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.