Diffusion by Turbulence

The turbulent diffusivity K of the atmosphere has first been studied by Richardson 1926 who empirically found that K depends on the scale l , K = Al α , with α = 4/3 and A = 0.6 cm 2/3 s −1 . This empirical scaling law is derived here from a unified theory (based on the Navier‐Stokes equation) together with an explicit result for the prefactor, A = 2.4 ϵ 1/3 . The mean atmospheric dissipation rate compatible with this is ϵ = 0.016 cm 2 s −3 . For windtunnels with typical dissipation rates ϵ ≅ 1 m 2 s −3 the turbulent diffusion coefficient should be K/cm 2 s −1 = 52 ( l /cm) 4/3 .