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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. The rotating deep convective structures possessing enhanced cyclonic vorticity within their cores have been dubbed 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 (θ<sub>e</sub>) that modulates the VHT activity, is a complex problem in moist helical turbulence. <br><br> To better understand the structural aspects of the three-dimensional intensification process, a Lagrangian perspective is explored that focuses on the coherent structures seen in the flow field associated with VHTs and their vortical remnants, as well as the evolution and localized stirring of θ<sub>e</sub>. Recently developed finite-time Lagrangian methods are limited in the three-dimensional turbulence and shear associated with the VHTs. In this paper, new Lagrangian techniques developed for three-dimensional velocity fields are summarized and we apply these techniques to study VHT and θ<sub>e</sub> phenomenology in a high-resolution numerical tropical cyclone simulation. The usefulness of these methods is demonstrated by an analysis of particle trajectories. <br><br> We find that VHTs create a locally turbulent mixing environment. However, associated with the VHTs are hyperbolic structures that span between adjacent VHTs or adjacent vortical remnants and represent coherent finite-time transport barriers in the flow field. Although the azimuthally-averaged inflow is responsible for the inward advection of boundary layer θ<sub>e</sub>, attracting Lagrangian coherent structures are coincident with pools of high boundary layer θ<sub>e</sub>. Extensions of boundary layer coherent structures grow above the boundary layer during episodes of convection and remain with the convective vortices. These hyperbolic structures form initially as boundaries between VHTs. As vorticity aggregates into a ring-like eyewall feature, the Lagrangian boundaries merge into a ring outside of the region of maximal vorticity.