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

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.