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Main Authors: Rota, Giulio Foggi, Singh, Rahul K., Chiarini, Alessandro, Amor, Christian, Soligo, Giovanni, Mitra, Dhrubaditya, Rosti, Marco Edoardo
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.13073
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author Rota, Giulio Foggi
Singh, Rahul K.
Chiarini, Alessandro
Amor, Christian
Soligo, Giovanni
Mitra, Dhrubaditya
Rosti, Marco Edoardo
author_facet Rota, Giulio Foggi
Singh, Rahul K.
Chiarini, Alessandro
Amor, Christian
Soligo, Giovanni
Mitra, Dhrubaditya
Rosti, Marco Edoardo
contents Elastic turbulence (ET), observed in flows of sufficiently elastic polymer solution at small inertia, is characterized by chaotic motions and power-law scaling of energy spectrum ($E$) in both wavenumber ($k$) and frequency ($ω$): $E(k) \sim k^{-α}$ and $E(ω) \sim ω^{-β}$. Experiments of ET have obtained a vast range of values for the exponent $β$. In inertial turbulence, Taylor's frozen-flow hypothesis implies $α= β$, i.e., spatial and temporal scales are linearly related to each other. In contrast, from high-resolution simulation in three different setups, a tri-periodic box, a channel, and a planar jet, we show that in ET $α\approx 4$ while $β$ varies significantly. Our analysis shows that in general Taylor's hypothesis does not hold in ET as there is no universal relation, linear or otherwise, between space and time. We thus clear the confusion of the different scaling exponents found in ET, and focus the attention of future research on understanding $α$. Our analysis also implies that waves-like dynamics with a linear dispersion relation (e.g., Alfvén waves) can not play a role in determining the scaling behavior of ET. The techniques introduced here can be useful for studying smooth chaotic flows in general, e.g., active turbulence.
format Preprint
id arxiv_https___arxiv_org_abs_2510_13073
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The broken link between space and time in elastic turbulence
Rota, Giulio Foggi
Singh, Rahul K.
Chiarini, Alessandro
Amor, Christian
Soligo, Giovanni
Mitra, Dhrubaditya
Rosti, Marco Edoardo
Fluid Dynamics
Elastic turbulence (ET), observed in flows of sufficiently elastic polymer solution at small inertia, is characterized by chaotic motions and power-law scaling of energy spectrum ($E$) in both wavenumber ($k$) and frequency ($ω$): $E(k) \sim k^{-α}$ and $E(ω) \sim ω^{-β}$. Experiments of ET have obtained a vast range of values for the exponent $β$. In inertial turbulence, Taylor's frozen-flow hypothesis implies $α= β$, i.e., spatial and temporal scales are linearly related to each other. In contrast, from high-resolution simulation in three different setups, a tri-periodic box, a channel, and a planar jet, we show that in ET $α\approx 4$ while $β$ varies significantly. Our analysis shows that in general Taylor's hypothesis does not hold in ET as there is no universal relation, linear or otherwise, between space and time. We thus clear the confusion of the different scaling exponents found in ET, and focus the attention of future research on understanding $α$. Our analysis also implies that waves-like dynamics with a linear dispersion relation (e.g., Alfvén waves) can not play a role in determining the scaling behavior of ET. The techniques introduced here can be useful for studying smooth chaotic flows in general, e.g., active turbulence.
title The broken link between space and time in elastic turbulence
topic Fluid Dynamics
url https://arxiv.org/abs/2510.13073