Lagrangian coherent structures in tropical cyclone intensification

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<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 localized stirring around VHTs and their vortical remnants, as well as the evolution and 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. <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 θ<sub>e</sub>, the Lagrangian coherent structures are found to modulate the convection emanating from the boundary layer by stirring θ<sub>e</sub> 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

Kinematics of a Fluid Ellipse in a Linear Flow

“…Here we verify that the kinematic condition for the motion of an elliptical boundary, Equation (43), recovers the first three ellipse evolution equations presented in Equation (42). Whereas Neu [2] and Ide and Wiggins [3] write out the entries of the matrix emerging from the derivative of the boundary…”

“…and equating the coefficients of the I, K and DJD −1 − J matrices between Equations (111) and (117), we recover the first three evolution equations given in Equation (42). Note that as DJD −1 − J contributes only to the J and L components, it does not interfere with the I or K components and therefore need not be written out explicitly.…”

Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear

“…These LCS are the finite-time manifolds of the time-dependent flow. First analyses of such LCS in TCs have recently been performed by Sapsis and Haller (2009) and Rutherford et al (2010). We anticipate that the analysis of LCS in a vertically sheared TC will yield further insight into the interaction of the TC with environmental air.…”

Lagrangian vortices in developing tropical cyclones

“…The Lagrangian structures and their role in the merger of these smaller vorticity anomalies and diabatic activation represents an important mechanism for genesis which deserves further study. The methods used in this study are capable of resolving the features at smaller scales, but finer model resolution will be required to resolve the flow boundaries that exist between these vortices (Rutherford and Dangelmayr, ).…”