Physical mechanism of turbulence attenuation by polymers from a timescale perspective
Abstract
To elucidate the physical mechanism of turbulence attenuation by polymers at each scale, we conduct direct numerical simulations of homogeneous isotropic turbulence in dilute polymer solutions. We model polymers as FENE dumbbells and simulate them using Brownian dynamics. By visualising the hierarchical structures of coherent vortices, we demonstrate that as the Weissenberg number increases, polymers progressively suppress vortices from smaller to larger scales, attenuating their turbulent energy. While inspired by Lumley's theory, we propose a novel timescale-based framework for analysing this attenuation process using the scale decomposition. We define a scale-dependent Weissenberg number, Wisd(k), as the ratio of the polymer relaxation time to the turnover time of multiscale vortices at each wave-number. We reveal that when expressed in terms of Wisd(k), the energy attenuation rate at each scale collapses onto a single curve that rises at Wisd(k) ≳ 1, proving that Wisd(k) successfully describes both the onset and the degree of turbulence attenuation at any given scale k−1. Furthermore, the scale decomposition uncovers that polymers preferentially align with the turbulent stretching direction at the scale satisfying Wisd(k) ≈ 1. Based on these results, we establish a physical picture of the polymer--turbulence interaction and explicitly link it to the statistics in turbulence attenuated by polymers.
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BibTeX
@misc{masuda2026physical,
title = {{Physical mechanism of turbulence attenuation by polymers from a timescale perspective}},
author = {Hayato Masuda and Yusuke Koide and Yutaro Motoori and Susumu Goto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12881},
eprint = {2609.12881},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12881},
}
RIS
TY - UNPB
TI - Physical mechanism of turbulence attenuation by polymers from a timescale perspective
AU - Hayato Masuda
AU - Yusuke Koide
AU - Yutaro Motoori
AU - Susumu Goto
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12881
UR - https://arxiv.org/abs/2609.12881
AB - To elucidate the physical mechanism of turbulence attenuation by polymers at each scale, we conduct direct numerical simulations of homogeneous isotropic turbulence in dilute polymer solutions. We model polymers as FENE dumbbells and simulate them using Brownian dynamics. By visualising the hierarchical structures of coherent vortices, we demonstrate that as the Weissenberg number increases, polymers progressively suppress vortices from smaller to larger scales, attenuating their turbulent energy. While inspired by Lumley's theory, we propose a novel timescale-based framework for analysing this attenuation process using the scale decomposition. We define a scale-dependent Weissenberg number, Wi_sd(k), as the ratio of the polymer relaxation time to the turnover time of multiscale vortices at each wave-number. We reveal that when expressed in terms of Wi_sd(k), the energy attenuation rate at each scale collapses onto a single curve that rises at Wi_sd(k) ≳ 1, proving that Wi_sd(k) successfully describes both the onset and the degree of turbulence attenuation at any given scale k^−1. Furthermore, the scale decomposition uncovers that polymers preferentially align with the turbulent stretching direction at the scale satisfying Wi_sd(k) ≈ 1. Based on these results, we establish a physical picture of the polymer--turbulence interaction and explicitly link it to the statistics in turbulence attenuated by polymers.
ER -