The computation of a hurricane eyewall is necessary to determine mixing between the eyewall and the neighbouring eye and environment regions. We define a Lagrangian eyewall region by computing the Lagrangian structures of hyperbolic stability that distinguish the eyewall from surrounding regions. The methods used guarantee the stability and continuity of the eyewall for time-dependent velocity fields. As an added benefit of our methods, fast convergence gives the opportunity to utilize the methods in real-time simulations. The exact location of Lagrangian coherent structures is accomplished through a ridge-extraction algorithm, which is efficient for locating the ridges found in this model. A complete construction of three-dimensional coherent structures is accomplished by overlaying horizontally continuous ridge curves on z levels.

Abstract. 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 e ) that modulates the VHT activity, is a complex problem in moist helical turbulence.To better understand the structural aspects of the threedimensional 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 e . 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 e phenomenology in a high-resolution numerical tropical cyclone simulation. The usefulness of these methods is demonstrated by an analysis of particle trajectories.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 e , attracting Lagrangian coherent structures are coincident with pools of high boundary layer θ e . 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.

Abstract. This paper studies Lagrangian mixing in a twodimensional barotropic model for hurricane-like vortices. Since such flows show high shearing in the radial direction, particle separation across shear-lines is diagnosed through a Lagrangian field, referred to as R-field, that measures trajectory separation orthogonal to the Lagrangian velocity. The shear-lines are identified with the level-contours of another Lagrangian field, referred to as S-field, that measures the average shear-strength along a trajectory. Other fields used for model diagnostics are the Lagrangian field of finite-time Lyapunov exponents (FTLE-field), the Eulerian Q-field, and the angular velocity field. Because of the high shearing, the FTLE-field is not a suitable indicator for advective mixing, and in particular does not exhibit ridges marking the location of finite-time stable and unstable manifolds. The FTLE-field is similar in structure to the radial derivative of the angular velocity. In contrast, persisting ridges and valleys can be clearly recognized in the R-field, and their propagation speed indicates that transport across shear-lines is caused by Rossby waves. A radial mixing rate derived from the Rfield gives a time-dependent measure of flux across the shearlines. On the other hand, a measured mixing rate across the shear-lines, which counts trajectory crossings, confirms the results from the R-field mixing rate, and shows high mixing in the eyewall region after the formation of a polygonal eyewall, which continues until the vortex breaks down. The location of the R-field ridges elucidates the role of radial mixing for the interaction and breakdown of the mesovortices shown by the model.

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 &theta;_e 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 localized stirring around VHTs and their vortical remnants, as well as the evolution and stirring of &theta;_e. 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 &theta;_e phenomenology. <br><br> Our primary findings are that VHTs are coherent Lagrangian vortices that create a turbulent mixing environment. Associated with the 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 are found to modulate the convection emanating from the boundary layer by stirring &theta;_e along organized attracting boundaries. Extensions of boundary layer coherent structures grow above the boundary layer during episodes of convection are responsible for organizing the remnants of the convective vortices. These hyperbolic structures form initially as boundaries between VHTs, but persist above the boundary layer and outlive the VHTs to eventually form the primary eyewall as the vortex attains maturity

The tropical cyclogenesis sequence of Hurricane Sandy is examined. It is shown that genesis occurs within a recirculating Kelvin cat's-eye flow of a westward-propagating tropical wave. The cat's-eye flow is able to provide a protective environment for the mesoscale vortex to grow and is characterized by gradual column moistening and increased areal coverage of deep cumulus convection. These findings are generally consistent with a recently proposed tropical cyclogenesis sequence referred to as the ''marsupial paradigm.'' Sandy's cyclogenesis provides a useful illustration of the marsupial paradigm within a partially open recirculating region, with the opening located south of the pouch center. It is suggested that the opening acts to enhance the genesis process because it is adjacent to an environment characterized by warm, moist air, conditions favorable for tropical cyclogenesis. From a dynamical perspective, accretion of low-level cyclonic vorticity filaments into the developing vortex from several sources (the South American convergence zone, an easterly wave located west of the pre-Sandy wave, and cyclonic vorticity generated along Hispaniola) is documented. Organization and growth of the nascent storm is enhanced by this accretion of cyclonic vorticity. A Lagrangian trajectory analysis is used to assess potential contributions to Sandy's spinup from a Caribbean gyre and the easterly wave that formed Hurricane Tony. This analysis indicates that these features are outside of the Lagrangian flow boundaries that define the pre-Sandy wave and do not directly contribute to spinup of the vortex. Finally, the effectiveness of forecasts from the U.S. and European operational numerical weather prediction models is discussed for this case.