Causally significant structures in fully developed wall turbulence*

We investigated events with strong causal effects on the future state of wall turbulence by interventional way. Numerical experiments were conducted in a fully developed turbulent open channel flow at a friction Reynolds number of Re_τ=609 by introducing spatially localized perturbations. The experiments were repeated 38,000 times, varying the initial snapshots and locations of the perturbations. Causal effect of the perturbation was defined as the amplification of the perturbation velocity energy relative to its initial value. We examined common characteristics in the perturbed flow structure of causally significant and irrelevant samples. The analysis was performed at the time when the strength of causality showed the highest variation.

Near the wall, strong causality was found to be associated with high shear regions, namely high-speed streaks. Similarly, sweep regions were found to be associated with causality in the far wall. Taking those results into account, we conducted the second experiment by dividing the flow field into a grid-like structure and perturbing each cell, which allowed us to create a complete map of causal significance. Using the map, correspondence between canonical sweep & ejection pairs and causal & non-causal structures were studied in detail.