The fluid dynamics of spontaneous tropical cyclogenesis

This thesis presents a theoretical framework of spontaneous tropical cyclogenesis in an idealized environment with a uniform sea surface temperature and no background wind. The investigation spans from the nucleation of the midlevel vortex to the formation of the surface vortex. The key is quantifying the multiscale interaction between convection and eddies. The investigation starts from the small amplitude stage. Within the first two days, the convective stretching of planetary vorticity and tilting of random vertical shear generate fluctuating mesoscale vertical vorticity. The standard deviation of mesoscale vorticity is analytically shown to be proportional to the square root of the domain-averaged accumulated rainfall. The randomly generated mesoscale vortices then undergo a small amplitude development stage, where a low signal-to-noise ratio prevents quantitative study. We overcame this problem by amplifying the longwave radiative feedback. The spectral growth rate shows a 10 km scale short-wavelength cutoff by cold pools and anvil clouds, a convective spreading length explained with a wavepacket diffusion model. The long-wavelength cutoff is explained as an effective Rossby deformation radius set by the coupling of the shallow and deep cells. Using a four-layer quasi-geostrophic model, the most unstable wavelength is shown to be proportional to the geometric average of the convective spreading length and the effective Rossby deformation radius. The finite-amplitude evolution involves the vertical and horizontal aspects. For the vertical aspect, the extension of the midlevel vortex to the surface is studied with a column model along the vortex axis. The vertical advection and stretching of the relative vorticity play crucial roles. In a thermodynamic view, we use asymptotic analysis to show that they adiabatically drive a low-level cold anomaly that enhances deep convection, making diabatic heating more bottom-heavy. In a mechanical view, we use a low-order spectral model to show that the nonlinear vortex dynamics generates a surface cyclone via the production of barotropic mode, facilitated by vertical eddy diffusion. A particularly intriguing finding is the resonant growth of the barotropic vorticity in a vortical hot tower (VHT), which could grow upscale and accelerate the formation of a mesoscale surface cyclone. For the horizontal aspect, a quasi-2D model is built to study the upscale and up-strength growth of convectively coupled vortices. The convectively driven convergent flow causes the up-strength growth, a pseudo-3D effect accelerated by the 2D upscale effect. By modeling the vorticity histogram evolution with a Markov chain model, the tangential flow is predicted to be faster when the convective mass flux is more concentrated in an individual VHT. The theoretical framework is rooted in an idealized environment without synoptic-scale disturbances. It provides a reference for understanding the evolution of the vortex size and intensity in the real atmosphere.

Keywords: Sustainability.
Earth System Science.
Advisor: O'Neill Morgan (Morgan E.)
Koseff Jeffrey Russell
Ouellette Nicholas (Nicholas Testroet)
Thomas Leif N.
Wu Zhaohua