Characterization of turbulence in inhomogeneous anisotropic flows

TL;DR

This paper introduces a new global quantity, δ, to characterize turbulence in inhomogeneous anisotropic flows, providing a practical way to analyze turbulent fluctuations through experimental measurements.

Contribution

The paper proposes a novel global quantity δ based on spatial averages, enabling effective characterization of turbulence in complex flows, and studies its properties in von Kármán flow.

Findings

δ effectively characterizes turbulent fluctuations

Properties of δ are experimentally validated in von Kármán flow

δ helps analyze energy budgets and flow topology transitions

Abstract

We introduce a global quantity $\delta$ that characterizes turbulent fluctuations in inhomogeneous anisotropic flows. This time-dependent quantity is based on spatial averages of global velocity fields rather than classical temporal averages of local velocities. $\delta(t)$ provides a useful quantitative characterization of any turbulent flow through generally only two parameters, its time average $\bar \delta$ and its variance $\delta_2$. Properties of $\bar \delta$ and $\delta_2$ are experimentally studied in the typical case of the von K\'arm\'an flow and used to characterize the scale by scale energy budget as a function of the forcing mode as well as the transition between two flow topologies.