Nonlinear Wave Problems in Fluid Flows

流体流动中的非线性波问题

• 批准号: 0071939
• 负责人: Paul Milewski
• 金额: $ 8.8万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-15 至 2003-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071939&HistoricalAwards=false
• 关键词: Nonlinear; Wave; Problems; Fluid; Flows

0071939MilewskiThe project will consist of the study of three problems in fluid mechanics and nonlinear waves. The first project involves understanding certain aspects of dispersive wave turbulence, that is, the statistical description of a large number of interacting dispersive waves, such as those on the ocean surface. First, a reduced model will be used which contains the fundamental nonlinear processes and can yield the scaling for the energy transfer mechanisms. Second, spectra of two-- and three--dimensional ocean waves with a reduced equation valid for finite depth and deep water will be computed and compared with results from the reduced model. The second project involves the study of three-dimensional solitary waves in regimes where surface tension is an important part of the dynamics. These are waves that can be generated, for example, by flow of a thin fluid layer over a small obstacle. Here, it is proposed to use solutions that have already been computed to find additional solutions in regimes of physical interest, such as increasing depth. The third project is to study the dynamics of reaction-diffusion equations in the presence of spatial inhomogeneities, as for example, in models of certain chemical reactions where the reactant concentration is not uniform in space. In the spatially homogeneous case, one obtains various coherent patterns in the reaction. How these patterns and their boundaries are modified by the inhomogeneities will be studied.The goal of this research is to understand several aspects of wave dynamics in fluids using a combination of theory and advanced computation. There are three distinct phenomena that will be studied. First, the evolution of wave turbulence will be studied: the physical situation in which many waves of different wavelengths and traveling in different directions are superposed. The simplest example is the apparent random mix of waves on the surface of the ocean. The goal is to predict the relative energy in the different waves and the mechanisms by which waves of different sizes exchange energy. These are important predictions whose applications range from understanding satellite remote sensing data to climate dynamics. Second, a class of water waves called lump solitons will be studied: localized coherent waves that travel in a particular direction. The goal is to obtain the range of physical situations in which these waves can exist. This work has implications in a variety of thin film and coating applications. Lastly, the dynamics of the components of biological and chemical reacting systems where the concentration of the reactants vary in space will be studied. The particular case where a catalyst for the reaction is not distributed uniformly and therefore the reaction proceeds differently in different places will be studied. The goal is to understand how the reaction varies from place to place and what happens at the boundaries where the reactions change character.

[00:39 . 39]这个项目将包括流体力学和非线性波中的三个问题的研究。第一个项目涉及了解色散波湍流的某些方面，即对大量相互作用的色散波进行统计描述，例如海洋表面的色散波。首先，将使用一个简化模型，该模型包含基本的非线性过程，并可以产生能量传递机制的缩放。其次，计算具有有限深度和深水有效的简化方程的二维和三维海浪谱，并与简化模型的结果进行比较。第二个项目涉及三维孤立波的研究，其中表面张力是动力学的重要组成部分。这些是可以产生的波，例如，由一个薄的流体层流过一个小障碍物。在这里，建议使用已经计算过的解决方案来找到物理感兴趣的制度的额外解决方案，例如增加深度。第三个项目是研究存在空间非均匀性的反应-扩散方程的动力学，例如，在某些化学反应模型中，反应物浓度在空间上不均匀。在空间均匀的情况下，人们在反应中得到各种相干模式。这些模式和它们的边界如何被非均质性所改变将被研究。本研究的目的是利用理论和先进计算的结合来理解流体中波动动力学的几个方面。我们将研究三种不同的现象。首先，研究波浪湍流的演化：许多不同波长和不同方向的波叠加在一起的物理情况。最简单的例子就是海面上波浪的随机混合。目标是预测不同波的相对能量，以及不同大小的波交换能量的机制。这些都是重要的预测，其应用范围从了解卫星遥感数据到气候动力学。其次，将研究一类被称为块状孤子的水波：沿特定方向传播的局部相干波。目标是获得这些波可以存在的物理情况的范围。这项工作对各种薄膜和涂层的应用具有重要意义。最后，将研究生物和化学反应系统中反应物浓度随空间变化的组分的动力学。在特殊情况下，反应的催化剂分布不均匀，因此反应在不同的地方进行不同的情况将被研究。目的是了解不同地方的反应是如何变化的，以及在反应改变特征的边界处发生了什么。