Potential Momentum and the equilibration of short Charney waves

Abstract

This paper proposes a new formalism for studying the extratropical circulation, based on the concept of potential momentum. Mathematically, the potential momentum is defined as the zonal momentum profile that produces the same potential vorticity distribution as the baroclinic term. Physically, easterly (westerly) potential momentum is associated with isentropic layers that open up (close down) with latitude. The former is the case in the extratropical troposphere, and gives a negative contribution to the interior potential vorticity gradient. Likewise, the surface temperature variance is interpreted in this framework as a reservoir of easterly potential momentum at the surface. With this redefinition of the mean flow, the wave-mean flow interaction problem can be recast in a form that is reminiscent of the barotropic framework. In particular, the eddy PV flux is the only wave-mean flow interaction term, and exchanges eddy pseudomomentum and mean flow momentum (which includes both the standard momentum and potential momentum) locally. On the other hand, the partition of the mean flow momentum between its physical and potential components is determined remotely, subject to the thermal wind constraint. This constraint is enforced by a residual circulation that exchanges both terms without affecting the total momentum or the full PV gradient. The potential momentum framework relates thermal homogenization at the surface to the net interior eddy absorption, regardless of whether this results from a meridional or a vertical EP convergence. This helps explain previous results by the same authors that a limited interior PV gradient does not constrain thermal homogenization at the surface, since in the 3D problem the waves can also refract meridionally to be absorbed at other latitudes.