Dynamics of the self-sustaining process in the minimal flow unit and fully turbulent channel flow: comparison of integral quantities*

Minimal flow units (MFUs) of channel flow have facilitated the understanding of the self-sustaining process (SSP) of wall-bounded turbulence. While their statistics are comparable to those of fully turbulent channel flow, it is unclear whether the dynamics of the SSP remain unchanged in the larger domain. We aim to identify the SSP in large-domain turbulent channel flow and quantify how it differs from the one observed in MFUs. To compare the MFU and turbulent channel flow, subdomains comparable in size to the MFU are tracked in time in the larger domain at Re_τ = 180. We compute the key integral quantities of interest to the SSP (turbulent production, dissipation, and energy contained in specific length scales) in the MFU and the tracked subdomain at each timestep and assemble them into a temporal trajectory in variable-space. We compare state-transition probabilities of the MFU and turbulent channel flow based on the temporal trajectories. In addition, the trajectories are broken into short sequences of connections, and the most frequently occurring sequences of connections, known as motifs, are identified. These two metrics suggest similar dynamical processes occur in MFUs and the larger domain turbulent channel flow, albeit over shorter time scales in the large domain.