Taming Complexity of Mesoscale Dynamics with Low-Order Models

本研究试图建立低阶模型（LOMs），以继承流体动力学方程的基本守恒特性，从而表现出良好的物理行为。新的三维流动LOMs包含了不同的物理机制，以增强我们对海洋边界层（MBLs）观测到的对流现象的理解。对流MBLs需要考虑几何形状（2D卷与3D单元）、环流方向（开放与封闭单元）以及独特的过渡对流模式（如活动性云的形成）。LOMs的物理机制包括：a)热通量，b)大尺度垂直运动，c)气旋与反气旋背景涡度，d)水平风中的垂直切变。此外，将探索源自物理健全非线性LOMs的时间序列，作为更传统（随机）模型产生的时间序列的有价值的补充。期望前者在大气动力学的各种研究中将比借用标准时间序列分析的常用的通用方法更有用。本研究中发展的概念和方法将增强我们对地球物理流体动力学现象的理解，特别是对MBLs中尺度对流的理解。这个项目的成功还将促进人们更深入地了解统计和非线性动力学在大气研究中相互作用的性质。更广泛的影响这项研究可能对大气和相关科学的许多领域产生更广泛的影响，因为它为解决非线性偏微分方程所描述的物理现象提供了一种可行的工具（而不是数值模拟）。这项研究在许多方面也涉及一个新兴的科学领域，通常被称为“复杂性”。

This research makes an attempt at developing low-order models (LOMs) that inherit fundamental conservation properties of the fluid dynamical equations, thereby exhibiting sound physical behavior. The new LOMs of 3D flows incorporate different physical mechanisms to enhance our understanding of convective phenomena observed in marine boundary layers (MBLs). Consideration in convective MBLs will address the geometry (2D rolls versus 3D cells), circulation direction (open vs. closed cells), and unique transitional convective patterns such as actiniae cloud formations. Physical mechanisms incorporated into the LOMs are a) heat flux, b) large-scale vertical motion, c) cyclonic vs. anticyclonic background vorticity, and d) vertical shear in the horizontal wind.Additionally, time series originating from physically sound nonlinear LOMs will be explored as a valuable complement to those generated by the more traditional (stochastic) models. The expectation is that the former will become more useful in various studies of atmospheric dynamics than commonly used all-purpose ones borrowed from standard time series analysis.Intellectual merit The concepts and methods developed in this study will enhance our understanding of geophysical fluid dynamics phenomena, and in particular mesoscale convection in MBLs. Success in this project will also promote a greater insight into the nature of the interacting roles of statistics and nonlinear dynamics in atmospheric studies.Broader impacts The research may have broader impacts on many areas within the atmospheric and related sciences since it brings into focus a viable tool (other than numerical simulation) for addressing physical phenomena described by nonlinear partial differential equations. This research also addresses in many ways an emerging new field of science, commonly referred as "complexity".