Hysteresis in the dissipation in turbulent flows

TL;DR

This paper demonstrates that in unsteady turbulent flows, energy dissipation exhibits hysteresis depending on flow acceleration or deceleration, with experimental and simulation evidence showing larger dissipation during deceleration phases.

Contribution

It reveals the hysteretic behavior of dissipation in turbulent flows and quantifies its dependence on flow parameters, linking it to the unsteady term in the Karman-Howarth equation.

Findings

Dissipation constant is larger during decelerating flows.

Hysteresis cycle area scales with Strouhal number and forcing amplitude.

Unsteady term in Karman-Howarth explains the phenomenon.

Abstract

We present evidence of the hysteretic nature of dissipation in unsteady turbulent flows. Wind tunnel experiments and direct numerical simulations in oscillating flows show that, at fixed mean Reynolds number, the dissipation constant is larger for decelerating flows. Consequently, a periodic behavior of the flow produces a hysteresis cycle, whose area scales with a parameter combining the Strouhal number and the relative amplitude of the forcing. This phenomenon can be explained and quantified through the influence of the unsteady term in the Karman-Howarth equation, with implications for a wide range of out-of-equilibrium systems.