Turbulence Intermittency & Multifractal Cascade

Kolmogorov's K41 theory predicts self-similar turbulence, but real turbulence is intermittent — energy dissipation concentrates in fractal regions. The multifractal model captures structure functions S_p(r) ~ r^{ζ(p)} with nonlinear ζ(p) via the singularity spectrum f(α).

Parameters

Intermittency μ: 0.25 Reynolds Re: 1000 Cascade levels: 10

S_p(r) = ⟨|δu(r)|^p⟩ ~ r^{ζ(p)}
ζ(p) = p/3 − μ/2·(p/3)² (She-Lévêque)
f(α) = Legendre transform of ζ(p)
α_0 = 1 (K41), width ∝ μ