The equilibration of short Charney waves: Implications for potential vorticity homogenization in the extratropical troposphere

In this paper the authors discuss the vertical distribution of the interior potential vorticity gradients in the extratropical troposphere in an ideal ized setting. This structure is characterized by large positive gradients a t the top of the boundary layer and a narrow homogenized region in the inte rior. To understand this partial homogenization, the authors have looked at how Charney waves of different scales equilibrate. It is shown that when t he interior gradients of potential vorticity are small compared to the delt a function at the ground, the modes can equilibrate without eliminating the lower-level shear. As is the case in the Eady model, these neutral states can exist even though they violate the Charney-Stern condition for stabilit y. The equilibration process also produces a concentration of the potential vorticity gradients at heights of the order of the Rossby depth, which can be regarded as a boundary to the interior mixing of potential vorticity. The extent of interior potential vorticity mixing required for equilibratio n depends on the ratio between the boundary and interior potential vorticit y gradients. It is implicit in the analysis of previous authors that this r atio is close to 1 in midlatitudes, which implies that an Eady model with f ull homogenization of the interior potential vorticity gradients is not an appropriate paradigm for the midlatitude troposphere. Nevertheless, it is a rgued that localized interior potential vorticity mixing could be sufficien t for neutralizing the shortest waves.