Taming Complexity of Mesoscale Dynamics with Low-Order Models

这项研究试图开发低阶模型(LOM)，它继承了流体动力学方程的基本守恒性质，从而表现出良好的物理行为。新的三维流动LOM融合了不同的物理机制，以加强我们对海洋边界层中观察到的对流现象的理解。对流MBLS的考虑将涉及几何形状(2D卷与3D单体)、环流方向(开放单体与闭合单体)以及独特的过渡对流模式，如猕猴桃云的形成。LOM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，以及d)水平风中的垂直切变。此外，来自物理上健全的非线性LOM的时间序列将被探索为对更传统的(随机)模型所产生的时间序列的有价值的补充。预计前者在大气动力学的各种研究中将比从标准时间序列分析中借用的常用通用方法更有用。本研究中发展的概念和方法将加深我们对地球物理流体动力学现象的理解，特别是对MBLS中的中尺度对流现象的理解。这一项目的成功还将促进人们更深入地了解统计学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会对大气和相关科学的许多领域产生更广泛的影响，因为它使人们关注到一个可行的工具(而不是数值模拟)来解决由非线性偏微分方程组描述的物理现象。这项研究还在许多方面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".