In the first part of the lecture, I will present systematic matched asymptotic analyses for concentrated atmospheric vortices in the gradient wind regime, which corresponds to hurricane strengths H1 or H2. Both dry and moist flows will be addressed. The theory relates the leading order axisymmetric vortex core flow, described by Eliassen-type balanced vortex model equations, and its vertical tilt to the large scale motion of the vortex center. In the dry case, we obtain explicit equations for a slow precessing motion of the vortex column akin to that observed recently in 3D numerical simulations by Montgomery and co-workers. To address the moist case, we include a bulk microphysics closure in the asymptotic scheme. We find much stronger vertical velocities, weaker tilts, and again a closed equation for the motion of the vortex center.
One open issue in this context, which we hope to discuss with participants during the workshop, is whether Emanuel's Carnot-Engine-analogue should include a closed secondary circulation and, if so, how the dry stable stratification of the environment is overcome in the downward circulation branch.
The second part of the lecture summarizes ongoing work with A.J. Majda on a multiscale theory for mechanisms of hurricane formation. Deep convective towers of small horizontal extent interact with a mesoscale WTG-type environment to both contract and concentrate planetary rotation and to amalgamate small-scale vorticity generated in conjunction with the deep convective turrets.