Fluctuation theorem and extended thermodynamics of turbulence.

TitleFluctuation theorem and extended thermodynamics of turbulence.
Publication TypeJournal Article
Year of Publication2020
AuthorsA Porporato, M Hooshyar, AD Bragg, and G Katul
JournalProceedings. Mathematical, Physical, and Engineering Sciences
Volume476
Start Page20200468
Issue2243
Date Published11/2020
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.

DOI10.1098/rspa.2020.0468
Short TitleProceedings. Mathematical, Physical, and Engineering Sciences