Alternative physics to understand wall turbulence: Navier-Stokes equations with modified linear dynamics

TL;DR

This study investigates the linear mechanisms underlying wall turbulence by modifying Navier-Stokes equations in numerical simulations, revealing the roles of transient growth and parametric instability in sustaining turbulence.

Contribution

It introduces a novel numerical approach to isolate and analyze linear instability mechanisms in wall turbulence, clarifying their individual roles in turbulence sustenance.

Findings

Transient growth alone does not sustain turbulence.

Suppression of exponential instabilities does not eliminate turbulence.

Combination of transient growth and parametric instability maintains turbulence.

Abstract

Despite the nonlinear nature of wall turbulence, there is evidence that the energy-injection mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities from mean-flow inflection points, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in simplified theories and conceptual arguments. Whether the flow follows any or a combination of them remains unclear. In the present study, we devise a collection of numerical experiments in which the Navier-Stokes equations are sensibly modified to quantify the role of the different linear mechanisms. This is achieved by direct numerical simulation of turbulent channel flows with constrained energy extraction from the streamwise-averaged mean-flow. We demonstrate that (i) transient growth alone is not sufficient to sustain wall turbulence and (ii) the flow remains turbulent when the exponential instabilities are suppressed. On the other hand, we show that (iii) transient growth combined with the parametric instability of the time-varying mean-flow is able to sustain turbulence.