic harmonic wave and the first baroclinic component of nonlinear forcing by the primary waves. The irreversible processes that are implicitly assumed in the PV homogenization theory (Rhines and Young) do not substantially affect the southward PV flux. The qualitative features of the PV flux remain unchanged even when nonlinearity is increased beyond the range in which the perturbation theory is exactly applicable.