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 SURD (synergistic–unique–redundant decomposition of causality). The causal inference methods are first applied to several canonical problems to illustrate their abilities and differences, including a linear problem, a non-linear 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 self-sustained and independent of each other, supporting the self-sustaining mechanism of turbulent motions at all scales. We also find that there are top-down and bottom-up influences in the outer motions and their near-wall footprints, challenging the traditional sole top-down view. 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.