论文标题
湍流的随机方法：全面评论
Stochastic Approach to Turbulence: A Comprehensive Review
论文作者
论文摘要
自Kolmogorov的理论以来，已经使用各种方法研究了湍流，现在可以在概率框架中理解其中的许多方法。在此，自Kolmogorov提供了关于随机湍流的进步的全面综述。已经提出，随机理论将能够为统一的湍流理论提供自然基础，因为可以使用随机方法来处理与湍流相关的广泛问题。首先，已经研究了随机流体动力学的数学理论，并且已经讨论了有关随机汉堡和Naiver-Stokes方程的结果和成真性的结果。然后评估了湍流理论在对随机方法特别注意的情况下进行评估。已经研究了包括汉堡湍流，标量对流，不可压缩的湍流，现场理论方法和随机变分原理的概念，以提供有关湍流随机理论的详细讨论。此外，还提供了一些随机数值方法的介绍。由于确定性理论的派生或固有的局限性，涵盖的方法在确定性理论中没有任何对应方法。
Since Kolmogorov's theory, turbulence has been studied using various methods, many of which could be now be understood in a probabilistic framework. Herein, a comprehensive review of the advances made on stochastic theory of turbulence since Kolmogorov has been provided. It has been suggested that stochastic theory would be able to provide a natural foundation for a unified theory of turbulence as a wide range of problems related to turbulence could be treated using stochastic methods. At first, the mathematical theory of stochastic hydrodynamics has been studied and the results such as well-Posedness and ergodicity have been discussed for stochastic Burgers and Naiver-Stokes equations. The theory of turbulence was then assessed where a special attention was paid to stochastic methods. Concepts including Burgers turbulence, scalar advection, incompressible turbulence, field theoretic methods, and stochastic variational principle have been studied to provide detailed discussion on the stochastic theory of turbulence. Moreover, an introduction to some stochastic numerical methods has also been provided. None of the covered methods have a counterpart in deterministic theories due to their derivation or inherent limitations of deterministic theories.
