Informative and non-informative decomposition of turbulent flow fields

Abstract

Not all the information in a turbulent field is relevant for understanding particular regions or variables in the flow. Here, we present a method for decomposing a source field into its informative $\boldsymbol{\Phi}_I(\boldsymbol{x},t)$ and residual $\boldsymbol{\Phi}_R(\boldsymbol{x},t)$ components relative to another target field. The method is referred to as informative and non-informative decomposition (IND). All the necessary information for physical understanding, reduced-order modelling, and control of the target variable is contained in $\boldsymbol{\Phi}_I(\boldsymbol{x},t)$, whereas $\boldsymbol{\Phi}_R(\boldsymbol{x},t)$ offers no substantial utility in these contexts. The decomposition is formulated as an optimisation problem that seeks to maximise the time-lagged mutual information of the informative component with the target variable while minimising the mutual information with the residual component. The method is applied to extract the informative and residual components of the velocity field in a turbulent channel flow, using the wall-shear stress as the target variable. We demonstrate the utility of IND in three scenarios: (i) physical insight of the effect of the velocity fluctuations on the wall-shear stress, (ii) prediction of the wall-shear stress using velocities far from the wall, and (iii) development of control strategies for drag reduction in a turbulent channel flow using opposition control.