## Abstract

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker-Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.

Original language | English (US) |
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Article number | 0468 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 476 |

Issue number | 2243 |

DOIs | |

State | Published - 2020 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

## Keywords

- cascade
- fluctuation theorem
- turbulence