GOY shell model of turbulence — energy cascades from large scales to small, revealing Kolmogorov's k⁻⁵/³ spectrum.
Total E: 0.00
Dissipation ε: 0.00
K41 slope: -1.67
Inertial shells: 0
Re_λ ≈ 0
Kolmogorov 1941 (K41): Energy injected at large scales (low k) cascades to small scales through an inertial range where
E(k) = C_K ε^{2/3} k^{−5/3} (Kolmogorov spectrum, shown as dashed line). Dissipation occurs at Kolmogorov scale η=(ν³/ε)^{1/4}.
GOY/Sabra shell model: Simplified 1D model retaining energy/helicity conservation. Shell n has wavenumber k_n = k₀·2ⁿ.
Intermittency: Real turbulence deviates slightly — anomalous scaling exponents ζ_p ≠ p/3 for structure functions.
She-Leveque (1994) prediction: ζ_p = p/9 + 2[1−(2/3)^{p/3}].