Wave Dynamics in Tropical Cyclones

智力价值：这个项目将分几个阶段建立一个框架，用于解释复杂的波浪动力学，据信这些波浪动力学部分调节了飓风的强度。第一阶段：以前的波浪动力学理论忽略了飓风内部的云层。这种忽视很难证明是合理的，因为云层覆盖密集的地区，如眼壁，极大地降低了静态稳定性。该项目的第一阶段将在一个相对简单的模式中研究云覆盖对波浪和波-均流相互作用的影响。具体地说，研究人员将检查重力稳定、不沉淀的多云涡旋中的波，该涡旋没有平均的二次环流，也不与行星边界层相互作用。从第一性原理出发，研究人员导出了该系统的一组线性化波动方程。此外，他们已经开始(通过分析和计算)研究云层覆盖如何影响眼壁不稳定和内部重力波辐射。这两个过程很有意义，因为它们原则上可以改变涡旋的最大平均切向风速。第二阶段：该项目的第二阶段将用不太接近的计算实验来补充第一阶段。主要的工具可能是科罗拉多州立大学开发的区域大气模拟系统(RAMS)。研究人员计划使用RAMS来(I)独立验证第一阶段的结果，以及(Ii)检查理想化的多云涡旋中的非线性波动现象。第三阶段：研究人员预计该项目将进入第三阶段，在这一阶段中，他们将继续使用RAMS来研究其他因素，如降水、平均二次环流以及边界层的热通量和角动量如何影响波动动力学。更广泛的影响：这项研究工作将导致建模专家、观测气象学家和应用数学家之间的合作。此外，结果将立即纳入科罗拉多州立大学的高级研究生课程。

Intellectual Merit: In several stages, this project will build a framework for interpreting the complex wave dynamics that are believed to partially regulate hurricane intensity. Stage 1: Previous theories of wave dynamics neglected clouds within the hurricane. Such neglect is difficult to justify, because regions with dense cloud coverage, such as the eyewall, have greatly reduced static stability. The first stage of this project will examine the influence of cloud coverage on waves and wave-mean-flow interactions in a relatively simple model. Specifically, the investigators will examine waves in a gravitationally stable, nonprecipitating cloudy vortex that has no mean secondary circulation and does not interact with the planetary boundary layer. Starting from first principles, the investigators have derived a set of linearized wave equations for this system. Furthermore, they have begun to examine (analytically and computationally) how cloud coverage affects eyewall instability and internal gravity wave radiation. These two processes are of interest because they can in principle alter the maximum mean tangential wind speed of the vortex. Stage 2: The second stage of the project will complement the first with less approximate computational experiments. The main tool will likely be the Regional Atmospheric Modeling System (RAMS), developed at Colorado State University. The investigators plan to use RAMS to (i) independently verify results from Stage 1, and (ii) examine nonlinear wave phenomena in an idealized cloudy vortex. Stage 3: The investigators anticipate a third stage of the project, in which they will continue use of RAMS to study how additional factors, such as precipitation, mean secondary circulation and boundary layer fluxes of enthalpy and angular momentum affect the wave dynamics. Broader Impacts: The research effort will lead to collaborations between modeling specialists, observational meteorologists and applied mathematicians. In addition, results will be immediately incorporated into advanced graduate level courses at Colorado State University.