Hamlington Peter E, Dahm Werner J A
Laboratory for Turbulence and Combustion (LTC), Department of Aerospace Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2140, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046311. doi: 10.1103/PhysRevE.80.046311. Epub 2009 Oct 15.
A new fundamentally based formulation of nonlocal effects in the rapid pressure-strain correlation in turbulent flows has been obtained. The resulting explicit form for the rapid pressure-strain correlation accounts for nonlocal effects produced by spatial variations in the mean-flow velocity gradients and is derived through Taylor expansion of the mean velocity gradients appearing in the exact integral relation for the rapid pressure-strain correlation. The integrals in the resulting series expansion are solved for high- and low-Reynolds number forms of the longitudinal correlation function f(r), and the resulting nonlocal rapid pressure-strain correlation is expressed as an infinite series in terms of Laplacians of the mean strain rate tensor. This formulation is used to obtain a nonlocal transport equation for the turbulence anisotropy that is expected to provide improved predictions of the anisotropy in strongly inhomogeneous flows.
在湍流中快速压力应变关联的非局部效应方面，已获得一种基于基本原理的新公式。所得快速压力应变关联的显式形式考虑了平均流速度梯度空间变化产生的非局部效应，并且是通过对快速压力应变关联的精确积分关系中出现的平均速度梯度进行泰勒展开推导得出的。针对纵向关联函数f(r)的高雷诺数和低雷诺数形式求解所得级数展开中的积分，并且所得非局部快速压力应变关联以平均应变率张量的拉普拉斯算子表示为无穷级数。该公式用于获得湍流各向异性的非局部输运方程，预计该方程能改进对强非均匀流中各向异性的预测。
