Integral One-Point Statistical Characteristics of Density Field

  • Valery I. KlyatskinEmail author
Part of the Understanding Complex Systems book series (UCS)


Above, we derived the equations for the one-point probability densities of the density field under the assumption that effects of dynamic diffusion are absent. The one-point probability density allow calculating arbitrary one-point characteristics of this field. Combined with the ideas of statistical topography, it is sufficient to obtain the conditions of possible formation of cluster structures. However, the analysis of derivatives of this field requires the knowledge of at least the two-point probability density. In principle, equations for such probability densities can be obtained in the standard manner, by using the general procedure for the linear partial differential equations of the first order. However, this derivation requires very cumbersome calculations, and examination of consequences of such description is a very difficult task. Moreover, effects of dynamic diffusion cannot be included in such probabilistic description.


Correlation Function Random Velocity Probabilistic Description Cumbersome Calculation Variance Dissipation 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.A.M. Obukhov Institute of Atmospheric Physics Russian Academy of SciencesMoscowRussia

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