Abstract
Abstract Prior studies of the linear response to asymmetric heating of a balanced vortex showed that the resulting intensity change could be very closely approximated by computing the purely symmetric response to the azimuthally averaged heating. The symmetric response to the purely asymmetric part of the heating was found to have a very small and most often negative impact on the intensity of the vortex. This result stands in contrast to many previous studies that used asymmetric vorticity perturbations, which suggested that purely asymmetric forcing could lead to vortex intensification. The issue is revisited with an improved model and some new methods of analysis. The model equations have been changed to be more consistent with the anelastic approximation, but valid for a radially varying reference state. Expressions for kinetic and available potential energies are presented for both asymmetric and symmetric motions, and these are used to quantify the flow of energy from localized, asymmetric heat sources to kinetic energy of the wind field of the symmetric vortex. Previous conclusions were based on simulations that used instantaneous temperature perturbations to represent rapid heat release in cumulus updrafts. Purely asymmetric heat sources that evolve over time and move with the local mean wind are shown to also cause vortex weakening. Weakening of the symmetric vortex is due to extraction of energy by the evolving asymmetries that undergo significant transient growth due to downgradient transport of momentum across the radial and vertical shears of the symmetric wind field. While much of this energy is returned during the axisymmetrization of the resulting potential vorticity anomalies, there is typically a net loss of energy for the symmetric vortex. Some variations on the rotation rate and duration of the heat sources can lead to intensification rather than weakening, as does a deeper (more barotropic) vertical structure of the symmetric vortex. However, it is reaffirmed that these asymmetrically forced changes are small compared to the response to the azimuthally averaged heating of an isolated heat source. Following the work of Hack and Schubert, the efficiency of the intensification process, defined as the ratio of injected heat energy to the kinetic energy change of the symmetric vortex, is computed for vortices of different sizes and strengths. In the limit of small perturbations, the efficiency does not depend on the temporal distribution of the heating. The efficiency is shown to increase with the intensity of the vortex and with the Coriolis parameter, with substantial efficiency increases for weak vortices. Potential applications of these results for predicting tropical cyclone formation and rapid development are discussed.
