Eddy-Mean Flow Interactions in the Along-Stream Development of a Western Boundary Current Jet: An Idealized Model Study

A theoretical study on the role of eddy-mean flow interactions in the time-mean dynamics of a zonally evolving, unstable, strongly inertial jet in a configuration and parameter regime that is relevant to oceanic western boundary current (WBC) jets is described. Progress is made by diagnosing the eddy effect on the time-mean circulation, examining the mechanism that permits the eddies to drive the time-mean recirculation gyres, and exploring the dependence of the eddy effect on system parameters. It is found that the nature of the eddy-mean flow interactions in this idealized configuration is critically dependent on along-stream position, in particular relative to the along-stream evolving stability properties of the time-mean jet. Just after separation from the western boundary, eddies act to stabilize the jet through downgradient fluxes of potential vorticity (PV). Downstream of where the time-mean jet has (through the effect of the eddies) been stabilized, eddies act to drive the time-mean recirculations through the mechanism of an upgradient PV flux. This upgradient flux is permitted by an eddy enstrophy convergence downstream of jet stabilization, which results from the generation of eddies in the upstream region where the jet is unstable, the advection of that eddy activity along stream by the jet, and the dissipation of the eddies in the region downstream of jet stabilization. It is in this region of eddy decay that eddies drive the time-mean recirculations through the mechanism of nonlinear eddy rectification, resulting from the radiation of waves from a localized region. It is found that similar mechanisms operate in both barotropic and baroclinic configurations, although differences in the background PV gradient on which the eddies act implies that the recirculation-driving mechanism is more effective in the baroclinic case. This study highlights the important roles that eddies play in the idealized WBC jet dynamics considered here of stabilizing the jet and driving the flanking recirculations. In the absence of eddy terms, the magnitude of the upper-ocean jet transport would be significantly less and the abyssal ocean recirculations (and their significant enhancement to the jet transport) would be missing altogether.