Coherent-structure dynamics in wall turbulence from state-space trajectories
Abstract
We identify dynamical processes in the near-wall region of turbulent wall-bounded flow by representing coherent-structure energy as trajectories in a low-dimensional state space and analyzing recurring trajectory patterns using network motifs. Direct numerical simulations (DNS) are performed for three configurations: a minimal flow unit (MFU) at Reτ≈ 180 to isolate the self-sustaining process (SSP), a full-scale channel at the same Reynolds number to study interactions between near-wall structures, and an MFU at Reτ≈ 2200 to investigate near-wall/outer-layer coupling. Proper orthogonal decomposition (POD) is used to identify modes corresponding to streaks, rolls, and meandering structures of the SSP, and the flow is projected onto these modes to track their energy over time. Motif analysis then identifies statistically significant dynamical pathways in the resulting state-space trajectories. Several motifs are common to all three configurations, indicating robust near-wall dynamics across different background flows. While motifs associated with the classical SSP are recovered, equally prominent motifs with no direct SSP analogue are also identified, demonstrating that preferred near-wall dynamics extend beyond the canonical regeneration cycle. Conditioning the Reτ≈ 180 MFU on outer-layer energy further shows that quiescent outer-layer states produce dynamics resembling those of the low-Reynolds-number full channel, whereas energetic outer-layer states promote high-energy bursting events. These results demonstrate that near-wall turbulence evolves along preferred dynamical pathways whose prevalence is modified, but not eliminated, by outer-layer activity.
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BibTeX
@misc{lenz2026coherentstructure,
title = {{Coherent-structure dynamics in wall turbulence from state-space trajectories}},
author = {Emma Lenz and Ahmed Elnahhas and H. Jane Bae},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04515},
eprint = {2609.04515},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04515},
}
RIS
TY - UNPB
TI - Coherent-structure dynamics in wall turbulence from state-space trajectories
AU - Emma Lenz
AU - Ahmed Elnahhas
AU - H. Jane Bae
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04515
UR - https://arxiv.org/abs/2609.04515
AB - We identify dynamical processes in the near-wall region of turbulent wall-bounded flow by representing coherent-structure energy as trajectories in a low-dimensional state space and analyzing recurring trajectory patterns using network motifs. Direct numerical simulations (DNS) are performed for three configurations: a minimal flow unit (MFU) at Re_τ≈ 180 to isolate the self-sustaining process (SSP), a full-scale channel at the same Reynolds number to study interactions between near-wall structures, and an MFU at Re_τ≈ 2200 to investigate near-wall/outer-layer coupling. Proper orthogonal decomposition (POD) is used to identify modes corresponding to streaks, rolls, and meandering structures of the SSP, and the flow is projected onto these modes to track their energy over time. Motif analysis then identifies statistically significant dynamical pathways in the resulting state-space trajectories. Several motifs are common to all three configurations, indicating robust near-wall dynamics across different background flows. While motifs associated with the classical SSP are recovered, equally prominent motifs with no direct SSP analogue are also identified, demonstrating that preferred near-wall dynamics extend beyond the canonical regeneration cycle. Conditioning the Re_τ≈ 180 MFU on outer-layer energy further shows that quiescent outer-layer states produce dynamics resembling those of the low-Reynolds-number full channel, whereas energetic outer-layer states promote high-energy bursting events. These results demonstrate that near-wall turbulence evolves along preferred dynamical pathways whose prevalence is modified, but not eliminated, by outer-layer activity.
ER -