Modeling Mesoscale Circulations by Coupled Nonlinear Systems

通过耦合非线性系统模拟中尺度环流

• 批准号: 0413382
• 负责人: Alexander Gluhovsky
• 金额: $ 6万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-10-01 至 2005-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0413382&HistoricalAwards=false
• 关键词: Modeling; Mesoscale; Circulations; Coupled; Nonlinear

Low-order models (LOMs) have played an important role in understanding of basic mechanisms of atmospheric dynamics through a focus on key elements and retaining only minimal number of degrees of freedom. LOMs are low-order systems of nonlinear ordinary differential equations derived from basic equations of atmospheric dynamics, commonly by the Galerkin method. Despite a number of highly attractive features, the method does not prevent a LOM from violations of fundamental conservation properties of the original equations, which often results in unphysical behavior. In previous studies, the investigators have developed a modular approach to constructing physically sound LOMs of atmospheric circulations, in which classical mechanical systems, the Volterra gyrostats (the simplest one being the celebrated Lorenz model of two dimensional Rayleigh-Benard convection), serve as elementary building blocks. Systems of coupled gyrostats avoid unphysical behavior by always conserving energy in the inviscid, unforced limit. At the same time, because the conservative part of most models in atmospheric dynamics (e.g., the primitive, shallow water and quasi-geostrophic equations) is Hamiltonian, maintaining the Hamiltonian structure in a LOM is viewed as an effective way to retain in it the fundamental conservation properties of the original system. As demonstrated in the Principal Investigators' preliminary studies, the gyrostatic approach is particularly promising in this endeavor. Under this project, an attempt will be made to develop useful Hamiltonian LOMs for important fluid dynamical systems, beginning with Rayleigh-Benard convection that provides the principal mechanism for mesoscale shallow convection.Relatively simple gyrostatic (particularly Hamiltonian) LOMs inherently possessing fundamental conservation properties of the fluid dynamical equations will provide a new effective tool to further a scientific understanding of essential mechanisms and their interaction in atmospheric dynamics. From the Broader Impacts perspective, eventually this research could lend new insights into issues of atmospheric predictability and, hence, limits to forecasting.

低阶模式（LOMs）通过关注关键要素和仅保留最小数量的自由度，在理解大气动力学的基本机制方面发挥了重要作用。 LOMs是由大气动力学基本方程推导出的低阶非线性常微分方程组，通常采用Galerkin方法。 尽管该方法具有许多非常有吸引力的特征，但它并不能防止LOM违反原始方程的基本守恒性质，这通常会导致非物理行为。 在以前的研究中，研究人员已经开发出一种模块化的方法来构建大气环流的物理上合理的LOMs，其中经典的力学系统，沃尔泰拉陀螺仪（最简单的一个是著名的二维瑞利-贝纳德对流的洛伦兹模型），作为基本的积木。 耦合陀螺仪系统始终将能量保存在无粘、非受迫极限中，从而避免非物理行为。同时，由于大气动力学中大多数模型的保守部分（例如，原始浅水和准地转方程）是哈密顿的，保持LOM中的哈密顿结构被认为是保持原始系统的基本守恒性质的有效方法。 正如主要研究人员的初步研究所表明的那样，陀螺仪方法在这奋进特别有前途。 在这个项目下，将尝试为重要的流体动力系统开发有用的哈密顿LOMs，首先是Rayleigh-Benard对流，它提供了中尺度浅层对流的主要机制。（特别是哈密尔顿）LOMs本身具有流体动力学方程的基本守恒性质，这将为进一步科学地理解基本机制提供新的有效工具，它们在大气动力学中的相互作用。 从更广泛影响的角度来看，最终这项研究可以为大气可预测性问题提供新的见解，从而限制预测。