Multifractal Cascade & Turbulence Intermittency

Simulate a multiplicative cascade — the key model for turbulent energy dissipation. Watch intermittency emerge, compute structure functions S_p(l) ~ l^{ζ_p}, and fit the multifractal spectrum f(α).

Multiplicative cascade: dissipation ε_l = ε · Π_{j=1}^J W_j at scale l=L·2^{-J}. K41 predicts ζ_p=p/3 (monofractal, no intermittency). Log-normal model (Kolmogorov-Obukhov 1962): μ parameter → ζ_p = p/3 - μp(p-3)/18 (K62). She-Leveque (1994): ζ_p = p/9 + 2(1-(2/3)^{p/3}) — exact for filament structures. Multifractal spectrum f(α) = inf_p{pα - τ(p) + 1} via Legendre transform.