Transition from a weak-elastic to an elastic-activated regime in two-dimensional polymeric turbulence
Abstract
We conduct direct numerical simulations to investigate the effects of dilute polymers on flow structure, statistical properties and energy transfer in 2D turbulence. As the Weissenberg number (Wi) increases, the flow undergoes a sharp but continuous crossover between a weak-elastic regime and an elastic-activated regime. In the weak-elastic regime, the flow remains close to its Newtonian counterpart and polymer stresses have weak dynamical effects. In the elastic-activated regime, elastic stresses attenuate vortical motions and promote shear-dominated filaments. Scale-by-scale energy analysis shows that polymer addition weakens both the inverse kinetic-energy cascade and the forward enstrophy cascade in the two regimes, whereas the kinetic--elastic exchange and the inter-scale redistribution of elastic energy differ between them. Kinetic-to-elastic conversion dominates over the analysed range of scales in the weak-elastic regime, whereas a partial transfer from elastic to kinetic energy emerges at small scales in the elastic-activated regime. The inter-scale transfer of elastic energy is dominated by inverse transfer over the large-scale range in the weak-elastic regime but by forward transfer over the small-scale range in the elastic-activated regime. These results link the crossover to the onset of strong elastic feedback from the polymers and the associated reorganisation of the scale-by-scale transfer pathways. Downstream-decay statistics also show the same qualitative two-regime behaviour.
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BibTeX
@misc{wang2026transition,
title = {{Transition from a weak-elastic to an elastic-activated regime in two-dimensional polymeric turbulence}},
author = {Haoyu Wang and Hangyu Zhu and Xiaoqiu He and Yongliang Xiong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27292},
eprint = {2609.27292},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27292},
}
RIS
TY - UNPB
TI - Transition from a weak-elastic to an elastic-activated regime in two-dimensional polymeric turbulence
AU - Haoyu Wang
AU - Hangyu Zhu
AU - Xiaoqiu He
AU - Yongliang Xiong
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27292
UR - https://arxiv.org/abs/2609.27292
AB - We conduct direct numerical simulations to investigate the effects of dilute polymers on flow structure, statistical properties and energy transfer in 2D turbulence. As the Weissenberg number (Wi) increases, the flow undergoes a sharp but continuous crossover between a weak-elastic regime and an elastic-activated regime. In the weak-elastic regime, the flow remains close to its Newtonian counterpart and polymer stresses have weak dynamical effects. In the elastic-activated regime, elastic stresses attenuate vortical motions and promote shear-dominated filaments. Scale-by-scale energy analysis shows that polymer addition weakens both the inverse kinetic-energy cascade and the forward enstrophy cascade in the two regimes, whereas the kinetic--elastic exchange and the inter-scale redistribution of elastic energy differ between them. Kinetic-to-elastic conversion dominates over the analysed range of scales in the weak-elastic regime, whereas a partial transfer from elastic to kinetic energy emerges at small scales in the elastic-activated regime. The inter-scale transfer of elastic energy is dominated by inverse transfer over the large-scale range in the weak-elastic regime but by forward transfer over the small-scale range in the elastic-activated regime. These results link the crossover to the onset of strong elastic feedback from the polymers and the associated reorganisation of the scale-by-scale transfer pathways. Downstream-decay statistics also show the same qualitative two-regime behaviour.
ER -