湍流平均速度方程的经典统计力学方法
Mean Velocity Equation for Turbulent Fluid Flow: An Approach via Classical Statistical Mechanics
摘要：
本文探讨了用经典统计力学导出湍流平均速度场方程的可能性。投影算子技术在文献中的应用是用于此目的。有人认为，流体动力学速度定义有，在流体是湍流的情况下，被解释为平均速度场，在这种情况下，推导出的广义传输方程的动量分量有平均速度方程。本文考虑定常质量密度和定常温度的定常不可压缩流动。应力张量作为平均速度场的非线性泛函得到，其中线性部分是斯托克斯张量。该公式包含局部平衡时的时间关联函数。目前，存在一个微观理论的时间相关性，只有在总平衡。由于这个原因，作为初步措施，该公式已扩展为平均速度的幂级数;尽管这限制了对低雷诺数流动的适用性。二阶项已在作者的前一篇文章中得到了估计。对于三阶项，导出了核函数的形式。它的计算与模式耦合理论的帮助下完成，它将在一个单独的文件中报告。圆形射流数据的数值应用正在进行中。
英文摘要：
The possibility to derive an equation for the mean velocity field in turbulent flow by using classical statistical mechanics is investigated. An application of projection operator technique available in the literature is used for this purpose. It is argued that the hydrodynamic velocity defined there, in situations where the fluid is turbulent, is to be interpreted as the mean velocity field; in that case, the momentum component of the generalized transport equation derived there is the mean velocity equation. In this paper, stationary incompressible flow for constant mass density and temperature is considered. The stress tensor is obtained as a nonlinear functional of the mean velocity field, the linear part of which is the Stokes tensor. The formula contains a time correlation function in local equilibrium. Presently, there exists a microscopic theory for time correlations in total equilibrium only. For this reason and as a preliminary measure, the formula has been expanded into a power series in the mean velocity; though this limits the applicability to low Reynolds number flow. The second order term has been evaluated in a former paper of the author. For the third order term, the form of the kernel function is derived. Its calculation with the aid of the mode-coupling theory is completed; it will be reported in an separate paper. An numerical application with the data of the circular jet is under way.
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