The relative diffusion of two particle pairs was first investigated by Richardson in a pioneer paper written in 1926. His model allowed to describe the mean squared separation with respect to time by the celebrated t cubed law. In his model, he introduced a scale dependent coefficient known as the effective eddy-diffusivity in order to describe the diffusion process. Why do Richardson express this coefficient as half the time derivative of the mean squared separation?
Dear Abdallah
This is just "by definision", NOT LAW !
As mentioned in many related articles. The relative dispersion coefficient is defined as like you wrote. There are lots of definitions similar to this, e.g. drag & lift , ...
Prof. A.A. Ranjbar
Thank you Ali for your answer, so it is just a definition! Things are now clearer.
Hi Abdallah,
please read Albert Einstein (1905) with his work on molekular diffusion/Brownian motion. There you find the details. Richardson simply adopted to large-scale phenomena. There are all the fundamental ideas. Cheers, Helmut
Hi Jens, you're right with Kubo, good source. Much simpler but also nice is Okubo with his book about Diffusion and ecological problems. Much more challenging: Feynman with his Statistical Mechanics. However, all these modern texts miss the point of originality which is still on board with Einstein. He made one of the first and elementary steps into the diffusion business and brought convincing arguments in all of his derivations. If you read the original you dont need other sources and you become fit to create own new ideas. At least this is my personal experience. I told my students always to go back to the original, if possible. Today this is an easy exercixe, see attachment. Regards, Helmut
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