A BBGKY framework for fluid turbulence
Abstract
A kinetic theory for fluid turbulence is developed from the Liouville equation and the associated BBGKY hierarchy. Real and imaginary parts of Fourier coefficients of fluid variables play the roles of particles. Closure is achieved by the assumption of negligible fivecoefficient correlation functions and probability distributions of Fourier coefficients are the basic variables of the theory. An additional approximation leads to a closedmoment description similar to the socalled eddydamped Markovian approximation. A kinetic equation is derived for which conservation laws and an Htheorem can be rigorously established, the Htheorem implying relaxation of the absolute equilibrium of Kraichnan. The equation can be cast in the FokkerPlanck form, and relaxation times estimated from its friction and diffusion coefficients. An undetermined parameter in the theory is the free decay time for triplet correlations. Some attention is given to the inclusion of viscous damping and external driving forces.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1975
 Bibcode:
 1975STIN...7527296M
 Keywords:

 Bbgky Hierarchy;
 Kinetic Theory;
 Probability Distribution Functions;
 Turbulent Flow;
 Approximation;
 Conservation Laws;
 Correlation;
 FokkerPlanck Equation;
 Fourier Transformation;
 Viscous Damping;
 Fluid Mechanics and Heat Transfer