Kolmogorov Energy Cascade
Energy injected at large scales cascades down to the Kolmogorov microscale η, following E(k) ~ k
-5/3
Cascade Parameters
Energy injection rate ε:
1.00
Viscosity ν:
0.010
Number of scales:
6
Animation speed:
1.0x
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.