Linear stability of turbulent channel flow with one-point closure

TL;DR

This study investigates whether linear stability analysis of turbulent mean flows can predict large-scale spatial modulations, finding that such flows are linearly stable and that simple models are insufficient.

Contribution

It demonstrates that linear stability analysis around turbulent mean flows does not predict observed instabilities, highlighting limitations of one-point closure models.

Findings

Turbulent channel flow is linearly stable across different models and domain sizes.

One-point closure models are inadequate for predicting flow instabilities.

Observed large-scale modulations are not explained by linear stability of mean flow.

Abstract

For low enough flow rates, turbulent channel flow displays spatial modulations of large wavelengths. This phenomenon has recently been interpreted as a linear instability of the turbulent flow. We question here the ability of linear stability analysis around the turbulent mean flow to predict the onset and wavelengths of such modulations. Both the mean flow and the Reynolds stresses are extracted from direct numerical simulation (DNS) in periodic computational domains of different size. The Orr-Sommerfeld-Squire formalism is used here, with the turbulent viscosity either ignored, evaluated from DNS, or modeled using a simple one-point closure model. Independently of the closure model and the domain size, the mean turbulent flow is found to be linearly stable, in marked contrast with the observed behavior. This suggests that the one-point approach is not sufficient to predict instability, at odds with other turbulent flow cases. For generic wall-bounded shear flows we discuss how the correct models for predicting instability could include fluctuations in a more explicit way.