Statistical Theory of Time-Space Dimensions of Clusters of Particles

[摘要] Universal equations of diffusion are introduced. These equations can be applied to diffusion from a point source with infinite releasing time-interval to relative diffusion from an instantaneous source and to any other types of diffusion. Dependences of eddy diffusivity on time-distribution and spatial dimensions of clusters are clarified.In the course of the derivation of the equations, local time-space correlation of velocities is formulated, as a product of the correlation coefficient and local energy. The equation of local variance of stochastic time series is applied to the local energy in two-dimensional clusters with spatial and time-dimensions, by introducing the virtual one-dimensional scales of the clusters. Taylor's hypothesis about the relations between the Eulerian and Taylor-Karman correlations are made.The universal equations derived are solved numerically and for special cases analytically. The solutions for some cases are calculated and illustrated.

[学科分类] 大气科学