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.

摘要提案编号： CTS-0442845主要制造商：MARK STREMLER机构： 范德比尔特大学二维连续涡尾流的无粘模型本基金支持发展周期性涡尾流的新分析方法。 虽然这需要在寻找非线性控制方程的解决方案的数学练习，主要是在物理理解的涡流尾流，可以从这样的解决方案。 这种涡流尾流与许多工程应用有关。 虽然有证据支持交错涡街的这种解的存在，但很有可能它不存在，或者它不能像建议的那样以封闭形式表示。 这项工作可以被认为是在两个方面对一个既定的研究课题应用了一种新的方法。首先，交错的涡街的无粘分析集中在点涡或恒定涡量补丁。拟议的工作似乎是第一次尝试用连续的涡量场来模拟涡街。其次，孤立子和涡旋动力学之间的类比最近导致了欧拉方程的几个新的精确解，但所使用的方法仅适用于静止涡旋配置。拟议的工作将研究这种方法的扩展到相对涡平衡，统一翻译。这项工作的智力价值将是它对基本流体力学的基本理解的贡献。交错涡街是流体力学中的一个经典问题，也是一种常见的物理现象，精确解的确定将大大提高研究其有趣行为的能力。特别是，拟议的工作将调查交错街道的表面稳定性的原因，这仍然是一个悬而未决的问题。这项工作也将为寻找欧拉方程的其他精确解提供一个框架。一个预期的成果，拟议的工作是一个合作调查的异国情调的涡流尾流，包含三个或更多的涡流每一个周期。 这项工作的更广泛影响将包括促进发现和理解，同时促进教学，扩大代表性不足群体的参与，以及广泛传播成果，以提高科学和技术的理解。