Abstract

Developed turbulent flow of a viscous incompressible fluid in a channel of small width at high Reynolds numbers is considered. The instantaneous flow velocity is represented as the sum of a stationary component and small perturbations, which are generally different from the traditional averaged velocity and fluctuations. The study is restricted to the search for and consideration of stationary solution components. To analyze the problem, an asymptotic multiscale method is applied to the Navier–Stokes equations, rather than to the RANS equations. As a result, a steady flow in the channel is found and investigated without using any closure hypotheses. The basic phenomenon in the Poiseuille flow turns out to be a self-induced fluid flow from the channel center to the walls, which ensures that kinetic energy is transferred from the maximum-velocity zone to the turbulence generation zone near the walls, although the total averaged normal velocity is, of course, zero. The stationary solutions for the normal and streamwise velocities turn out to be viscous over the entire width of the channel, which confirms the well-known physical concept of large-scale “turbulent viscosity.”

中文翻译：

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渐近方法模拟平坦通道中的湍流Poiseuille-Couette流

摘要

考虑了在高雷诺数下小宽度的通道中粘性不可压缩流体的湍流发展。瞬时流速表示为固定分量和小扰动的总和，通常与传统的平均速度和波动不同。该研究仅限于寻找和考虑固定解的组成部分。为了分析问题，将渐进多尺度方法应用于Navier–Stokes方程，而不是RANS方程。结果，无需使用任何封闭假设即可发现并研究通道中的稳定流动。Poiseuille流动的基本现象是从通道中心到壁的自感应流体流动，尽管总的平均法向速度当然为零，但这确保了动能从最大速度区域转移到壁附近的湍流产生区域。法向速度和流向速度的固定解在通道的整个宽度上都是粘滞的，这证实了众所周知的大规模“湍流粘度”的物理概念。