Géométrie de l'intermittence en turbulence développée

Abstract

A geometrical interpretation of intermittency in fully developed turbulence is realized through an hierarchy of fractal structures Ω_p of dimensions Δ_p linked each other by the relations Ω_{p + 1} − Ω_p (i.e. Δ_{p + 1} < Δ_p) and γ = (Δ_{p + 1} − Δ_∞)/(Δ_p − Δ_∞) with γ = ((1 + 3/√8)^1/3 + (1 − 3/√8)^1/3)³ and Δ_∞ = 1 and Δ_∞ = 1. This is obtained by the introduction of an entropy jump, defined at the scale r, ΔS_p(r) = (Δ_{p + 1} − Δ_p) ln (r/r₀) characterizing the order level of each sub-structure Ω_p and verifying a linear relation ΔS_p(r) = γ ΔS_{p − 1}(r).