Relative Diffusion of a Pair of Fluid Particles in Turbulence
Abstract
The effective Hamiltonian method is used to find the distribution function describing the positions as a function of time of a given pair of fluid particles subject to convection in steady, incompressible, statistically isotropic turbulent flow. By assuming a joint Gaussian distribution for the velocity field, a reasonable time dependence is obtained for the statistical average of the distance between the pair of fluid particles. The basis for Richardson’s fourthirds law is indicated and the proportionality constant C^{*} is shown to be related to the Kolmogorov constant C by C^{*}{=}3^{1/3}C^{1/2}/2^{1/2}.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 June 1984
 DOI:
 10.1143/JPSJ.53.1995
 Bibcode:
 1984JPSJ...53.1995S
 Keywords:

 Distribution Functions;
 Incompressible Flow;
 Isotropic Turbulence;
 Turbulent Flow;
 Hamiltonian Functions;
 Integral Equations;
 Kolmogoroff Theory;
 Normal Density Functions;
 Fluid Mechanics and Heat Transfer