Wave Dynamics in Tropical Cyclones

智力优势：在几个阶段中，该项目将建立一个框架，用于解释被认为部分调节飓风强度的复杂波浪动力学。第一阶段：以前的波动力学理论忽略了飓风中的云。这种忽视是很难证明的，因为有密集云层覆盖的区域，如眼墙，已经大大降低了静态稳定性。该项目的第一阶段将在一个相对简单的模型中研究云层覆盖对波浪和波浪-平均流相互作用的影响。具体来说，研究人员将研究重力稳定，无沉淀的多云涡旋中的波，该涡旋没有平均二次环流，也不与行星边界层相互作用。从第一性原理出发，研究人员推导出了该系统的一组线性化波动方程。此外，他们已经开始研究（分析和计算）云覆盖如何影响眼壁不稳定性和内部重力波辐射。这两个过程是令人感兴趣的，因为它们原则上可以改变涡流的最大平均切向风速。第二阶段：该项目的第二阶段将通过较少的近似计算实验来补充第一阶段。主要工具可能是科罗拉多州立大学开发的区域大气模拟系统。研究人员计划使用RAMS（i）独立验证第1阶段的结果，以及（ii）检查理想化多云涡旋中的非线性波现象。第三阶段：研究人员预计该项目的第三阶段，他们将继续使用RAMS来研究其他因素，如降水，平均二次环流和边界层焓通量和角动量如何影响波浪动力学。更广泛的影响：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，研究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.