Kolmogorov Turbulent Cascade
Energy cascades from large eddies to small scales — E(k) ∝ k⁻⁵/³
Parameters
Energy injection rate ε:
1.0
Viscosity ν:
0.001
Forcing scale L:
1.0
Animation speed:
1.0
Reset eddies
Toggle log/lin
K41 theory
(Kolmogorov 1941):
E(k) = C_K ε²/³ k⁻⁵/³
Energy injected at large scales (small k) cascades through inertial range to Kolmogorov microscale η=(ν³/ε)^(1/4) where viscous dissipation occurs.
Inertial range
: eddies break up without direct viscous effect — universal scaling.
Exact result: ⟨(δu)³⟩ = −4/5 εℓ (4/5 law)