The Stochastic Spin-up of Vorticity in Spontaneous Tropical Cyclogenesis

Cloud-permitting simulations have shown that tropical cyclones can form spontaneously in a quiescent environment with uniform sea surface temperature. While several mesoscale feedbacks are known to amplify an existing midlevel vortex, how the noisy deep convection produces the initial midlevel vortex remains unclear. This paper develops a theoretical framework to understand the evolution of the midlevel mesoscale vorticity's histogram in the first two days of spontaneous tropical cyclogenesis, which we call the ``stochastic spin-up stage". The mesoscale vorticity is produced by two random processes related to deep convection: the random stretching of planetary vorticity (f) and the tilting of random vertical shear. The random vertical shear can be caused by the spontaneous tilting of the convective plumes, as well as the convectively generated gravity waves and eddies. Cloud-permitting simulations show that the contribution of random tilting to the mesoscale vorticity, independent of f, cannot be ignored below f∼3e-5 (1/s) (around 12N). The theory predicts that the standard deviation of the midlevel mesoscale vorticity is universally proportional to the square root of the domain-averaged accumulated rainfall, in agreement with simulations.