Nonlinear Problems in Fluid Mechanics, Meteorology & Oceanography

这位研究人员和他的同事利用分析、非线性偏微分方程组理论、动力系统理论和计算提供的数学工具，研究了气象学、海洋学和流体力学中的非线性问题。本项目与气象和海洋学有关的部分集中在以下几个方面：(1)有限区域模拟的开放边界条件和气象和海洋学问题的良好假设。(2)大气科学中的平衡模型和非平衡模型。(3)海洋学中的适定性和稳定性问题。流体力学侧重于湍流理论的几个方面，包括传统湍流理论、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部关于湍流某些方面的研究专著。气象学和海洋学中的中心问题涉及理解和预测大气和海洋的行为-这些流体，空气和水，以什么模式运动？描述运动的数学方程很难分析，计算也很困难，因为物理现象是复杂的和非线性的。在流体力学中，了解一般的流体流动，特别是湍流，并开发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行为及其有效计算有关的问题。他们还研究和发展了对工业过程具有重要意义的湍流流动的计算方法。

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.