Mechanisms for Energy Conservation in Onsager Supercritical Fluids

Onsager 超临界流体的节能机制

• 批准号: 1515705
• 负责人: Roman Shvydkoy
• 金额: $ 27.45万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-15 至 2019-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1515705&HistoricalAwards=false
• 关键词: Mechanisms; Energy; Conservation; Onsager; Supercritical

The complexity of turbulent motion of fluids like water presents many theoretical as well as technological challenges. From the practical standpoint laws of turbulence are crucial in many real-life applications. They stand behind the modern design of a plane airfoil or development of weather and climate forecast models. One of the features of turbulence is called anomalous energy dissipation. This phenomenon arises when the motion of a fluid is so chaotic or rough that the the classical laws of smooth dynamics no longer apply. Anomalous energy dissipation is harnessed in many commonly used energy-dumping mechanisms, such as automobile wheel struts. Common though it is, in some cases energy dissipation does not occur even in what otherwise would be considered a flow turbulent enough to facilitate such dissipation. It has been observed that in various natural phenomena, such as vortex sheets that develop behind the wing of a plane, energy dissipation does not occur until motion reaches a supercritical state. The project goal is to isolate several mechanisms responsible for energy preservation or dissipation in fluid motion that is turbulent or nearly so. A main focus is on investigation of the role of symmetries in energy conservation. Students are included in the project. The investigator studies weak solutions to the Euler equation and its viscous Navier-Stokes counterpart in the vanishing viscosity limit regime, by considering the role of energy conservation or dissipation in the fluid flows described by these equations. The equations have been shown to describe turbulence rather accurately from a numerical point of view, although theoretically they present many challenges. Following Onsager, in terms of regularity a solution reaches its turbulent state when smoothness of the flow is reduced to a third of one full derivative, also known as Onsager regularity. In that regularity regime the investigator examines four main mechanisms as candidates responsible for energy conservation or dissipation: Hamiltonian structure of the underlying governing equation, incompressibility condition, basic scaling symmetries and transport nature of the motion, and the vanishing viscosity limit in the two-dimensional setting. The last point connects energy dissipation to regularity of solutions of the Euler equations. The project involves active participation of students.

水等流体的湍流运动的复杂性提出了许多理论和技术挑战。 从实践的角度来看，湍流定律在许多实际应用中至关重要。 他们支持飞机机翼的现代设计或天气和气候预报模型的开发。 湍流的特征之一称为反常能量耗散。 当流体的运动非常混乱或粗糙以至于光滑动力学的经典定律不再适用时，就会出现这种现象。 许多常用的能量转储机制都利用了异常能量耗散，例如汽车车轮支柱。 尽管很常见，但在某些情况下，即使在被认为足以促进这种耗散的湍流流动中，也不会发生能量耗散。 据观察，在各种自然现象中，例如在飞机机翼后面形成的涡片，直到运动达到超临界状态才会发生能量耗散。 该项目的目标是隔离在湍流或近乎湍流的流体运动中负责能量保存或耗散的几种机制。 主要重点是研究对称性在能量守恒中的作用。 学生也被纳入该项目。 研究人员通过考虑这些方程描述的流体流动中能量守恒或耗散的作用，研究欧拉方程及其在消失粘度极限状态下的粘性纳维-斯托克斯方程的弱解。 这些方程已被证明可以从数值角度相当准确地描述湍流，尽管理论上它们提出了许多挑战。 遵循 Onsager，就正则性而言，当流动的平滑度降低到全导数的三分之一（也称为 Onsager 正则性）时，解就会达到湍流状态。 在该规律性体系中，研究人员检查了四种主要机制作为负责能量守恒或耗散的候选机制：基础控制方程的哈密顿结构、不可压缩条件、基本标度对称性和运动的输运性质，以及二维中的消失粘度极限环境。 最后一点将能量耗散与欧拉方程解的正则性联系起来。 该项目需要学生的积极参与。