Turbulence Intermittency

Multifractal structure of velocity increments & anomalous scaling exponents

— K41 (p/3)
— She-Lévêque
— Measured ζₚ
Turbulence Intermittency: Kolmogorov (K41) predicts structure function scaling ⟨|δᵣu|ᵖ⟩ ∝ r^(p/3). But real turbulence shows anomalous (multifractal) exponents due to intermittent bursts of dissipation: ζₚ = p/3 − μ p(p−3)/18 (K62)    or    ζₚ = p/9 + 2[1−(2/3)^(p/3)] (She-Lévêque 1994) The multifractal spectrum f(α) encodes the fractal dimension of regions with Hölder exponent α. Intermittency manifests as heavy tails in the PDF of velocity increments δᵣu at small scales.