Turbulence Structure Functions
S_p(r) = ⟨|δu(r)|^p⟩ ~ r^ζ_p — Kolmogorov K41 vs She-Leveque intermittency
Structure Functions S_p(r) (log-log)
Anomalous Exponents ζ_p
Parameters
Intermittency μ:
0.25
Re (×10³):
10.0
Max order p:
6
Noise level:
0.05
ζ₂ (K41):
2/3
ζ₂ (SL):
—
ζ₃ (exact):
1.000
ζ₆ (SL):
—
Inertial range:
—
K41: ζ_p = p/3 (Kolmogorov 1941)
SL: ζ_p = p/9 + 2[1−(2/3)^(p/3)] (She-Leveque 1994)
ζ₃ = 1 exactly (4/5 law, rigorous)
Intermittency: dissipation is multifractal
Velocity Increment PDF (Gaussian vs Stretched-Exp)