On the Evolution of Vorticity and Potential Vorticity in the Presence of Diabatic Heating and Frictional or Other Forces

Abstract

Some consequences of regarding potential vorticity as a tracer are considered. It is shown that neither diabatic heating, nor frictional forces, nor external forces such as might be used to model gravity-wave drag, can bring about any net transport or Rossby-Ertel potential vorticity (PV) across an isotropic surface?notwithstanding the diabatic, cross-isentropic transport of mass and chemical tracers. Nor can PV be created or destroyed within a layer bounded by two isentropic surface. It can only be transported along the layer. and diluted or concentrated by cross-isentropic mass inflow or outflow. This constitutes a systematic difference between the behavior of PV and that of other tracers, recognition of which simplifies thinking about PV budgets and gives insight into the relationships between dynamical processes, departures from radiatively determined temperatures, and chemical tracer transport including stratosphere-troposphere exchange. The results just stated are true by virtue of the way in which the PV is constructed mathematically, and are therefore true not only of the exact PV constructed from the exact wind and potential-temperature fields, but true also, for example, of any ?coarse-gain PV? constructed from observed or avenged fields. Some related results on vorticity and on generalizations of the potential vorticity concept are noted, together with their implications for vorticity and potential-vorticity budgets (in the tropics and elsewhere) and for the cumulonimbus parameterization problem.