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 four-thirds 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 .
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