Multifractal Turbulence

Turbulent velocity fields are multifractal — dissipation concentrates on a fractal set with a spectrum of Hölder exponents. The D(h) singularity spectrum generalizes K41. She-Leveque model: ζ_p = p/9 + 2[1−(2/3)^(p/3)].

Cascade Model

Intermittency μ 0.25 Cascade levels 8 Max p (moments) 6.0 Display mode

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K41: ζ_p = p/3 (dashed)
She-Leveque: exact log-Poisson
μ=0: K41, μ>0: intermittent