Granger causality in wall-bounded turbulence

Granger causality is based on the idea that if a variable helps to predict another one, then they are probably involved in a causality relationship. This technique is based on the identification of a predictive model for causality detection. The aim of this paper is to use Granger causality to study the dynamics and the energy redistribution between scales and components in wall-bounded turbulent flows. In order to apply it on flows, Granger causality is generalized for snapshot-based observations of large size using linear-model identification methods coming from model reduction. Optimized DMD, a variant of the Dynamic Mode Decomposition, is considered for building a linear model based on snapshots. This method is used to link physical events and extract physical mechanisms associated to the bursting process in the logarithmic layer of a turbulent channel flow.