Dynamical Hysteresis in the Dissipation in Turbulent Flows.

We present evidence of the dynamical hysteretic nature of dissipation in unsteady turbulent flows. Wind tunnel experiments and direct numerical simulations in oscillating flows show that, at stationary 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 Kármán-Howarth equation, with implications for a wide range of out-of-equilibrium systems.