The stochastic spin-up of vorticity in spontaneous tropical cyclogenesis

Cloud-permitting simulations have shown that tropical cyclones (TCs) 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 mesoscale vorticity is modeled as the sum of three independent normal distributions, which include the cyclones produced by stretching, cyclones produced by tilting, and anticyclones produced by tilting. Their collective effect is calculated with the central limit theorem. 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, agreeing with simulations. The theory predicts a critical latitude below which tilting is dominant in producing mesoscale vorticity. Treating the magnitude of random vertical shear as a fitting parameter, the critical latitude is shown to be around 12°N. Because the magnitude of vertical shear should be larger in the real atmosphere, this result suggests tilting is an important source of mesoscale vorticity fluctuation in the tropics.