Single-eddy contributions to streamwise velocity variance in turbulent pipe flow. Part 1. The single-eddy intensity function
Abstract
Townsend's attached-eddy hypothesis explains the asymptotic statistics of wall turbulence through a superposition of self-similar attached eddies. At a given observation location, active portions contribute to momentum transfer, whereas inactive portions retain only wall-parallel fluctuations. Since this distinction depends on the observation height relative to the eddy height yl, we extract single-eddy intensity functions from DNS of turbulent pipe flow at Reτ≃930--$6000$. Spectral linear stochastic estimation and differencing isolate wall-coherent contributions at prescribed yl, yielding the streamwise and wall-normal intensity functions Iuu and Ivv. When expressed in y*=y/yl, both collapse across yl and share a peak at ya*, close to the von K'arm'an constant. Near ya*, both components remain significant, whereas for y*≪ ya*, Ivv diminishes while Iuu remains finite, identifying active and inactive portions. Over the self-similar range, both peak intensities scale as yl−1, and Iuu retains this scaling in both portions. Integrating the active portion yields an approximately constant contribution, while the inactive portion recovers the classical near-wall logarithmic variation. An outer logarithmic tendency with a slope close to the Townsend--Perry constant arises from integrating active contributions up to their outer cutoff. At the near-wall peak of ⟨ uu⟩+, the scaling steepens to Iuu∼ yl−(1+β) with β≃1/4, yielding a finite asymptote with a Reτ−1/4 defect. The additional exponent is attributed to viscous attenuation of inactive footprints associated with a yl-dependent dissipative scale. Wall-coherent motions also produce a broad outer shoulder, while a localized wall-incoherent residual may contribute to a secondary peak.
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BibTeX
@misc{hwang2026singleeddy,
title = {{Single-eddy contributions to streamwise velocity variance in turbulent pipe flow. Part 1. The single-eddy intensity function}},
author = {Jinyul Hwang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12637},
eprint = {2609.12637},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12637},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Single-eddy contributions to streamwise velocity variance in turbulent pipe flow. Part 1. The single-eddy intensity function
AU - Jinyul Hwang
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12637
UR - https://arxiv.org/abs/2609.12637
AB - Townsend's attached-eddy hypothesis explains the asymptotic statistics of wall turbulence through a superposition of self-similar attached eddies. At a given observation location, active portions contribute to momentum transfer, whereas inactive portions retain only wall-parallel fluctuations. Since this distinction depends on the observation height relative to the eddy height y_l, we extract single-eddy intensity functions from DNS of turbulent pipe flow at Re_τ≃930--$6000$. Spectral linear stochastic estimation and differencing isolate wall-coherent contributions at prescribed y_l, yielding the streamwise and wall-normal intensity functions I_uu and I_vv. When expressed in y^*=y/y_l, both collapse across y_l and share a peak at y_a^*, close to the von K'arm'an constant. Near y_a^*, both components remain significant, whereas for y^*≪ y_a^*, I_vv diminishes while I_uu remains finite, identifying active and inactive portions. Over the self-similar range, both peak intensities scale as y_l^−1, and I_uu retains this scaling in both portions. Integrating the active portion yields an approximately constant contribution, while the inactive portion recovers the classical near-wall logarithmic variation. An outer logarithmic tendency with a slope close to the Townsend--Perry constant arises from integrating active contributions up to their outer cutoff. At the near-wall peak of ⟨ uu⟩^+, the scaling steepens to I_uu∼ y_l^−(1+β) with β≃1/4, yielding a finite asymptote with a Re_τ^−1/4 defect. The additional exponent is attributed to viscous attenuation of inactive footprints associated with a y_l-dependent dissipative scale. Wall-coherent motions also produce a broad outer shoulder, while a localized wall-incoherent residual may contribute to a secondary peak.
ER -