Causal links between inner and outer turbulent motions in wall-bounded flows

Determine the causal links among energy-containing coherent turbulent motions in wall-bounded flows, specifically between inner motions (the universal near-wall cycle) and outer motions residing in the logarithmic layer that exhibit a near-wall footprint, and resolve whether their interactions are bottom-up, top-down, co-supporting, or independently self-sustained across scales.

Background

Wall-bounded turbulent flows contain coherent structures across scales, including near-wall streaks and vortices (inner motions) and larger structures in the logarithmic region (outer motions). How these structures causally interact has been debated, with proposed mechanisms including bottom-up, top-down, co-supporting, and independent self-sustaining processes at all scales.

The paper defines inner motions as the self-sustained near-wall cycle and outer motions as those in the logarithmic layer that leave a footprint in the near-wall region. To investigate causal relationships, the paper applies transfer entropy and Liang–Kleeman information-flow methods to linear and nonlinear test systems, a low-dimensional near-wall turbulence model, and DNS of turbulent channel flow at Re_tau = 1000.