Statistical properties of two-dimensional elastic turbulence

TL;DR

This study uses numerical simulations to analyze the statistical properties of elastic turbulence in a 2D viscoelastic fluid, revealing large velocity fluctuations and partial breakdown of Taylor's hypothesis, with implications for experimental interpretation.

Contribution

It provides a detailed numerical analysis of spatial and temporal statistics in elastic turbulence, highlighting differences in higher-order statistics and flow anisotropy.

Findings

Large velocity fluctuations challenge Taylor's hypothesis.

Second-order statistics show consistent spatial-temporal scaling.

Flow remains highly anisotropic across scales.

Abstract

We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylor's hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static point-like numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylor's frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly non-homogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.