Understanding the Development and Application of Simplified Dynamical Models

这项研究的目的是通过开发和应用过滤模式来更好地了解热带大气的动力学。过滤模型是简化的动力学模型，它描述了低频大气运动，但不允许惯性重力波自由传播。这个项目建立在首席研究员(PI)在热带动力学方面的研究专长的基础上，并推进了他之前的工作。该项目有两个主要部分，都涉及热带大气过滤模式的应用。第一部分侧重于大尺度热带动力学，并涉及将要使用的新的和改进的过滤模式的理论发展。第二部分利用基于现有过滤模型的理论，重点介绍飓风动力学。长波模式是为大尺度热带应用而设计的一种现有的过滤模式，已成为热带研究的重要工具。它准确地描述了Kelvin波和长Rossby波，但存在严重扭曲短Rossby波的不足。在这个项目的第一部分，PI将改进长波模式，从而为热带研究界提供一个理解大尺度热带运动的重要新工具。此外，他还将把这个在赤道贝塔平面理论框架下发展起来的新的过滤模型推广到球体中。这将第一次提供一个过滤的动力学模型，准确地描述Rossby-Haurwitz波的全球PV动力学和Kelvin波的非PV动力学。在这些新过滤模式的许多可能的推广和应用中，将详细研究以下内容：(A)改进的MJO模拟；(B)生成拉普拉斯潮汐方程的精确解析解；(C)“热带omega方程”的推导和解，以了解与Hadley环流和Walker环流有关的垂直运动场；(D)推导和应用球面上惯性重力波和Rossby-Haurwitz波的射线跟踪理论，目的是改进对中纬度-热带相互作用的理解；(E)开发用于地球物理湍流的新的球谐(而不是球谐)分析工具，目的是将莱茵河屏障的概念从二维波数空间扩展到三维波数空间。该项目的第二部分将利用埃利亚森平衡涡旋模型，这是一个为热带气旋应用设计的过滤模型，以帮助我们更好地了解飓风动力学，特别是快速增强的过程。在这里，PI将使用由原始动量、连续性和热力学方程导出的位势趋势方程，来分离热带气旋中暖核和暖环热力结构快速发展的条件和接近稳定状态的条件。智力上的功绩。虽然气候模拟和数值天气预报通常依赖原始方程模型，但对基本大气动力学的理解主要来自于使用简化模型的研究。这项研究将创造新的过滤模型工具，以进一步了解大气动力学，特别是热带地区的大气动力学。将这些模型应用于本项目所研究的问题所获得的知识，将有助于回答有关大规模大气动力学和飓风迅速加剧的一些关键问题。更广泛的影响。将在该项目期间为新的过滤模型开发用户友好的软件，并将提供给其他研究人员，以促进对大气动力学的进一步研究。参与这项工作的研究生将接受培训和经验，这将有助于他们为从事研究工作做好准备。该项目增加了对基本大尺度动力学和基本飓风动力学的了解，有朝一日应有助于提高预测导致飓风强度变化的大尺度热带天气模式和中尺度模式的能力。

The goal of this research is to provide improved understanding of the dynamics of the tropical atmosphere through the development and application of filtered models. Filtered models are simplified dynamical models that describe low-frequency atmospheric motions but do not allow freely propagating inertia-gravity waves. This project builds on the Principal Investigator's (PI's) research expertise in tropical dynamics and advances his previous work. The project has two main parts, both of which involve the application of filtered models to the tropical atmosphere. Part I focuses on large-scale tropical dynamics and involves the theoretical development of the new and improved filtered models to be used. Part II utilizes theory based on an existing filtered model and focuses on hurricane dynamics. The longwave model is an existing filtered model designed for large-scale tropical applications and has been an important tool in tropical research. It accurately describes Kelvin waves and long Rossby waves, but has the deficiency that it badly distorts short Rossby waves. In part I of this project, the PI will improve the longwave model and thereby provide the tropical research community with an important new tool for understanding large-scale tropical motions. In addition, he will generalize this new filtered model, developed in the framework of equatorial beta-plane theory, to the sphere. This will provide, for the first time, a filtered dynamical model that accurately describes both the global PV dynamics of Rossby-Haurwitz waves and the non-PV dynamics of Kelvin waves. Among the many possible generalizations and applications of these new filtered models, the following will be studied in detail: (a) improved simulations of the MJO; (b) generation of accurate analytical solutions to Laplace's tidal equations; (c) derivation and solution of a "tropical omega-equation" to understand vertical motion fields associated with the Hadley and Walker circulations; (d) derivation and application of a ray tracing theory on the sphere for both inertia-gravity waves and Rossby-Haurwitz waves, with the goal of improved understanding of midlatitude-tropical interactions; (e) development of new spheroidal harmonic (as opposed to spherical harmonic) analysis tools for geophysical turbulence, with the goal of extending the concept of the Rhines' barrier from two-dimensional wavenumber space to three-dimensional wavenumber space.Part II of this project will utilize the Eliassen balanced vortex model, a filtered model designed for tropical cyclone applications, to help us better understand hurricane dynamics, especially the process of rapid intensification. Here the PI will use the geopotential tendency equation, derived from the original momentum, continuity, and thermodynamic equations, to isolate the conditions under which warm-core and warm-ring thermal structures can rapidly develop in a tropical cyclone and the conditions under which a steady state can be approached. Intellectual Merit. While climate simulation and numerical weather prediction usually rely on primitive equation models, understanding of the underlying atmospheric dynamics has come primarily from studies using simplified models. The research will create new filtered model tools for further understanding of atmospheric dynamics, especially in the tropical region. The knowledge gained from applying these models to the problems studied in this project will help answer a number of key questions concerning large-scale atmospheric dynamics and the rapid intensification of hurricanes. Broader Impacts. User-friendly software for the new filtered models will be developed during this project and will be made available to other researchers to facilitate additional studies of atmospheric dynamics. The graduate students involved in this work will receive training and experience which will help prepare them for careers in research. The increased knowledge of fundamental large-scale dynamics and fundamental hurricane dynamics gained from this project should someday contribute to an improved ability to predict both large-scale tropical weather patterns and the mesoscale patterns that lead to changes in hurricane intensity.