On the efficacy of minimal flow units in simulating "healthy" turbulence in plane Poiseuille flows*

We present results on a comparison between turbulent channel flows simulated using minimal flow units (MFUs) and extended domains. The goal of the study was to analyze the effect of inherent periodic boundary conditions of MFUs in faithfully capturing turbulent dynamics of plane Poiseuille flow for a range of Reynolds numbers, 200 ≤ Re_τ ≤ 1000. Turbulent statistics of the MFU were compared with those computed in a sub-domain (SD) of an extended domain at the same Reynolds number. The dimensions of the MFU and SD were matched and set such that the artificial periodicity in the MFU was minimized. MFU streamwise and spanwise dimensions were chosen such that “healthy” turbulence, or turbulence which corresponds to a saturated friction Reynolds number and valid mean velocity profile, was achieved. Streamwise and spanwise dimensions of healthy MFUs were found to increase linearly. Statistics of the MFU were in good agreement with SD for each Reynolds number, other than Re_τ = 200. The agreement between MFU and SD dynamics suggest that MFUs may be used to faithfully represent turbulence dynamics up to Re_τ = 1000. The comparison between MFU and SD is extended using quadrant analysis, which further confirms the agreement between MFU and SD dynamics. A diminished log-law region may occur even when the friction Reynolds number is saturated, suggesting that further criterion may need to put in place when using MFUs to simulate higher Reynolds number flows.