The Effect of Cumulus Momentum Mixing on the Development of a Symmetric Model Hurricane

Abstract

The effect of the vertical transport of horizontal momentum by cumulus clouds on the development of a symmetric model hurricane is investigated. This is accomplished by using Sundqvist's symmetric hurricane model with parameterized cumulus friction. The scheme used to include cumulus friction in the model is essentially the same as that given by Stevens and Lindzen in 1978 and Lindzen in 1981. The results of two sets of numerical integrations are presented. In one, the initial wind and moisture distributions were derived from atmospheric observations in Atlantic intensifying cyclones as composited by McBride. In the other, the initial vortex was specified as that which corresponds to the linearly most unstable mode in Mak's 1980 linear analysis of the effect of cumulus friction on hurricane formation. Given each initial wind, temperature and moisture distribution, numerical integrations were performed with and without cumulus friction present in the model. With cumulus friction included, the growth rates of the initial disturbances and their final intensities are smaller than those obtained in the absence of cumulus friction. The Atlantic intensifying cyclone with cumulus friction reaches storm strength, whereas without cumulus friction it develops into a hurricane. In the second pair of numerical integrations with the initial vortex specified as described above, the model develops hurricanes with and without cumulus frictions, but the rate of intensification and final strength of the vortex are significantly smaller when cumulus friction is included. The damping effect of cumulus friction is attributed to the fact that the angular momentum transported from the lower into the upper troposphere by cumulus mixing is not fully replenished in the lower troposphere by the cumulus induced secondary (radial) circulation. This contrasts with the effect of the inward eddy flux of momentum, reported on previously, which was found to enhance the intensification of hurricanes. The crucial difference between the two mechanisms, both of which induce secondary radial circulations due to a vertical differential in cyclonic torque, appears to be the net increase of momentum in the vortex due to inward eddy flux of momentum, which is not present in the case of cumulus friction. The latter mechanism simply redistributes the momentum vertically, actually reducing the strength of both the low-level cyclone and the upper-level anticyclone.