Kolmogorov Turbulence

2D turbulence, inverse energy cascade, and the k⁻⁵/³ spectrum

Vorticity Field ω

Energy Spectrum E(k)

Forcing scale 4 Viscosity ν 0.001 Inject rate 0.5

K41: E(k) ~ k⁻⁵/³ in inertial range. 2D turbulence: dual cascade — energy goes to large scales (inverse), enstrophy to small (forward). Forcing injects energy at intermediate k.