Potential vorticity thickness fluxes and wave-mean flow interaction

The use of eddy flux of thickness between density surfaces has become a Fam iliar starting point in oceanographic studies of adiabatic eddy effects on the mean density distribution. In this study, a dynamical analogy with the density thickness flux approach is explored to reexamine the theory of nonz onal wave-mean now interaction in two-dimensional horizontal flows. By anal ogy with the density thickness flux, the flux of thickness between potentia l vorticity (PV) surfaces is used as a starting point for a residual circul ation formulation for nonzonal mean flows. Mean equations for barotropic PV dynamics are derived in which a modified mean velocity with an eddy-induce d component advects a modified mean PV that also has an eddy-induced compon ent. For small-amplitude eddies, the results are analogous to recent result s of McDougall and McIntosh derived for stratified flow. The dynamical implications of this approach are then examined. The modified mean PV equation provides a decomposition of the eddy forcing of the mean how into contributions from wave transience, wave dissipation, and wave-ind uced mass redistribution between PV contours. If the mean flow is along the mean PV contours, the contribution from wave-induced mass redistribution i s "workless" in Plumb's sense that it is equivalent to an eddy-induced stre ss that is perpendicular to the mean flow. This contribution is also associ ated with the convergence along the mean streamlines of a modified PV flux that is equal to the difference between the PV flux and the rotational PV f lux term identified by Illari and Marshall. The cross-stream component of t he modified PV flux is related to wave transience and dissipation.