Causal analysis of inner and outer motions in near-wall turbulence

In this work we study the causality of near-wall inner and outer turbulent motions. The inner motions are defined as the self-sustained near-wall cycle and the outer motions as those living in the logarithmic layer exhibiting footprints on the near-wall region. Causal inference with three typical methods is performed, i.e. transfer entropy, information flow and the synergistic–unique–redundant decomposition of causality. The causal inference methods are first applied to several canonical problems to illustrate their abilities, including a linear problem, a nonlinear problem and a low-dimensional model of near-wall turbulence. It is demonstrated that all three methods can produce consistent causal findings. Furthermore, we study the causalities between the inner and outer turbulent motions in a channel flow using the three methods with an improved inner–outer decomposition method. It is revealed that both the inner and outer motions are causally self-sustained, supporting the self-sustaining mechanism of turbulent motions at all scales. We also find that there are top-down and bottom-up causalities between the outer motions and their near-wall footprints owing to the dynamical coherence of inclined large-scale turbulent motions. More interestingly, pressure is identified to play an active role in the inner–outer causalities and may act as a bridge in linking the inner and outer turbulent motions.