Distributions in the Physical and Engineering Sciences, Volume 3 by Alexander I. Saichev & Wojbor A. Woyczyński

Author:Alexander I. Saichev & Wojbor A. Woyczyński
Language: eng
Format: epub
ISBN: 9783319925868
Publisher: Springer International Publishing

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of its coordinate and Jacobian J, which quantitatively describes the effects of compression and expansion of the volume of the passive tracer. The subscript L signifies that the probability distribution of the random field is considered in the Lagrangian representation. In what follows we shall simply call similar statistical characteristics, and related probability distributions, Lagrangian.

Our problem has been already significantly simplified by an assumption that the velocity field is Gaussian, with a known correlation tensor (20.1.1). However, even in this case, for arbitrary spatial and temporal characteristic scales of the velocity field, the problem of statistical analysis of evolution of a passive tracer field remains quite intractable. For that reason, we will make one more simplifying assumption in our model, and suppose that

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