Fluctuation theorem and extended thermodynamics of turbulence. (25th November 2020)

• Record Type: Journal Article
• Authors: Porporato, Amilcare; Hooshyar, Milad; Bragg, Andrew D.; Katul, Gabriel
• Is Part Of: Proceedings. Volume 476:Number 2243(2020)
• Publication Date: 2020-11-25
• Subjects: cascade -- fluctuation theorem -- turbulence; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2020.0468
• Languages: English
• ISSNs: 1364-5021

Abstract

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.