Abstract
Direct numerical simulations were performed to study the effects of the domain size of a minimal flow unit (MFU) and its inherent periodic boundary conditions on flow physics of a turbulent channel flow in a range of 200≤Reτ≤1000. This was accomplished by comparing turbulent statistics with those computed in sub-domains (SD) of extended domain simulations. The dimensions of the MFU and SD were matched, and SD dynamics were set to minimize artificial periodicities. Streamwise and spanwise dimensions of healthy MFUs were found to increase linearly with Reynolds number. It was also found that both MFU and SD statistics and dynamics were healthy and in good agreement. This suggests that healthy MFU dynamics represent extended-domain dynamics well up to Reτ=1000, indicating a nearly negligible effect of periodic conditions on MFUs. However, there was a small deviation within the buffer layer for the MFU at Reτ=200, which manifested in an increased mean velocity and a tail in the Q2 quadrant of the u′-v′ plane. Thus, it should be noted that when considering an MFU domain size, stricter criteria may need to be put in place to ensure healthy turbulent dynamics.
Highlights
Embedded in a turbulent flow is inherent intermittency
The present study provides statistical information about the flow at increasing Reynolds numbers, with the goal of offering insights into the effect of periodic boundary conditions used in minimal flow units on MFU statistics and their connections to statistics of a sub-domain embedded within an extended domain
It should be noted that when the spanwise length L+z < 0.75Reτ, it caused MFU dynamics to become unhealthy for the Reynolds numbers studied
Summary
The dynamics of wallbounded turbulence fluctuate between high, intermediate, and low-drag states in a stochastic fashion, which illuminates the self-sustaining process in shear flows [1,2,3,4]. The most straightforward simulation approach to identify the intermittency and self-sustaining structures is the so-called minimal flow unit (MFU) approach [5]. A minimal flow unit is the smallest simulation domain for a given set of parameters, such as Reynolds numbers, containing the essential self-sustaining elements for which turbulence persists. In MFUs, turbulent statistics are spatially correlated, indicating that the entire domain completely experiences the same dynamics. The MFU dynamics allow one to concentrate only on the temporal intermittency of turbulence. An MFU should be able to contain a single ejection and sweep event by which streamwise streaks and vortices are sustained [10]
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