Scaling law of fine scale eddies in turbulent channel flows up to Reτ=800

Abstract

To clarify the scaling law of fine scale eddies in turbulent channel flows, direct numerical simulations are conducted for Re τ =180, 400 and 800. The diameter and the maximum azimuthal velocity of coherent fine scale eddies can be scaled by Kolmogorov microscale ( η) and Kolmogorov velocity ( u k ). The most expected diameter and maximum azimuthal velocity are 8–10 η and 1.2–2.0 u k , respectively. Near the wall, the most expected diameter increases to 10 η from 8 η and the most expected maximum azimuthal velocity increases to 2.0 u k from 1.2 u k . Strain rates at the center of the coherent fine scale eddies are small compared with the mean strain rate of the whole flow field. The strain rates acting on the fine scale eddies away from the wall coincide with those in homogeneous isotropic turbulence and turbulent mixing layer. However, relatively large strain rates are acting on the near-wall coherent fine scale eddies. The most expected angle between the intermediate eigenvector and the rotating axis of the fine scale eddy is about 15–17°, which is independent of the turbulent flow fields. The probability that coherent fine scale eddies exist in low-speed streaks is higher than that in high-speed streaks. Large scale structures of wall turbulence are visualized by showing spatial distributions of central axes of coherent fine scale eddies.