The equilibration of short Charney modes: implications for PV homogenization

Baroclinic adjustment theories postulate that baroclinic instability equilibrates in the Earth's atmosphere by smoothing the PV gradients in the interior and the temperature gradients at the surface. However, observations suggest that the temperature gradients at the surface are not as well mixed as the interior PV gradients, which is often attributed to surface damping.

In fact, short waves can achieve neutrality in the continuous problem without full homogenization. In this work, we have studied how short Charney modes equilibrate. For the Boussinesq-Charney problem, the Held height scale gives the depth over which the integrated positive PV gradient in the interior balances the negative delta function at the surface. We have shown that waves with Rossby depth smaller than this scale have a very narrow PV flux and can equilibrate by mixing the gradients across a narrow neigborhood of the steering level alone. However, when the Rossby depth is larger than the Held scale, as is the case for the most unstable Charney mode, neutrality requires PV mixing over a broader region. An important constraint for these modes is how the steering level changes during the equilibration process, which is sensitive to surface friction.

In the midlatitudes, the meridional wavenumber imposed by the jet limits the depth over which the PV flux can extend. As a result, for typical values of beta and vertical wind shear, a substantial part of the baroclinic spectrum is short in the sense defined above. We suggest that the equilibration of these short waves may explain the observed partial homogenization of the tropospheric PV gradients. We further argue that, considered in an integral sense, the tropospheric PV gradients are in fact as poorly mixed as the lower boundary PV gradients, consistent with the critical shear of the two-layer model.