PDF of Velocity Fluctuation in Turbulence by a Statistics based on Generalized Entropy

Abstract

An analytical formula for the probability density function (PDF) of the velocity fluctuation in fully-developed turbulence is derived, non-perturbatively, by assuming that its underlying statistics is the one based on the generalized measures of entropy, the Rényi entropy or the Tsallis-Havrda-Charvat (THC) entropy. The parameters appeared in the PDF, including the index $q$ which appears in the measures of the Rényi entropy or of the THC entropy are determined self-consistently with the help of the observed value $\mu$ of the intermittency exponent. The derived PDF explains quite well the experimentally observed density functions.

10 pages, 2 figures

Cited by in corpus (16)

• Nonextensive statistical mechanics and economics
• Constructing a statistical mechanics for Beck-Cohen superstatistics
• Fluxes of cosmic rays: A delicately balanced stationary state
• Nonequilibrium Probabilistic Dynamics of the Logistic Map at the Edge of Chaos
• On observability of Renyi's entropy
• Nonextensive statistical mechanics: Some links with astronomical phenomena
• Metastable states, anomalous distributions and correlations in the HMF model
• On the Role of Information Theoretic Uncertainty Relations in Quantum Theory
• Metastability, negative specific heat and weak mixing in classical long-range many-rotator system
• Quasi-stationary states in low-dimensional Hamiltonian systems
• On q-non-extensive statistics with non-Tsallisian entropy
• Tsallis thermostatics as a statistical physics of random chains
• Stability of the entropy for superstatistics
• Analysis of Velocity Derivatives in Turbulence based on Generalized Statistics
• The world according to Renyi: Thermodynamics of multifractal systems
• Mixing and relaxation dynamics of the Henon map at the edge of chaos