Lagrangian coherent structures in tropical cyclone intensification

Recent work has suggested that tropical cyclones intensify via a pathway of rotating deep moist convection in the presence of enhanced fluxes of moisture from the ocean. Although the updrafts within these convective structures typically have short lifetimes of about an hour, the updrafts act to stretch vertical vorticity in the low- to mid-troposphere and intensify the vorticity locally above ambient values by one to two orders of magnitude. The rotating deep convective structures possessing intense cyclonic vorticity within their cores are called Vortical Hot Towers (VHTs). In general, the interaction between VHTs and the system-scale vortex, as well as the corresponding evolution of equivalent potential temperature $\theta_e$, is a complex problem in moist helical turbulence.

To better understand the structural aspects of the intensification process, a Lagrangian perspective is explored herein of the localized stirring around VHTs and their vortical remnants, as well as the evolution and stirring of $\theta_e$. Recently developed finite-time Lagrangian methods can locate time-dependent structures effectively, but are designed for two-dimensional flows with weak time-dependence rather than the highly time-dependent, three-dimensional, turbulence associated with the VHTs. In this paper, we summarize new Lagrangian techniques that have been developed for three-dimensional velocity fields and we apply these techniques to study VHT and $\theta_e$ phenomenology. Our primary findings are that VHTs are coherent Lagrangian vortices that create a turbulent mixing environment; and associated with VHTs are hyperbolic structures that modulate the aggregation of VHTs and their vortical remnants. Although the azimuthally-averaged inflow is responsible for the inward advection of boundary layer $\theta_e$, the Lagrangian coherent structures modulate the boundary layer convection by stirring $\theta_e$ along organized attracting boundaries. We identify additional coherent structures above the boundary layer, which are responsible for organizing the remnants of the convective vortices. These hyperbolic structures form initially as boundaries between VHTs, but they outlive the VHTs and eventually form the primary eyewall as the vortex attains maturity.