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

龙卷风和飓风是威胁美国人口的两种最具破坏性的自然现象。 这些风暴的一个普遍特征是在核心区域有一个垂直排列的强烈涡旋。 分析涡旋小扰动的线性动力学的经典方法已经对强烈大气涡旋的行为产生了实质性的洞察力，有助于解释龙卷风中的多个涡旋形成和飓风中的快速内核结构变化等现象。 然而，这些研究中的绝大多数基本上都应用于二维涡的二维扰动。 在一些研究中，三维扰动已经被考虑，但基本状态的涡是均匀的垂直方向。 首先，将涡稳定性分析的经典方法扩展到允许研究真正的三维涡。 运动方程将是三维滞弹性方程，这样就不需要流体静力、准地转或其它平衡近似。 所有类型的强大气涡旋沿其垂直轴沿着不是均匀的，但其风场和密度场往往随高度有相当大的变化。 稳定性分析将考虑随高度任意变化的本征函数，以便主要研究人员可以在三维旋涡的核心中找到真正的三维本征模式，无论是否不稳定。 根据数值模拟的结果和现有或未来的龙卷风和飓风观测数据集，这一方法将适用于轴对称基本状态涡流，其次，已知在龙卷风和飓风的发展和维持中起关键作用的次级环流将被纳入基本状态流。 以前关于径向入流和垂直出流对这些涡稳定性影响的研究仅限于高度理想化的涡。 二次环流，特别是垂直风的剪切通过涡旋的核心，稳定或不稳定的涡旋仍然是一个开放的和有趣的问题，可能是关键的了解内核动力学在龙卷风和飓风。 对于稳定的涡旋，例如正在形成的热带气旋或“单胞”龙卷风涡旋，研究的自然延伸将是确定三维、非对称、非流体静力扰动的线性演变和对基本状态涡旋的影响，这项研究的成功完成将导致更好地理解和潜在地更好地预报破坏性的大气涡旋。

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.