Kolmogorov Energy Cascade

Energy injected at large scales cascades down to the Kolmogorov microscale η, following E(k) ~ k-5/3

Cascade Parameters

K41 Theory (Kolmogorov 1941):

E(k) = C_K ε^(2/3) k^(-5/3)

Energy cascades from large eddies (wavenumber k₀) to small ones (Kolmogorov scale η = (ν³/ε)^(1/4)).

The unique exact result: ⟨(δu∥)³⟩ = -4/5 εℓ

Eddies at each scale spin faster, containing less energy, until viscosity dissipates them.