Anomalous Reynolds stress and dynamic mechanisms in two-dimensional elasto-inertial turbulence of viscoelastic channel flow

TL;DR

This paper investigates the statistical and dynamic mechanisms of two-dimensional elasto-inertial turbulence (EIT) in viscoelastic channel flow, highlighting unique behaviors like anomalous Reynolds stress and similarities to three-dimensional EIT.

Contribution

It provides a systematic analysis of 2D EIT, revealing distinct elastic effects, an anomalous negative Reynolds stress, and dynamical similarities to 3D EIT, filling a research gap.

Findings

2D EIT exhibits a progressive enhancement with elasticity, unlike 3D EIT.

Anomalous Reynolds stress in 2D EIT contributes negatively to flow resistance.

Dynamical budget analysis shows similarities between 2D and 3D EIT.

Abstract

Elasto-inertial turbulence (EIT) has been demonstrated to be able to sustain in two-dimensional (2D) channel flow; however the systematic investigations on 2D EIT remain scare. This study addresses this gap by examining the statistical characteristics and dynamic mechanisms of 2D EIT, while exploring its similarities to and differences from three-dimensional (3D) EIT. We demonstrate that the influence of elasticity on the statistical properties of 2D EIT follows distinct trends compared to those observed in 3D EIT and drag-reducing turbulence (DRT). These differences can be attributed to variations in the underlying dynamical processes. As nonlinear elasticity increases, the dominant dynamic evolution in 3D flows involves the gradual suppression of inertial turbulence (IT). In contrast, 2D flows exhibit a progressive enhancement of EIT. More strikingly, we identify an anomalous Reynolds stress in 2D EIT that contributes negatively to flow resistance, a behavior opposite to that of IT. Quadrant analysis of velocity fluctuations reveals the predominance of motions in the first and third quadrants. These motions are closely associated with polymer sheet-like extension structures, which are inclined from the near-wall region toward the channel center along the streamwise direction. Finally, we present the dynamical budget of 2D EIT, which shows significant similarities to that of 3D EIT, thereby providing compelling evidence for the objective existence of the 2D nature of EIT.