Fully Three-Dimensional Stability Analyses and Evolution of Hurricanes and Tornadoes with Secondary Circulations

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Tornadoes and hurricanes are two of the most destructive natural phenomena that threaten the U.S. population. A universal characteristic of these storms is a vertically aligned, intense vortex in the core region. The classical approach of analyzing the linearized dynamics of small perturbations to vortices has yielded substantial insight into the behavior of intense atmospheric vortices, helping to explain such phenomena as multiple vortex formation in tornadoes and rapid inner-core structure change in hurricanes. The vast majority of these studies, however, have been applied to essentially two-dimensional perturbations to two-dimensional vortices. In some studies, three-dimensional perturbations have been considered, but the basic-state vortices were homogenous in the vertical direction.This research will advance the study of intense atmospheric vortices in two ways. First, the classical methods of vortex stability analysis will be extended to allow for the study of truly three-dimensional vortices. The equations of motion will be the three-dimensional anelastic equations such that neither hydrostatic, quasi-geostrophic, or other balance approximations are required. Intense atmospheric vortices of all types are not homogenous along their vertical axis, but often have considerable variation of their wind and density fields with height. The stability analysis will allow for eigenfunctions that vary arbitrarily with height, so that the Principal Investigators can find truly three-dimensional eigenmodes, unstable or otherwise, in the cores of three-dimensional vortices. This approach will be applied to axisymmetric basic-state vortices, based on the results of numerical simulations and existing or future observational data sets of tornadoes and hurricanes.Secondly, the secondary circulation, which is known to play a critical role in the development and maintenance of tornadoes and hurricanes, will be incorporated into the basic state flow. Previous investigations on the influence of radial inflow and vertical outflow on the stability of these vortices have been limited to highly idealized vortices. Whether the secondary circulation, and in particular the shear of the vertical wind up through the core of the vortex, stabilizes or destabilizes the vortex remains an open and intriguing question and may be critical in understanding inner-core dynamics in tornadoes and hurricanes. For stable vortices, such as developing tropical cyclones or "one-celled" tornadic vortices, a natural extension of the research will be to determine the linearized evolution and impact on the basic-state vortex of three-dimensional, asymmetric, nonhydrostatic perturbations.Successful completion of this research will lead to better understanding and, potentially, better forecasts of destructive atmospheric vortices.