Causality between streaks and bursts in wall-bounded turbulence

Abstract

We use an information-theoretic method, referred to as information flux, to quantify the causal relationships between streaks and bursts in a non-intrusive manner. Within this framework, causality is quantified as the flux of Shannon information from the present of the quantities of interest to their future. We also use the so-called information leak to measure the information that is not accounted for due to unobserved variables. We investigate data from a direct numerical simulation of turbulent channel flow at the friction Reynolds number Re τ ≈ 180. The spatial distribution of causality is investigated as two time scales based on 50% value of the information leak and maximum of the normalized cross-induced information flux. It is found that the most causal spatial configuration for streaks and bursts is always streamwise-aligned. Furthermore, four dominant causal spatial configurations between streaks and bursts are identified. At the short time scale around 10 viscous units (when information flux is 50%), streaks and bursts have comparable causality to one another. At the longer time scale (corresponding to the maximum cross-induced causality), there is greater causality from streaks to bursts.