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 four-thirds law is indicated and the proportionality constant C* is shown to be related to the Kolmogorov constant C by C*{=}31/3C1/2/21/2.
- 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