Analytical Theory of Turbulent Diffusion (Classic Reprint)

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Excerpt from Analytical Theory of Turbulent DiffusionThe aim of the theory of turbulent diffusion is to determine in a statistical sense the migration of marked particles as they are carried along with a turbulent flow. Like molecular motion in a dilute gas of discrete particles, turbulent diffusion is a linear process if the con vected particles have no reaction on the flow, i.e. The probability distribution for the position of a marked particle in space obeys the superposition rule and changes in time according to a linear equation. Unlike classical molecular motion, the motion of neighboring fluid ele ments in a continuum is correlated, although one expects that over dis tances large compared to the macroscale L of the turbulence this corre lation is weak and that elements separated by such distances move almost independently. Furthermore, unlike classical molecular diffusion, turbulent diffusion is not a Markoff process. However, one expects that over times large compared to L/vo, where V0 is the root mean square fluid velocity, the fluid elements will suffer many essentially uncorrelated deflections by the energy containing eddies and that accordingly their motion over such long times will be almost Brownian. Under such circum stances, one expects that the spread of marked particles carried by the fluid will indeed resemble classical diffusion, and that it will be possible to define a coefficient of eddy diffusivity. An analytical basis for these qualitative observations is given in Sec. 2.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.