The role of random vorticity stretching in tropical depression genesis

Abstract

Tropical deep convection plays a key role at the tropical depression stage of tropical cyclogenesis by aggregating vorticity, but no existing theory can depict such a stochastic vorticity aggregation process. Vorticity probability distribution function (PDF) is proposed as a tool to predict the horizontal structure and wind speed of the tropical depression, a tropical cyclone in its early stage. The reason lies in the tendency for a vortex to adjust to an axisymmetric and monotonic vorticity structure. Assuming deep convection as independent and uniformly distributed vortex tube stretching events in the lower troposphere, repetitive vortex tube stretching will make the air column area shrink many times and significantly increase vorticity. A theory of vorticity PDF is established by modelling the random stretching process as a Markov chain. The PDF turns out to be a weighted Poisson distribution, in good agreement with a randomly-forced divergent barotropic model (weak temperature gradient model), and in rough agreement with a cloud-permitting simulation. The result shows that a strong and sparse deep convective mode tends to produce more high vorticity air columns, which favors tropical cyclogenesis.

A theory of cloud spacing for equilibrium deep convection

“…• Knowledge of cloud spacing tells us how the total convective mass flux distributes in each cloud. It is a measure of convective intermittency that has been shown to significantly influence the stochastic vorticity accumulation process in tropical cyclogenesis (Fu and O'Neill 2021a;Fu and O'Neill 2021b).…”

“…We initialize the model with a radiative-convective equilibrium (RCE) state sounding, from the horizontally averaged water vapor mixing ratio and potential temperature profiles of a 120 × 120 km 2 cloudpermitting simulation with 2 km horizontal resolution at the end of day 100. This sounding is the same as that used by Fu and O'Neill (2021a).…”