Turbulence Intermittency & Multiscaling
Structure functions Sₚ(r) = ⟨|δu(r)|ᵖ⟩ ∝ r^ζₚ — anomalous exponents & departure from K41
Turbulence Model
Intermittency μ:
0.25
Reynolds Re:
1000
Max order p_max:
8
Samples N:
5000
⚡ Generate
↺ Regenerate
μ (She-Lévêque):
—
ζ₂ (measured):
—
ζ₂ (K41=2/3):
0.667
ζ₆ (measured):
—
ζ₆ (K41=2):
2.000
Kolmogorov 1941 (K41):
ζₚ = p/3
She-Lévêque (1994):
ζₚ = p/9 + 2[1−(2/3)^(p/3)]
Intermittency causes ζₚ to deviate
below K41 for p > 3.
Top: velocity increments δu(r)
Bottom: ζₚ vs p (K41, SL, measured)