Accession Number : AD0603628

Title :   KOLMOGOROV'S HYPOTHESES AND EULERIAN TURBULENCE THEORY.

Descriptive Note : Research rept. no. 6,

Corporate Author : KRAICHNAN (ROBERT H) PETERBOROUGH N H

Personal Author(s) : Kraichnan,Robert H.

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 loworder 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. (Author)

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

Distribution Statement : APPROVED FOR PUBLIC RELEASE