Finite-Amplitude Behavior of a Single Baroclinic Wave with Multiple Vertical Modes: Effects of Thermal Damping

Abstract

The effects of thermal damping on the finite-amplitude behavior of a baroclinic wave are investigated using a quasi-geostrophic, ?-plane model The model possesses high vertical resolution so that there are many vertical eddy modes, but both the wave field and the zonal-mean flow are truncated to a single horizontal mode; the wave-mean flow interaction is thus purely baroclinic. In addition to thermal dissipation, lower boundary Ekman friction is incorporated. The regime characteristics of the model are qualitatively fairly similar to those of the two-layer models previously studied. For sufficiently strong thermal damping, steady wave flows are obtained, while for weaker damping, nonsteady vacillating behavior is found. In the absence of damping the vacillations are relatively irregular and the minimum eddy amplitude relatively large, as has been found to be the case in the two-layer model with multiple horizontal wave modes. In the steady wave flows the mean flow is linearly neutral, and this neutrality is qualitatively suggested by Lindzen et al. Similar considerations apply in a time-mean sense to at least some of the nonsteady flows, but in the absence of all damping the mean flow is ?overstabilized??a substantial fraction of the mean available potential energy being removed by the wave. A particularly interesting type of vacillation characterized by two widely separated time scales constituting a sort of long ?Life-cycle? of eddy activity, occurs in the model nonsteady regime, and appears to be similar in some respects to behavior found in the two-layer model with only lower-layer dissipation. In the present model, the life-cycle behavior is closely linked to the strength of the Ekman dissipation and to the asymmetry in the forcing and dissipation time scales which is most pronounced for relatively weak thermal damping. The regime behavior of the model examined here is considered to be suggestive, in spite of the model's simplicity, of the importance of the thermal damping time scale. The terrestrial and Martin atmosphere may represent examples of weakly and strongly damped behavior, respectively.