Construction of a turbulent measure for the set of NavierStokes equations
Abstract
The previously reported statistical solution (Foias, 1972) for a measure, from which an average overall solution of the NavierStokes equations in the theory of turbulence is derived, is generalized. The extended formalism of the statistical solution permits the averaging of functionals which are nonlocal in time from the solution of the NavierStokes equations for a given set of initial data and outside forces. The pure measure satisfies an expression which coincides in essence with a generalization of Hopf's equation for the characteristic functional proposed by Leuvis and Kraichenan (1962).
 Publication:

Akademiia Nauk SSSR Doklady
 Pub Date:
 November 1975
 Bibcode:
 1975DoSSR.225...18A
 Keywords:

 Flow Theory;
 Measure And Integration;
 NavierStokes Equation;
 Turbulence;
 Functional Integration;
 Perturbation Theory;
 Statistical Mechanics;
 Wiener Hopf Equations;
 Fluid Mechanics and Heat Transfer