Adjustment to heating, potential vorticity and cyclogenesis

Solutions of an isentropic coordinate model of the atmosphere, permitting acoustic waves and inertial gravity waves, demonstrate that a vertically symmetric heat source in the troposphere usually induces a vertically asymmetric dipole anomaly in the potential vorticity (PV), with an intense, tall and thin positive (cyclonic) anomaly below a less intense, flat and broad negative (anticyclonic) anomaly. The emergence of this asymmetry is associated with the vertical gradient of the PV, which is an important factor in the local PV budget, even when this gradient is zero initially. The degree of vertical asymmetry of the response to heating depends on the ‘thickness’ (in K) of the heated layer relative to the total heat added. The adjusted balanced state shows little sensitivity to the heating intensity (i.e. the time‐scale within which the heat is added), in spite of the existence of large‐amplitude waves when the heating is applied very abruptly relative to the adiabatic adjustment time‐scale. The surrounding (non‐heated) region shows little permanent change due to the process of adjustment as far as PV substance and mass is concerned, and only functions as a transmitter of acoustic waves and inertial gravity waves. The balanced state is sensitive to variations in the horizontal scale of the heat source. The response to heating within a PV stratified region (for example, in the region of the tropopause) is quite subtle. For example, it is shown that a heat source in the tropopause region induces a predominantly anticyclonic wind anomaly. Copyright © 2003 Royal Meteorological Society