2006/12/13 by S. F. Edwards, Edwards, S. F., Moshe Schwartz +1
Environmental Science · Physics and Astronomy · #Atmospheric aerosols and clouds #Ecosystem dynamics and resilience #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0612319
7 pages
arxiv created 2006/12/13 · openalex publication_date 2006/12/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classic meteorological law of diffusion in the atmosphere was given experimentally, by Richardson in 1926, whose result that the mean squared distance <R2>=cT3, the time cubed, is in accord with the scaling theory of Komogorov [ Obukhov (1941)]. In some cases it might be important to have more information than that provided by Richardson's law. An example would be the distribution of pollutants in time by turbulent flow. Here small amounts of material reaching relatively large distances are of importance. This motivates our interest in the full distribution of the location of particles swept by the fluid as a function of time. The distribution depends on the distance through the dimensionless quantity X2=R2/<R2(T)> . Using the Kolmogorov picture, we find that for small X, the distribution is proportional to exp(-aX2) and exp(-bX4/3) at its tail when X is large.