The minimal flow unit and origin of two-dimensional elasto-inertial turbulence

The research on elasto-inertial turbulence (EIT), a new type of turbulent flow, has reached the stage of identifying the minimal flow unit (MFU). On this issue, direct numerical simulations of FENE-P fluid flow in two-dimensional channels with variable sizes are conducted in this study. We demonstrate with the increase of channel length that the simulated flow experiences several different flow patterns, and there exists an MFU for EIT to be self-sustained. At Weissenberg number ( $Wi$ ) higher than the one required to excite EIT, when the channel length is relatively small, a steady arrowhead regime (SAR) flow structure and a laminar-like friction coefficient is achieved. However, as the channel length increases, the flow can fully develop into EIT characterized with high flow drag. Close to the size of the MFU, the simulated flow behaves intermittently between the SAR state with low drag and EIT state with high drag. The flow falling back to ‘laminar flow’ is caused by the insufficient channel size below the MFU. Furthermore, we give the relationship between the value of the MFU and the effective $Wi$ , and explain its physical reasons. Moreover, the intermittent flow regime obtained based on the MFU gives us an opportunity to look into the origin and exciting process of EIT. Through capturing the onset process of EIT, we observed that EIT originates from the sheet-like extension structure located near the wall, which is maybe related to the wall mode rather than the centre mode. The fracture and regeneration of this sheet-like structure is the key mechanism for the self-sustaining of EIT.