Fluctuation relations at large scales in three-dimensional hydrodynamic turbulence

- It has long been conjectured that, in three-dimensional turbulence, velocity modes at scales larger than the forcing scale follow equilibrium dynamics. Recent numerical and ex-perimental evidence shows that such modes share the same mean energy and therefore support this claim, but equilibrium dynamics does not reduce to equipartition of energy. In this work, a large set of direct numerical simulations is carried out to investigate if fluctuation-dissipation relations and the fluctuation theorem also apply at these scales. These two results link out-of-equilibrium properties of a forced system with its behavior at equilibrium. Both relations are verified quantitatively by the results of our simulations, further supporting that large-scale modes display equilibrium dynamics. They provide new tools to characterize both the mean value and the fluctuations of the injected energy by a large-scale force acting on turbulence driven by small scale random noise.