雷诺应力张量的几何演化
Geometric evolution of the Reynolds stress tensor
摘要：
用一个耦合几何效应和湍流源项的演化方程描述了湍流雷诺应力张量的动力学。当忽略源项时，平均流几何形状的影响显示出来：雷诺应力张量然后表示为由扭曲的陀螺方程支配的矢量场的三个张量积的和。沿平均流轨迹，速度的波动由微分方程描述，其系数仅取决于平均流变形。在平均流涡足够小的情况下，导出了一个近似的湍流模型，并提出了它在剪切浅水流动中的应用。此外，近似湍流模型承认一个变分公式，这是类似的毛细流体之一。
英文摘要：
The dynamics of the Reynolds stress tensor for turbulent flows is described with an evolution equation coupling both geometric effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are neglected: the Reynolds stress tensor is then expressed as the sum of three tensor products of vector fields which are governed by a distorted gyroscopic equation. Along the mean flow trajectories, the fluctuations of velocity are described by differential equations whose coefficients depend only on the mean flow deformation. If the mean flow vorticity is small enough, an approximate turbulence model is derived, and its application to shear shallow water flows is proposed. Moreover, the approximate turbulence model admits a variational formulation which is similar to the one of capillary fluids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
