Synthesis of Vortex Rossby Wave Dynamics

涡旋Rossby波(VRW)是一种有趣的物理现象，它在热带气旋(TC)动力学中的重要作用已被广泛接受。最早的分析假设了相对于TC的平均旋流向上传播的拖尾螺旋VRW携带的角动量向内涡流。不对称平衡理论的发展为在一系列物理环境中分析VRW奠定了基础。一个关键的概念是轴对称，在这种情况下，涡度守恒的波在径向剪切平均流中变得越来越细丝，并将其能量移交给基本态。对初始平衡势涡度(PV)扰动的日益逼真的模拟支持这一观点；尽管不平衡热扰动的效果要差得多。智力上的优点：VRW文献在大部分情况下在概念上是困难的，甚至是晦涩难懂的，达到知识的前沿是具有挑战性的。这个项目将支持以数值解的形式重塑大部分分析，其中动态变量在方位向进行傅里叶变换，时间及其径向(通常是垂直)结构使用三对角线求解器计算。在该公式中，每个傅立叶分量相对于地面具有固定的周向波数和视频率。传播的VRW解被限制在环形波导中，其中波的多普勒频移频率介于Rossby波截止频率和零点之间。这种方法在概念上比分段连续或WKB解析解简单得多。用时间上的傅立叶级数表示强迫，模拟了间歇强迫的非对称VRW波列。矛盾的是，在这些计算中，最大的涡旋角动量会聚跨越了强迫轨迹，即使大部分的波丝化发生在眼睛外数十公里外的Rossby波临界半径附近。与前人的工作基本一致，模拟的波具有向内和向上游的相传播，但向外的群传播和向内的涡动角动量通量。这种方法将被推广到大气压不稳定剖面和耦合的VRW和重力波的共振不稳定。它还将被用来解决理想涡旋运动研究中静止VRW和波-波相互作用的悬而未决的角色。广泛的影响：该项目旨在通过在数值解的背景下重新检查和加深对涡旋Rossby波特性的理解以及通过使理想化模拟广泛可用来促进科学发展。对对流强迫的大众汽车的新见解就是一个例子。将这种方法扩展到不稳定剖面、不稳定与共振重力波和涡旋运动相结合，有望进一步解释这些现象。对于佛罗里达国际大学的研究生来说，每项研究都是一个容易掌握的论文主题。数值解在概念上的简单性将有助于对VRW概念的解释。所有的模拟都将被编码成记录良好的matlab m文件，并与适当的支持文件一起发布在网络上。主要成果将是发表期刊文章，其中许多是学生第一作者，以及在项目接近完成时发表一篇可访问的评论文章。

Vortex Rossby Waves (VRWs) are intriguing physical phenomena whose significant role in Tropical Cyclone (TC) dynamics has gained wide acceptance. The earliest analyses hypothesized inward eddy fluxes of angular momentum carried by trailing spiral VRWs that propagate upstream relative to the TC's mean swirling flow. Development of the Asymmetric Balance theory set the stage for analysis of VRWs in a range of physical contexts. A key concept was axisymmetrization, in which the vorticity-conserving waves become increasingly filamented in a radially shearing mean flow and surrender their energy to the basic state. Increasingly realistic simulations of initially balanced Potential Vorticity (PV) perturbations support this idea; although unbalanced thermal perturbations are much less effective.Intellectual Merit:The VRW literature is, for the most part, conceptually difficult, even arcane, and reaching the frontier of knowledge is challenging. This project will support recasting much of the analysis in terms of numerical solutions in which the dynamic variables are Fourier transformed in azimuth and time with their radial (and often vertical) structure is computed using a tridiagonal solver. In this formulation, each Fourier component has fixed circumferential wavenumber and apparent frequency relative to the ground. Propagating VRW solutions are confined to an annular waveguide encompassing radii where the waves' Doppler shifted frequency lies between the Rossby wave cutoff frequency and zero.This approach is much simpler conceptually than piecewise continuous or WKB analytical solutions. Intermittently forced asymmetric VRW wavetrains are simulated by representing the forcing with a Fourier series in time. Paradoxically, the largest eddy angular momentum convergence in these calculations spans the locus of forcing even though most of the wave filamentation occurs near the Rossby wave critical radius tens of kilometers outside the eye. In general agreement with previous work, the simulated waves have inward and upstream phase propagation, but outward group propagation and inward eddy fluxes of angular momentum. This approach will be extended to baratropically unstable profiles and resonant instability of coupled VRWs and gravity waves. It will also be used to address the unresolved roles of standing VRWs and wave-wave interactions in idealized vortex motion studies.Broader Impacts: The project is designed to advance the science by reexamination and deepening understanding of the properties of vortex Rossby waves in the context of the numerical solutions and by making idealized simulations widely accessible. The new insights into convectively forced VRWs are an example. Extending this approach to unstable profiles, instability coupled with resonant gravity waves, and vortex motion promises to further elucidate these phenomena. Each of the studies is a manageable thesis topic for Florida International University graduate students. The conceptual simplicity of the numerical solutions will facilitate interpretation in terms of VRW concepts. All of the simulations will be coded as well documented MATLAB m-files and posted on the web with appropriate supporting documentation. Key outcomes will be publication journal articles, many with student first authors, and of an accessible review article as the project nears completion.