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Diffusion by Turbulence
Author(s) -
Grossmann Siegfried
Publication year - 1990
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19905020706
Subject(s) - turbulence , physics , dissipation , scaling , diffusion , thermal diffusivity , turbulent diffusion , scaling law , atmosphere (unit) , statistical physics , thermodynamics , mathematical physics , mathematics , geometry
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 .