THE ROLE OF DIFFUSIVE EFFECTS ON POTENTIAL VORTICITY IN FRONTS

Theoretical studies of two-dimensional fronts have shown that frictional processes at the time of occlusion and/or diabatic effects imply low-level, positive potential vorticity (PV) anomalies. It is shown here that significant amounts of PV can be produced in an evolving baroclinic wave (taken to be the two-dimensional semigeostrophic Eady wave) purely owing to the presence of a no-slip, insulating lower boundary. A simple analytic expression is given for the time evolution of the mass-weighted volume-average PV, (PVBAR), up to the point of frontal collapse. For the most unstable linear normal mode it is found, at the time of the formation of the frontal discontinuity, that the PVBAR has increased by approximately a third of its basic-state value. The bulk formulation for surface fluxes of heat and momentum is used to illustrate the general role of boundary-layer processes in modifying PV locally. Turbulent fluxes which decrease linearly from maximum values at the surface to zero at the top of the planetary boundary layer (PBL) are used to recover a simple analytical form for the PV generation tendency. The magnitudes of the PV anomalies produced by flows typical of mid-latitude cyclones and associated fronts are highlighted by vertically integrating the tendency equation over the PBL. It is shown that the generation of PV in the PBL depends on the vertical differences of velocity and potential temperature over the depth of the PBL; and on the vertical vorticity and horizontal potential-temperature gradient at the top of the PBL. For example, there is a local source of PV if there is cooler air at the top of the boundary layer to the right of the surface wind vector, i.e. if the thermal wind has a component opposing the wind at anemometer level. The production of PV anomalies by surface processes, using this formulation, is independent of the occlusion process. Purely horizontal mixing of heat in the vicinity of a potential-temperature anomaly is examined to predict the magnitude of local PV anomalies, consistent with the internal 'eddy' viscosity often used in numerical models. Numerical integrations of a two-dimensional Eady wave with a detailed surface-layer description and stability-dependent eddy viscosity coefficients also illustrate that significant growth in the PVBAR occurs before the warm sector is lifted off the surface. There is a direct correspondence between this growth and the decrease of the horizontally-averaged surface potential temperature, as predicted from the no-slip, insulating boundary theory. Also, the local PV anomalies predicted by the bulk PBL representation are shown to be in close agreement with those produced in the numerical simulation, which uses a more comprehensive scheme.