Transformed Eulerian-mean theory. II: Potential vorticity homogenization, and the equilibrium of a wind- and buoyancy-driven zonal ow

The equilibrium of a modeled windand buoyancy-driven, baroclinically unstable, ‡ow is analyzed using the transformed Eulerian-mean (TEM) approach described in Part I. Within the near-adiabatic interior of the ‡ow, Ertel potential vorticity is homogenized along mean isopycnals, a …nding readily explained using TEM theory, given the geometry of the domain. The equilibrium, zonal-mean buoyancy structure at the surface is determined entirely by a balance between imposed surface ‡uxes and residual mean and eddy buoyancy transport within a “surface diabatic layer.” Balance between these same processes and the wind stress determines the strati…cation, and hence potential vorticity, immediately below this layer. PV homogenization below then determines the mean buoyancy structure everywhere. Accordingly, the equilibrium structure of this ‡ow can be described— and quantitatively reproduced— from knowledge of the eddy mixing rates within the surface diabatic zone, and the depth of this zone, together with potential vorticity homogenization beneath. These results emphasize the need to include nearsurface buoyancy transport, as well as interior PV transport, in eddy parameterization schemes. They also imply that, in more realistic models, the surface buoyancy balances may be impacted by processes in remote locations that allow diapycnal ‡ow. 1 Introduction In Part I (Plumb and Ferrari, 2004) a nongeostrophic transformed Eulerian mean (TEM) theory was presented for analysis of eddy transport on a zonal-mean ‡ow. Here, we revisit a problem explored by Karsten et al. (2002; hereinafter KJM), considering the modeled equilibrium state of ‡uid in a cylindrical tank, forced at its top surface by applied stresses and buoyancy ‡uxes, in order to illustrate and to explore further the implications of that theory. The model set-up is brie‡y described in Section 2. The ‡ow becomes baroclinically unstable and eventually equilibrates to produce a strati…ed mean state, as shown by KJM and in Fig. 1(a), below. This equilibrium state is described in terms of conventional eddy transports in Section 3; aside from the buoyancy structure, other features of interest are the homogenization of mean Ertel potential vorticity (PV) along the mean isopycnals, and the eddy ‡uxes of buoyancy and of PV, both of which are “skew” (directed along the mean contours of buoyancy and PV respectively) except near the surface, where they are signi…cantly downgradient within an important region we refer to as the “surface diabatic layer” (SDL), which is analogous to the “surface layer” discussed by Treguier et al. (1997), Held and Schneider (1999) and Koh and Plumb (2004) in isopycnal or isentropic coordinate formalisms. The equilibrium state is then re-analyzed in Section 4 from a transformed Eulerian mean