Wall turbulence with constrained energy extraction from mean flow

TL;DR

This paper investigates the mechanisms of energy transfer from mean flow to turbulence in wall-bounded flows, testing the roles of modal and non-modal linear processes through numerical experiments with controlled forcing.

Contribution

It introduces a novel experimental approach to isolate and evaluate the impact of different linear mechanisms on turbulence maintenance in wall flows.

Findings

Modal instabilities can sustain turbulence in the experiments.

Transient growth mechanisms alone do not maintain turbulence.

Unforced turbulence may rely on modal instability mechanisms.

Abstract

We study the mechanism of energy injection from the mean flow to the fluctuating velocity necessary to maintain wall turbulence. This process is believed to be correctly represented by the linearized Navier--Stokes equations, and three potential linear mechanisms have been considered, namely, modal instability of the streamwise mean cross-flow $U(y,z,t)$, non-modal transient growth, and non-modal transient growth supported by parametric instability. We have designed three numerical experiments of plane turbulent channel flow with additional forcing terms aiming to neutralize one or various linear mechanisms for energy extraction. From our preliminary experiments, only cases with mean cross-flows capable of supporting modal instabilities were found to sustain turbulence. However, the question whether such a new turbulence complies with the same physical mechanisms as those occurring in actual (unforced) turbulence remains unanswered. On the other hand, cases exclusively supported by transient growth decayed until laminarization.