In this study, application of Eliassen's (1951) forced secondary circulation model to the hurricane vortex is reexamined. It is shown by scale analysis that the symmetric tangential flow is in hydrostatic and gradient balance if the asymmetric part of the tangential flow and the radial and vertical symmetric motions are appreciably smaller than the symmetric tangential flow. When surface friction and cumulus transports of heat and momentum are included, the forced symmetric radial and vertical motions may be diagnosed. The approximations on which this system of balanced equations is based are valid everywhere in the hurricane vortex except in the upper tropospheric outflow layer. In the absence of Fickian diffusion of momentum and heat, both deep inflow in the outer vortex and subsidence within the eye are forced by radial gradients of convective heating. If corresponding gradients of cooling arise in the upper troposphere by mechanisms such as detrainment from overshooting cumuli, descent may be induced in the lower stratosphere above and around the eye. Convective momentum transports act to weaken the thermally induced secondary flow somewhat. If the vertical resolution of the finite difference mesh is too coarse to resolve the detrainment layer properly, the model may diagnose an unrealistic secondary flow with ascent throughout the eye. In the absence of all cumulus processes, the frictionally converged air no longer rises to the tropopause but rather flows outward in a shallow layer in the lower troposphere. established by scale analysis of the primitive equations. These scaling arguments are related to those of Ogura [1964] and, to a lesser extent, to those of Anthes [1974]. The balanced equations are shown to be valid when the radial, vertical, and asymmetric motions are small in comparison to the symmetric tangential flow. The convective heating and momentum transports are parameterized with a 'second-generation' scheme [0oyama 1971; Fraedrich, 1973; Arakawa and Schubert, 1974; Schneider and Lindzen, 1976], and the secondary circulation is diagnosed with the balanced equations. This model ha• no explicit diffusion of either heat or momentum; the only forcing agents are the convective processes and surface friction. The results obtained allow novel interpretations of several features of hurricane dynamics. Recent work by ¾amasaki [1977a, b] and Rosenthal [1978, 1979] indicates that explicit calculation of convective effects may be preferable to parameterized schemes in full scale numerical models. Although it does seem that the future of hurricane modeling lies in this direction, it is still possible to obtain useful insight with the present formulation. SCALE ANALYSIS Consider the primitive equations expressed in cylindrical, log pressure coordinates centered on the vortex and moving with it. At the outset the anelastic approximation [Ogura and Phillips, 1962] is made to eliminate acoustic waves. Coriolis forces arising from the storm's motion, environmental pressure gradients, friction, and convective tr...
