Multiscale circulation in wall-parallel planes of turbulent channel flows

TL;DR

This study investigates the multiscale circulation properties in wall-parallel planes of turbulent channel flows using high-resolution simulations across various Reynolds numbers, revealing universal bifractality in outer flow and Gaussian behavior near the wall.

Contribution

It provides new insights into the multiscale circulation structures and their statistical properties in wall turbulence, highlighting the bifractal nature of outer flow circulation.

Findings

Outer flow circulation exhibits universal bifractality.

Near-wall circulation is space-filling and Gaussian.

Circulation PDFs are long-tailed and invariant to loop aspect ratio.

Abstract

Wall turbulence consists of various sizes of vortical structures that induce flow circulation around a wide range of closed Eulerian loops. Here we investigate the multiscale properties of circulation around such loops in statistically homogeneous planes parallel to the wall. Using a high-resolution direct numerical simulation database of turbulent channels at Reynolds numbers of $Re_\tau=180$, 550, 1000 and 5200, circulation statistics are obtained in planes at different wall-normal heights. Intermittency of circulation in the planes of the outer flow ($y^+ \gtrsim 0.1Re_\tau$) takes the form of universal bifractality as in homogeneous and isotropic turbulence. The bifractal character simplifies to space-filling character close to the wall, with scaling exponents that are linear in the moment order, and lower than those given by the Kolmogorov paradigm. The probability density functions of circulation are long-tailed in the outer bifractal region, {with evidence showing their invariance with respect to the loop aspect ratio}, while those in the inner region are closely Gaussian. The unifractality near the wall implies that the circulation there is not intermittent in character.