Causality analysis of turbulent channel flow based on massive computation*

The causally important flow features of wall turbulence are studied by measuring the effect of perturbing local flow structures in direct numerical simulations of turbulent channel flow at Re_τ=600. The flow is initially perturbed by substituting the velocity in a cubic cell with its mean velocity, and the perturbed and original flow fields are allowed to develop for a given time. The causal significance of the perturbation is quantified by the growth of the L₂ norm of the velocity difference between the perturbed and original flows. To avoid pre-assumptions as much as possible, the experiment is repeated many times, changing the location, the size of the perturbation cell and the initial flow field. The causal flow features are then studied from the ensemble of these realizations, which in this study includes 76320 simulation experiments. The rate of growth of the perturbations and their propagation normal to the wall show that the causal effect amplifies fastest when the perturbation hits the wall, where the energy production is high due to the mean shear. Which properties determine whether flow structures are more or less causal depend on the distance from the wall of the initial perturbations. High and low shear are found to be more and less causal, respectively, for near-wall perturbations, whereas sweeps and ejections are causal and less causal for perturbations farther from the wall. The growth of causal and less causal perturbations scales well when time is normalized by the local mean shear. This suggests that the causal effect of the flow structures depend on the total energy production that the structures experience during their lifetime.