SGER: Inviscid Models of Two-Dimensional Vortex Wakes with Continuous Vorticity

SGER：具有连续涡度的二维涡流尾流的无粘模型

• 批准号: 0442845
• 负责人: Mark Stremler
• 金额: --
• 依托单位: Vanderbilt 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: 2004-08-15 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0442845&HistoricalAwards=false
• 关键词: SGER; Inviscid; Models; Two; Dimensional

ABSTRACTPROPOSAL NO.: CTS-0442845PRINCIPAL INVESTIGATORS: MARK STREMLERINSTITUTION: VANDERBILT UNIVERSITYINVISCID MODELS OF TWO-DIMENSIONAL VORTEX WAKES WITH CONTINUOUS VORTICITYDevelopment of novel analysis methodology of periodic vortex wakes is supported under this grant. While this entails a mathematical exercise in finding solutions to the non-linear governing equation, the interest is primarily in the physical understanding of vortex wakes that can be gained from such a solution. Such vortex wakes are relevant to a number of engineering applications. While there is evidence supporting the existence of such a solution for the staggered vortex street, there is a strong possibility that it does not exist or that it cannot be expressed in closed form as proposed. This work can be considered the application of a new approach to an established research topic on two fronts. First, inviscid analysis of the staggered vortex street has focused on either point vortices or constant vorticity patches. The proposed work appears to be the first attempt to model the vortex street with a continuous vorticity field. Secondly, the analogy between solitons and vortex dynamics has led recently to several new exact solutions of the Euler equations but the approach that was used is applicable only for stationary vortex configurations. The proposed work will examine the extension of this approach to relative vortex equilibria that translate uniformly. The intellectual merit of this work will be its contributions to the fundamental understanding of basic fluid mechanics. The staggered vortex street is a classical problem in fluid mechanics and a commonly occurring physical phenomenon, and the determination of an exact solution will significantly advance the ability to investigate its intriguing behavior. In particular, the proposed work will investigate the reason for the apparent stability of the staggered street, which is still an open question. This work will also provide a framework for finding other exact solutions to the Euler equations. One anticipated outgrowth of the proposed work is a collaborative investigation of exotic vortex wakes that contain three or more vortices per period. The broader impacts of this work will include advancing discovery and understanding while promoting teaching and learning, broadening the participation of underrepresented groups, and broad dissemination of results for the enhancement of scientific and technical understanding.

Abstract Propopos no。：CTS-0442845原理研究人员：Mark Stremlerinstitution：vanderbilt UniversityInvissInviscid模型的二维涡旋唤醒模型，并在这笔拨款的遵守周期性涡流醒来的新型分析方法中持续涡流开发。 尽管这需要进行数学练习，以找到针对非线性管理方程的解决方案，但兴趣主要是在对涡旋唤醒的物理理解中可以从这种解决方案中获得的。 这种涡流唤醒与许多工程应用有关。 尽管有证据支持交错的涡流街有这种解决方案，但很可能它不存在，也不能以封闭形式表达。 可以将这项工作视为在两个方面的既定研究主题中采用新方法的应用。首先，对交错涡流街的无关分析将重点放在点涡流或恒定的涡度斑块上。拟议的工作似乎是将涡旋街与连续的涡流场建模的第一次尝试。其次，孤子和涡流动力学之间的类比最近导致了Euler方程的几种新的精确解决方案，但是所使用的方法仅适用于固定的涡旋配置。拟议的工作将检查这种方法扩展到均匀翻译的相对涡流平衡。这项工作的智力优点将是它对基本流体力学的基本理解的贡献。交错的涡流街是流体力学和通常发生的物理现象的经典问题，确切解决方案的确定将显着提高研究其有趣的行为的能力。尤其是拟议的工作将调查交错街道明显稳定的原因，这仍然是一个悬而未决的问题。这项工作还将提供一个为Euler方程找到其他精确解决方案的框架。拟议工作的预期生长是对每个时期包含三个或多个涡旋的异国涡流唤醒的协作调查。 这项工作的更广泛的影响将包括在促进教学，扩大代表性不足的群体的参与以及广泛传播结果以增强科学和技术理解的结果时提高发现和理解。