Causal analysis of very large-scale motions in wall-bounded turbulence

Structural models of wall-bounded turbulence are traditionally based on two distinct yet interacting features: streaks and bursts. These models posit that both structures participate in a self-sustaining cycle, operating at each scale in a relatively isolated manner. However, recent observations of very large-scale motions (VLSMs)—streamwise-elongated streaks without proportionally large bursts—challenge this notion and suggest the need for a revised understanding. In this study, we investigate the causal mechanisms underlying VLSMs in a turbulent channel flow at a friction Reynolds number of 5200. To this end, we apply the Synergistic-Unique-Redundant Decomposition (SURD) of causality, an observational, information-theoretic framework that quantifies causality as the information provided by past source states about future target states. The target variable is the future large-scale streamwise velocity field, obtained via anisotropic Gaussian filtering. The source variables include the past smaller-scale streamwise velocity field, along with the wall-normal and spanwise velocity components. To discretize the system for causal inference, we employ a deep autoencoder with a quantized latent space, assigning each snapshot to its nearest representative state based on energy reconstruction accuracy. Our findings show that coherent clusters of smaller-scale streamwise velocity fluctuations serve as causal precursors to future large-scale motions. When these clusters are aligned in the streamwise direction, the smaller-scale streamwise motions act as unique drivers. In contrast, when misaligned, the emergence of large-scale motions requires synergistic contributions from the smaller-scale streamwise motions with the wall-normal and spanwise fluctuations.