Effects of log-layer events on near-wall dynamics: a state-space trajectory approach

We study the modulation of near-wall dynamics from log-layer events in turbulent channel flow. Three direct numerical simulations of turbulent channels are performed: a minimal flow unit (MFU) at Re𝜏=186, a log-layer minimal flow unit (LLMFU) at Re𝜏=2200, and a full-scale turbulent channel flow at Re𝜏=186. A proper orthogonal decomposition (POD) of the near-wall region of the MFU is performed to identify dynamically important near-wall structures that play a role in the self-sustaining process. Flow fields of the other channels are projected onto these POD structures, and energy contained in the structures is tracked over time. The energy in multiple structures can be represented as a state space, and as the flow evolves over time, a trajectory through the state space is formed. The state space is partitioned into regions of high and low energy for each structure, and the series of regions that the trajectory passes through is analyzed and compared across the different flow configurations. Further, LLMFU trajectories are conditioned to high- and low-energy events in the log-layer and analyzed. Network motif identification is used to identify and quantify the significance of repeated patterns in the trajectories, and observe how significant patterns change with log-layer energy. This approach highlights the modified dynamics in the near-wall region in the presence of large-scale structures.