Accession Number : AD0603628

Title :   KOLMOGOROV'S HYPOTHESES AND EULERIAN TURBULENCE THEORY

Descriptive Note : Research rept. no. 6

Corporate Author : KRAICHNAN (ROBERT H) DUBLIN NH

Personal Author(s) : Kraichnan, Robert H

PDF Url : AD0603628

Report Date : Jun 1964

Pagination or Media Count : 35

Abstract : It is argued that Eulerian formulations are intrinsically unsuited for deriving the Kolmogorov theory because low-order Eulerian moments do not express sufficiently well a statistical dependence of nonsimultaneous amplitudes that accompanies the convection of small spatial scales by large spatial scales. Illustration is made by applying the direct-interaction approximation and a related, higher Eulerian approximation to an idealized convection problem and to a modified Navier-Stokes equation. Convection effects of low wave numbers on high wave numbers are removed in the modified equation, and as a consequence the direct-interaction approximation for it yields the Kolmogorov spectrum. Low-order Lagrangian moments provide a promisingly more complete description of the convection of small spatial scales by large, and a search for satisfactory Lagrangian closure approximations seems highly desirable.

Descriptors :   *CONVECTION, *FLUID FLOW, *TURBULENCE, FLUID MECHANICS, FOURIER ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, REYNOLDS NUMBER, STATISTICAL ANALYSIS, STATISTICAL DISTRIBUTIONS, STATISTICAL FUNCTIONS

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE