Understanding the dynamics of near-wall turbulence using network motif identification*

A graph-theoretic approach is used to identify and quantify key dynamical processes in wall-bounded turbulence. Classically, wall-bounded turbulence is considered to have a universal near-wall inner region where all velocity statistics are dependent only on the distance from the wall. However, as the Reynolds number and domain size increase, dynamic interactions between structures of different wall-normal sizes (inter-scale interactions) or different instances of structures of the same size (intra-scale interactions), modify this view. In this work, we aim to extract the signature of these dynamics and quantify their significance. This analysis is performed using direct numerical simulation data of a minimal flow unit (MFU) at Re_τ = 180, a larger-domain channel at Re_τ = 180 to capture the effect of intra-scale interactions of near-wall structures, and a channel at Re_τ = 550 to capture the effect of inter-scale interactions with flow further from the wall. A proper orthogonal decomposition of the Re_τ = 180 MFU is performed to identify energetic structures, and the energy captured by the structures is tracked over time, forming a temporal trajectory. Temporal patterns of high significance, known as network motifs, are then extracted from the trajectories. Similar analyses are performed on MFU-sized boxes embedded in the larger-domain simulations at Re_τ = 180 and Re_τ = 550 to understand the difference in the dynamics.