Turbulence Intermittency & Multifractal Spectrum

Structure functions S_p(ℓ) ~ ℓ^ζ_p. K41 predicts ζ_p = p/3 (linear). She-Leveque gives anomalous exponents ζ_p = p/9 + 2[1−(2/3)^p/3]. The multifractal spectrum f(α) follows via Legendre transform.

She-Leveque ζ_p

K41 ζ_p=p/3

f(α) spectrum

K41 f(α)

Max order p_max: 8

Intermittency μ: 0.25

Highlighted order p: 3