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Dynamical Hysteresis in the Dissipation in Turbulent Flows
M Ahmad1,2, P D Mininni3,4, M Obligado1,5
1Centrale Lille, Arts et Metiers, ONERA, CNRS, Université de Lille, Institute of Technology, UMR 9014-LMFL-Laboratoire de Mécanique des Fluides de Lille-Kampé de Fériet, F-59000 Lille, France.
Physical Review Letters
|August 10, 2026
Summary
Unsteady turbulent flows exhibit dynamical hysteresis in dissipation. Dissipation is higher during flow deceleration, creating a hysteresis cycle with implications for out-of-equilibrium systems.
Area of Science:
- Fluid dynamics
- Turbulence research
- Non-equilibrium thermodynamics
Background:
- Turbulent flows are often unsteady, exhibiting complex dissipation dynamics.
- Understanding energy dissipation is crucial for modeling out-of-equilibrium systems.
Purpose of the Study:
- To investigate the dynamical hysteretic nature of energy dissipation in unsteady turbulent flows.
- To quantify the factors influencing this hysteresis.
Main Methods:
- Conducted wind tunnel experiments on oscillating flows.
- Performed direct numerical simulations (DNS) of unsteady flows.
- Analyzed the Kármán-Howarth equation to explain dissipation dynamics.
Main Results:
- Evidence of dynamical hysteresis in turbulent flow dissipation was found.
- The dissipation constant is larger during flow deceleration at a stationary mean Reynolds number.
- A hysteresis cycle emerges, scaling with the Strouhal number and forcing amplitude.
Conclusions:
- The unsteady term in the Kármán-Howarth equation explains the observed hysteresis.
- This phenomenon has broad implications for various out-of-equilibrium systems.
- Dynamical hysteresis is a key characteristic of dissipation in unsteady turbulent flows.
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