# Causality of energy-containing eddies in wall turbulence

## TL;DR

This paper investigates the causal interactions of energy-containing eddies in wall turbulence using DNS, revealing self-similar causality across scales and suggesting new strategies for flow control and modeling.

## Contribution

It introduces a novel method to quantify causality of energy-eddies in wall turbulence and demonstrates scale-independent causality in buffer and logarithmic layers.

## Key findings

- Causality of energy-eddies is similar across buffer and logarithmic layers.
- Causality is independent of eddy size.
- Potential for new flow control and modeling strategies based on causality insights.

## Abstract

Turbulent flows in the presence of walls may be apprehended as a collection of momentum- and energy-containing eddies (energy-eddies), whose sizes differ by many orders of magnitude. These eddies follow a self-sustaining cycle, i.e., existing eddies are seeds for the inception of new ones, and so forth. Understanding this process is critical for the modelling and control of geophysical and industrial flows, in which a non-negligible fraction of the energy is dissipated by turbulence in the immediate vicinity of walls. In this study, we examine the causal interactions of energy-eddies in wall-bounded turbulence by quantifying how the knowledge of the past states of eddies reduces the uncertainty of their future states. The analysis is performed via direct numerical simulation (DNS) of turbulent channel flows in which time-resolved energy-eddies are isolated at a prescribed scale. Our approach unveils, in a simple manner, that causality of energy-eddies in the buffer and logarithmic layers is similar and independent of the eddy size. We further show an example of how novel flow control and modelling strategies can take advantage of such self-similar causality.