Entropy and fluctuation relations in isotropic turbulence
arXiv:2307.11311 · doi:10.1017/jfm.2023.808
Abstract
Based on a generalized local Kolmogorov-Hill equation expressing the evolution of kinetic energy integrated over spheres of size in the inertial range of fluid turbulence, we examine a possible definition of entropy and entropy generation for turbulence. Its measurement from direct numerical simulations in isotropic turbulence leads to confirmation of the validity of the fluctuation relation (FR) from non-equilibrium thermodynamics in the inertial range of turbulent flows. Specifically, the ratio of probability densities of forward and inverse cascade at scale is shown to follow exponential behavior with the entropy generation rate if the latter is defined by including an appropriately defined notion of ``temperature of turbulence'' proportional to the kinetic energy at scale .
References in corpus (16)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Localness of energy cascade in hydrodynamic turbulence, I. Smooth coarse-graining
- Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows
- The turbulent cascade in five dimensions
- Exact Second-Order Structure-Function Relationships
- Equations relating structure functions of all orders
- Is vortex stretching the main cause of the turbulent energy cascade?
- Local 4/5-Law and Energy Dissipation Anomaly in Turbulence
- The temporal evolution of the energy flux across scales in homogeneous turbulence
- Entropy, irreversibility and cascades in the inertial range of isotropic turbulence
- Generalised Fluctuation Formula
- Comparing local energy cascade rates in isotropic turbulence using structure function and filtering formulations
- Fluctuation-theorem and extended thermodynamics of turbulence
- Forward and inverse energy cascade and fluctuation relation in fluid turbulence adhere to Kolmogorov's refined similarity hypothesis