The Effect of Realistic Radiative Transfer on Potential Vorticity Structures, Including the Influence of Background Shear and Strain

Abstract

A modified version of the radiation scheme of Shine is used to investigate the decay of small-scale potential vorticity structures characteristic of those observed in the lower and middle stratosphere. Following Fels, effective thermal damping rates are presented as a function of vertical scale, including scales sufficiently small that the weak-line limit is reached. At 20 km the transition scale between weak- and strong-line regimes is at a vertical scale of about 1 m, and the corresponding damping rate is about 2.5 day?1. This is less than the damping rate associated with molecular diffusion at the same scale. The damping rates associated with molecular diffusion and radiative transfer are about equal at a vertical scale of about 10 m. The radiation scheme is incorporated into a number of simple dynamical models based upon quasigeostrophic theory. In the simplest there is no background flow. Solutions highlight the dependence of decay rate of potential vorticity anomalies on vertical scale and on aspect ratio. The scale-selective nature of radiative damping causes a significant change in the shape of anomalies as they decay. The effect of simple background shear and strain fields is to decrease the vertical scale of the anomaly, and thereby to accelerate the decay. Several examples are given. For strain fields characteristic of the lower stratosphere, an equilibrium scale (at which there is a balance between the effects on the potential vorticity of the radiative damping and of the strain) is shown to exist. This scale need not apply to chemical tracers, and observations of a difference in minimum scale between the potential vorticity and tracer fields would be one way of verifying that the scale cascade of potential vorticity is under radiative control. In the presence of an imposed beating structure, which maintains a broad vortex edge, there may be a steady balance between the strain field, which sharpens the edge, and the radiative transfer. An estimate of the equilibrium edge thickness as a function of strain rate is obtained. For strain rates that are believed to be appropriate, and that in a real flow would represent the systematic effects of many straining events, the equilibrium thickness of the edge is about 100 km in the horizontal and 500 m in the vertical. The structure of the edge is somewhat analogous to one that would form through an advective-diffusive balance, but the different form of scale dependence of the radiative damping from that for diffusion leads to important differences of detail. It is argued that evidence from AAOE observations suggests that the thickness of the edge is indeed controlled by radiative transfer rather than by other candidate processes.