Fluid Flows at Large

流体大流动

• 批准号: 0600692
• 负责人: Maria Schonbek
• 金额: $ 12万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0600692&HistoricalAwards=false
• 关键词: Fluid; Flows; Large

Fluid Flows at Large Abstract of Proposed ResearchMaria E. Schonbek This project is to continue work on the analysis of three fundamental equations that are basic for fluid mechanics. These are the Navier-Stokes and Magneto-hydrodynamic (MHD) equations of hydrodynamics and the 2d quasi-geostrophic (2dQG) equation of meteorology. For the Navier-Stokes equation, our efforts will center on analyzing the self-similar solutions on a half-space or, possibly, a conical domain. Interest will be on their regularity and describing the solutions explicitly. For the MHD equations, research will center on the asymptotic behavior of solutions when dissipation is solely dependent on velocity. For the geo-strophic equations, the research will focus on describing the long-time behavior of flows around obstacles. Analysis of the Navier-Stokes equations is fundamental for understanding fluid flows. Any explicit solution helps in describing what possible flows can be sustained. The MHD equations arise when one adds the effect of a magnetic field and the fluid is assumed to contain electrically charged particles and ions. This project will investigate the solutions of these equations in the absence of magnetic dissipation. The analysis of the QG equations is a model for air-flow around an obstacle; a common problem in meteorology.

拟议的ResearchMaria E. Schonbek的液体流量很大程度上是该项目继续研究三个基本方程的分析，这些方程是流体力学基本的。这些是流体动力学的Navier-Stokes和磁性 - 流动力学（MHD）方程，以及气象学的2D准地藻（2DQG）方程。对于Navier-Stokes方程式，我们的努力将集中在半空间或可能是圆锥形域上分析自相似的解决方案。兴趣将根据其规律性，并明确描述解决方案。对于MHD方程，当耗散仅取决于速度时，研究将集中在解决方案的渐近行为上。对于地质方程，该研究将重点介绍围绕障碍的长期行为。 Navier-Stokes方程的分析对于理解流体流是基础。任何明确的解决方案都有助于描述可以维持哪些可能的流动。当添加磁场的效果时，就会出现MHD方程，并假定流体包含电动颗粒和离子。该项目将在没有磁耗散的情况下研究这些方程的解。 QG方程的分析是围绕障碍物的气流的模型。 气象学中的一个常见问题。