Nonlinear Problems in Fluid Mechanics, Meteorology & Oceanography

流体力学、气象学中的非线性问题

• 批准号: 0074334
• 负责人: Roger Temam
• 金额: $ 37.5万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0074334&HistoricalAwards=false
• 关键词: Nonlinear; Problems; Fluid; Mechanics; Meteorology

Temam0074334 The investigator and his colleagues study nonlinear problemsfrom meteorology, oceanography, and fluid mechanics, using themathematical tools offered by analysis, the theory of nonlinearpartial differential equations, dynamical systems theory, andcomputation. The part of this project related to meteorology andoceanography focuses on the following areas: (1) Open boundaryconditions for limited domain simulations and well posednessissues for meteorology and oceanography problems. (2) Balancedand unbalanced models in atmosphere sciences. (3) Well-posednessand stability problems in oceanography. The fluid mechanicstopics focus on several aspects of turbulence theory, includingthe connection between the conventional theory of turbulence, thedynamical systems approach, and the Navier-Stokes equations. Theinvestigators intend also to complete a research monograph onsome of these aspects of turbulence. Central problems in meteorology and oceanography areconcerned with understanding and predicting the behavior of theatmosphere and the ocean --- in what patterns do these fluids,air and water, move? The mathematical equations that describethe motions are difficult to analyze, and computations are alsodifficult because the physical phenomena are complex andnonlinear. In fluid mechanics, understanding fluid flowsgenerally and turbulence in particular, and developing efficientnumerical methods to compute these flows, are major themes. Theinvestigators study several problems related to the behavior ofatmosphere and ocean fluid flows and to their effectivecomputation. They also study and develop computational methodsfor turbulent fluid flows of importance for industrial processes.

Temam0074334 研究者和他的同事们研究气象学、海洋学和流体力学的非线性问题，使用分析、非线性偏微分方程理论、动力系统理论和计算提供的数学工具。 （1）有限域数值模拟的开放边界条件和海洋气象问题的适定性。(2)大气科学中的平衡与非平衡模式。(3)海洋学中的适定性与稳定性问题。 流体力学集中在湍流理论的几个方面，包括传统的湍流理论，动力系统方法和Navier-Stokes方程之间的联系。 研究人员还打算完成一本关于湍流某些方面的研究专著。 气象学和海洋学的中心问题是关于理解和预测大气和海洋的行为-这些流体，空气和水，以什么样的模式运动？ 由于物理现象的复杂性和非线性，描述运动的数学方程很难分析，计算也很困难。 在流体力学中，理解流体流动，特别是湍流，并发展有效的数值方法来计算这些流动，是主要的主题。 研究人员研究了几个与大气和海洋流体流动及其有效计算有关的问题。 他们还研究和开发湍流流体流动的重要工业过程的计算方法。