The influence of interior gradients of potential vorticity on rapid cyclogenesis

Abstract

The evolution of cyclonic disturbances that are localized along the rigid upper and lower boundaries of a stratified, uniformly rotating, Boussinesq atmosphere is examined using an inviscid, adiabatic, two-dimensional, quasi-geostrophic model. The disturbances are characterized by either uniform or nonuniform potential vorticity. An imposed vertical shear of the geostrophic zonal wind provides the energy source for baroclinic development. The model simulations in this study are intended to address the possibility that a tropopause fold associated with an upperlevel jet-front system overrunning a low-level air-mass boundary can result in rapid cyclogenesis, in the absence of diabatic effects. The interaction of baroclinically stable upper- and lower-level disturbances characterized by nonuniform potential vorticity results in a significant initial increase of the relative vorticity at the surface, in contrast to the decrease in relative vorticity exhibited by an isolated lower-level disturbance. The increase in relative vorticity associated with this rapid growth phase exceeds that predicted by normal-mode theory. Similar, but less pronounced, development occurs if the upper-level anomaly has nonuniform potential vorticity while the lower-level anomaly has uniform potential vorticity. Upper- and lower-level anomalies associated with uniform potential vorticity do not interact. Each disturbance behaves as a surface-trapped baroclinic wave. There is no increase in surface relative vorticity prior to the onset of the normal-mode growth phase. A diagnostic omega equation is presented, wherein the forcing is expressed equivalently as the advection of potential vorticity and perturbation vertical stratification by the thermal wind or as the advection of relative vorticity by the thermal wind. The omega equation is used to interpret the evolution of surface vorticity in terms of an induced vortex stretching for the various combinations of upper- and lower-level anomalies. When properly configured in the vertical, interior anomalies of potential vorticity are particularly conducive to surface development, with the primary cyclogenetic contribution due to advection of potential vorticity by the thermal wind. This forcing contribution dominates that related to perturbation stratification, which is shown to be cyclolytic. Alternatively, the vorticity fields associated with the upper- and lower-level potential vorticity anomalies overlap and reinforce each other, resulting in strong cyclogenetic forcing at lower levels through vorticity advection by the thermal wind. This study illustrates and clarifies some of the concepts associated with “potential-vorticity thinking” and the initial-value approach to baroclinic instability. It is suggested that nonuniform distributions of interior potential vorticity with realistic length and depth scales provide a forcing mechanism sufficient for the rapid development of localized surface cyclones. DOI: 10.1034/j.1600-0870.1991.t01-2-00003.x