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Updated: Oct 16, 2025
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Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
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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.
Physical Review. E
|October 16, 2021
Summary
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
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.
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