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Updated: Oct 16, 2025

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Statistical properties of two-dimensional elastic turbulence.

Himani Garg1, Enrico Calzavarini1, Stefano Berti1

  • 1Université de Lille, ULR 7512-Unité de Mécanique de Lille Joseph Boussinesq (UML), F-59000 Lille, France.

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This study explores elastic turbulence in polymer solutions. While spatial and temporal statistics align for some properties, temporal analysis misses key velocity fluctuations, impacting Taylor

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Area of Science:

  • Fluid Dynamics
  • Polymer Physics
  • Rheology

Background:

  • Elastic turbulence is a chaotic flow state in viscoelastic fluids at low Reynolds and high Weissenberg numbers.
  • Understanding the relationship between spatial and temporal flow properties is crucial for interpreting experimental data and validating hypotheses like Taylor's frozen-field hypothesis.

Purpose of the Study:

  • To numerically investigate the spatial and temporal statistical properties of dilute polymer solutions in the elastic turbulence regime.
  • To elucidate the relationship between spatial and temporal measurements in elastic turbulence.
  • To assess the validity of Taylor's hypothesis in this regime.

Main Methods:

  • Direct numerical simulations of two-dimensional Kolmogorov flow using an Oldroyd-B viscoelastic fluid model.
  • Placement of static pointlike numerical probes at various locations, including extrema of mean flow amplitude.
  • Analysis of second- and third-order statistics, as well as spatial and temporal inhomogeneity and isotropy.

Main Results:

  • Large velocity fluctuations were observed in the elastic turbulence regime, partially invalidating Taylor's frozen-field hypothesis.
  • Second-order statistics (spectra, structure functions) showed consistent spatial and temporal scaling.
  • Third-order statistics revealed significant differences, with temporal analysis failing to capture the skewness of streamwise velocity increments.
  • The flow was found to be weakly inhomogeneous in the cross-stream direction but highly anisotropic across all scales.

Conclusions:

  • Taylor's frozen-field hypothesis is only partially valid in the elastic turbulence regime due to large velocity fluctuations.
  • While second-order statistics are comparable in spatial and temporal domains, third-order statistics show distinct differences.
  • The elastic turbulent flow is characterized by significant anisotropy and weak cross-stream inhomogeneity.