Turbulence: Inertial Range & Intermittency

K41 cascade · She-Leveque multifractal · anomalous scaling exponents

Parameters

Inertial Range

Kolmogorov scale η:-
Integral scale L:-
Inertial range decades:-
Spectral slope:-5/3
K41: E(k) = C_K ε²/³ k⁻⁵/³
Structure functions: ⟨δu^p⟩ ~ ℓ^(p/3)

She-Leveque (1994):
ζ_p = p/9 + 2[1-(2/3)^(p/3)]

Exact result (Kolmogorov 1941):
⟨(δu_∥)³⟩ = -4/5 ε ℓ