Lagrangian mixing and transport in hurricanes
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This study examines the role of transport and mixing in the dynamics of tropical cyclones from a mathematical viewpoint and their implications for intensity. While this topic has seen extensive study, much of it has lacked the mathematical rigor allowed by a new class of Lagrangian techniques, which allow the study of particle transport through time-dependent flows. Lagrangian coherent structures (LCS's) are time-dependent boundaries which partition the flow into distinct regions, controlling the systematic transport of material between regions. In this study, the mathematics of Lagrangian transport is developed, and adapted to several tropical cyclone models. Three models are utilized to study mixing; the axisymmetric model of Rotunno and Emanuel (1987), the nondivergent barotropic 2D model of Schubert et al. (1999), and the 3D Penn State-NCAR mesoscale model (MM5). For the study of mixing on the axisymmetric model, a new class of mixing rates is proposed which vary in initial time and integration time, and it is shown that mixing events precede changes in intensity. For the nondivergent barotropic model, orthogonal flow separation reveals coherent structures that are persistant through strong shear, and mixing is quantified through the shear during mesovortex interaction. The extension of the orthogonal separation methods to 3D provides a method for decomposing Lagrangian hyperbolicity from shear. The method is applied to the MM5 model to find the Lagrangian eye-eyewall interface (LEEI), which is responsible for dictating transport between the two regions. A new ridge extraction algorithm is used to extract the 2D manifolds of the 3D Lagrangian fields. By extending and automating this algorithm across varying initial time, a time-dependent and spatially smooth representation of the LEEI in terms of Fourier descriptors and radial basis functions is computed. The dynamics of the time-dependent LEEI indicate that the higher wavenumber asymmetries vanish, but the lower wavenumber asymmetries remain, quantifying the degree of axisymmetry in the storm from a transport perspective. The last study applies the new 3D techniques to an intensifying storm by studying the interaction of vortical hot towers (VHT's). VHT's are shown to not only be coherent structures, but to be associated with hyperbolic LCS's which play an important role in their interaction and in the formation of an eyewall. The length of the LCS's indicate that the VHT's have impact on a broad range that affects environmental flow into the primary vortex.