A Quasi-2D Model of Convectively Coupled Vortices

Abstract Tropical cyclone precursor vortices are convectively coupled vortices. They undergo significant changes in size and intensity before transitioning to a mature hurricane or typhoon. This paper designs a stochastic quasi-2D model to study the vortices’ formation and interaction. Based on the diagnostic result of a cloud-permitting simulation, we parameterize deep convection as random pulses whose probability of occurrence depends on the spatially smoothed vorticity. The dependence of convective probability on the vorticity field represents the mesoscale feedback. The smoothing represents the spontaneous spreading of convective activity by cold pools and other processes. Simulations show that the system exhibits two stages: the vortex formation stage and the vortex interaction stage. The vortex formation stage features the stochastic nucleation of vortices and their subsequent growth via the mesoscale feedback. The growth of mesoscale vorticity magnitude undergoes a power-law growth and then transitions to exponential growth. An analytical theory is proposed to capture this transition. The vortex interaction stage features vortex merging. The vortex size grows due to merging and spontaneous spreading of convective activity. When the vortex size grows sufficiently large, it is squeezed by the convection-induced convergent flow, which converts the growth in size to the growth in vorticity magnitude. This adjustment process corresponds to a bidirectional kinetic energy transfer, with the rotational wind producing an upscale energy transfer and the convergent wind producing a downscale energy transfer. This quasi-2D model provides a simple framework for understanding the multiscale interaction in tropical cyclogenesis.