Mathematical Basis of Turbulence Modeling
Mathematical Basis of Turbulence Modeling
复制标题
湍流建模的数学基础
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
R. Lewandowski
中科院分区：
文献类型：
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作者：
T. C. Rebollo;R. Lewandowski
量纲分析是形式化的抽象框架，这导致了广义雷诺数通过维基的介绍。我们给出了一个严格的数学声明的一个版本的雷诺相似律，基于无量纲形式的Navier-Stokes方程（NSE），突出了雷诺相似律和NSE的解决方案的唯一性问题之间的连接。我们回顾了Leray的弱解和Fujita-Kato的强解，讨论了这样一个定律的有效性。此外，弱的解决方案的NSE被证明有长时间的平均值，他们满足的方程被确定，这使得一些基本的湍流建模工具，如雷诺分解和雷诺应力的介绍。
Dimensional analysis is formalized in an abstract framework, which leads to the introduction of the generalized Reynolds numbers through dimensional bases. We give a rigorous mathematical statement of a version of the Reynolds similarity law, based on the dimensionless form of the Navier–Stokes equations (NSE), which highlights the connection between the Reynolds similarity law and the problem of uniqueness of solutions of the NSE. We review weak solutions a la Leray and strong solutions a la Fujita–Kato, to discuss the validity of such a law. Furthermore, weak solutions to the NSE are shown to have long-time averages, the equation they satisfy being determined, which allows the introduction of some basic tools of turbulence modeling, such as the Reynolds decomposition and the Reynolds stress.