Causality between streaks and bursts in wall-bounded turbulence

Structural models of wall-bounded turbulence are rooted in two distinctive but interacting entities: bursts and streaks. The prevailing understanding is that both structures are involved in a self-sustaining cycle at each scale in a relatively isolated manner. However, some recent evidence from numerical experiments and observations casts doubt on current models. The root problem is that the causal relation between streaks and bursts has yet to be elucidated. Traditional causal inference based on interventions, while powerful, might result in misleading causal relations by unintentionally altering key dynamics of the system. Here, we propose a non-intrusive method using information flux based on information theory to infer causality between streaks and bursts. By analyzing time-resolved signals representative of streaks and bursts obtained from direct numerical simulations, we investigate the causality between these structures at different proximity levels. Our results reveal that bursts are causal to streaks located closely downstream in the streamwise direction. Similarly, streaks are causal to bursts in the proximity of the streak located downstream. The analysis also shows that most of the causality on these localized structures cannot be explained merely by the dynamics of their single closest streak or burst.