Forced secondary circulations in hurricanes

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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.