Understanding the Development and Application of Simplified Dynamical Models

本研究的目的是通过发展和应用过滤模式，提高对热带大气动力学的认识。过滤模型是描述低频大气运动的简化动力学模型，但不允许自由传播惯性重力波。该项目建立在首席研究员（PI）在热带动力学方面的研究专长上，并推进了他以前的工作。该项目有两个主要部分，都涉及将过滤模式应用于热带大气。第一部分着重于大尺度热带动力学，并涉及将使用的新的和改进的过滤模型的理论发展。第二部分利用基于现有过滤模型的理论，重点研究飓风动力学。长波模式是一种为热带大尺度应用而设计的已有过滤模式，已成为热带研究的重要工具。它准确地描述了开尔文波和长罗斯比波，但存在严重扭曲短罗斯比波的缺陷。在该项目的第一部分中，PI将改进长波模式，从而为热带研究界提供理解大尺度热带运动的重要新工具。此外，他将把这个在赤道面理论框架下发展起来的新的滤波模型推广到球体上。这将首次提供一个过滤后的动力学模型，准确地描述rosssby - haurwitz波的全局PV动力学和开尔文波的非PV动力学。在这些新过滤模型的许多可能的推广和应用中，将详细研究以下内容：(a)改进MJO的模拟；(b)生成拉普拉斯潮汐方程的精确解析解；(c)推导和求解“热带ω -方程”，以理解与Hadley和Walker环流有关的垂直运动场；(d)推导和应用球面上的惯性-重力波和罗斯比-豪维茨波的射线追踪理论，目的是增进对中纬度-热带相互作用的了解；(e)发展新的球谐（相对于球谐）地球物理湍流分析工具，目标是将莱茵河障壁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Eliassen平衡涡模型，这是一种为热带气旋应用而设计的过滤模型，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结构可以快速发展的条件以及可以接近稳定状态的条件。知识价值。虽然气候模拟和数值天气预报通常依赖于原始的方程模式，但对潜在大气动力学的理解主要来自于使用简化模式的研究。这项研究将为进一步了解大气动力学，特别是热带地区的大气动力学创造新的过滤模型工具。将这些模型应用于本项目研究的问题中所获得的知识将有助于回答有关大尺度大气动力学和飓风快速增强的一些关键问题。更广泛的影响。在这个项目中，将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获得培训和经验，这将有助于他们为从事研究工作做好准备。从这个项目中获得的关于基本大尺度动力学和基本飓风动力学的知识的增加，将来会有助于提高预测大尺度热带天气模式和导致飓风强度变化的中尺度模式的能力。

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.