Flow Statistics in the Transitional Regime of Plane Channel Flow

TL;DR

This paper investigates the transitional regime of plane channel flow using direct numerical simulations, analyzing laminar-turbulent patterns, their geometry, and high-order statistics, revealing correlations similar to fully turbulent flows.

Contribution

It provides detailed statistical analysis of laminar-turbulent intermittency and pattern geometry in the transitional regime, with comparisons to experimental data.

Findings

Patterns characterized by specific angles similar to experiments

High kurtosis and skewness in velocity and stress distributions

Linear correlation between kurtosis and skewness squared

Abstract

The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal intermittency are reported. The geometry of the pattern is first characterized, including statistics for the angles of the laminar-turbulent stripes observed in this regime, with a comparison to experiments. High-order statistics of the local and instantaneous bulk velocity, wall shear stress and turbulent kinetic energy are then provided. The distributions of the two former quantities have non-trivial shapes, characterized by a large kurtosis and/or skewness. Interestingly, we observe a strong linear correlation between their kurtosis and their skewness squared, which is usually reported at much higher Reynolds number in the fully turbulent regime.