Perturbation growth over self-sustaining process in
wall turbulence beyond the Lyapunov time
wall turbulence beyond the Lyapunov time
Author(s)
Egerique-de-la-Concha, Pablo
Hwang, Yongyun
Type
Journal Article
Abstract
The evolution of small perturbations applied to turbulent Couette flow is examined over
a long time horizon, until the perturbed flow field becomes completely decorrelated
from the original state. To elucidate the fundamental physical processes involved, we
focus on the minimal flow unit, where the dynamics of coherent structures is well
understood in terms of the self-sustaining process (Hamilton etal.J.FluidMech.vol. 287,
1995, pp. 317–348). As expected, in the short term, perturbations exhibit exponential
growth governed by the leading Lyapunov exponent. This mechanism is driven by the
streamwise-dependent flow, which is known to involve intense turbulent dissipation events
within the self-sustaining process, consistent with previous findings. Beyond the initial
exponential phase, we observe a slow, sustained growth of perturbations over a long period– spanning tens of integral time scales– before eventual saturation. During this stage,
the perturbation energy increases approximately linearly with time. While this behaviour
resembles observations and predictions in other turbulent flows, the underlying physical
process here is fundamentally different. Specifically, the perturbation field during this
period is dominated by streaky structures and the growth mechanism is linked to the
saturation of the wall-normal streak length scale at the largest dimension permitted by the
flow geometry (i.e. the channel height). Finally, an evaluation of the dominant production
term components reveals that the well-known lift-up effect is primarily responsible for the
growth of these streaky perturbations.
a long time horizon, until the perturbed flow field becomes completely decorrelated
from the original state. To elucidate the fundamental physical processes involved, we
focus on the minimal flow unit, where the dynamics of coherent structures is well
understood in terms of the self-sustaining process (Hamilton etal.J.FluidMech.vol. 287,
1995, pp. 317–348). As expected, in the short term, perturbations exhibit exponential
growth governed by the leading Lyapunov exponent. This mechanism is driven by the
streamwise-dependent flow, which is known to involve intense turbulent dissipation events
within the self-sustaining process, consistent with previous findings. Beyond the initial
exponential phase, we observe a slow, sustained growth of perturbations over a long period– spanning tens of integral time scales– before eventual saturation. During this stage,
the perturbation energy increases approximately linearly with time. While this behaviour
resembles observations and predictions in other turbulent flows, the underlying physical
process here is fundamentally different. Specifically, the perturbation field during this
period is dominated by streaky structures and the growth mechanism is linked to the
saturation of the wall-normal streak length scale at the largest dimension permitted by the
flow geometry (i.e. the channel height). Finally, an evaluation of the dominant production
term components reveals that the well-known lift-up effect is primarily responsible for the
growth of these streaky perturbations.
Date Issued
2026-06-10
Date Acceptance
2026-04-28
Citation
Journal of Fluid Mechanics, 2026, 1036 (1)
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
1036
Issue
1
Copyright Statement
© The Author(s), 2026. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Identifier
10.1017/jfm.2026.11608
Subjects
turbulence theory
turbulent boundary layers
chaos
Publication Status
Published
Article Number
A52
Date Publish Online
2026-06-10