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

Elasto-inertial turbulence (EIT) has been demonstrated to be able to sustain in two-dimensional (2-D) channel flow; however the systematic investigations on 2-D EIT remain scarce. To address this gap, this study conducts direct numerical simulations of 2-D EIT at a modest Reynolds number ( $Re=2000$ ) to examine its statistical characteristics and dynamic mechanisms. Meanwhile, this paper explores the similarities and differences between 2-D EIT with the maximum drag reduction (MDR) state in three-dimensional (3-D) flow. We demonstrate that statistical characteristics of 2-D EIT follow distinct trends compared to those in viscoelastic drag-reducing turbulence as nonlinear elasticity increases. These differences can be attributed to two different underlying dynamical processes: the gradual suppression of inertial turbulence in 3-D flow, and the progressive enhancement of EIT in 2-D flow. Also, we present the role of pressure, energy budget and spectral characteristics of 2-D EIT, which show significant similarities to those in the MDR state, thus providing compelling evidence for the 2-D nature of EIT. More strikingly, we identify an anomalous Reynolds stress in 2-D EIT that contributes negatively to flow resistance, which differs from the extremely small but positive Reynolds stress observed in the MDR state. Although with small values of Reynolds stress, the correlation analysis indicates clearly moderate positive correlation between the streamwise and normalwise velocity fluctuations rather than their being uncorrelated. Moreover, quadrant analysis of velocity fluctuations reveals the predominance of motions in the first and third quadrants, which are closely associated with the typical polymer extension sheet-like structures.