Causal interactions between inner and outer layer flow motions in wall-bounded turbulence*

The interaction of turbulent motions of different sizes within the thin fluid layers immediately adjacent to solid boundaries poses a significant challenge for physical understanding and prediction of wall-bounded turbulent flows. This study investigates the flow of information between outer layer (far from the wall) and inner layer (close to the wall) motions in a turbulent channel flow. The data were obtained from a direct numerical simulation of a turbulent channel flow at a friction Reynolds number Re_τ≈1000. We use time-resolved signals of the streamwise velocity at two wall-normal locations within the inner and outer layers as the main quantities of interest. Then, we employ a method based on information theory to measure the causal relationship between the signals. The method, referred to as SURD (Synergistic-Unique-Redundant decomposition), assesses causality by quantifying the increments of information obtained about future events based on combinations of past events. The causal interactions among these events are further decomposed into redundant, unique, and synergistic contributions according to their nature. Our findings indicate that causality flows predominantly from outer-layer large-scale motions to inner-layer small-scale motions. These results are compared with those obtained from other causal inference methods and demonstrate that SURD offers a more reliable quantification of causality.