Turbulent Energy Cascade

Kolmogorov's 1941 theory: energy injected at large scales cascades through an inertial range E(k) ~ k−5/3 to viscous dissipation at small scales.

Controls

Kolmogorov's K41 Theory

Inertial range: E(k) = CK ε2/3 k−5/3

Kolmogorov scale: η = (ν³/ε)1/4

Energy cascades from large integral scale L to dissipation scale η. Inertial range extends as Re grows.