
Accession Number : AD0601159
Title : DIAGONALIZING APPROXIMATION FOR INHOMOGENEOUS TURBULENCE.
Descriptive Note : Research rept. no. 5
Corporate Author : KRAICHNAN (ROBERT H) PETERBOROUGH N H
Personal Author(s) : Kraichnan,Robert H.
Report Date : MAR 1964
Pagination or Media Count : 27
Abstract : An approximation for shear and Boussinesq turbulence was introduced which can greatly lessen the computational task associated with spatial inhomogeneity. It yields statistical equations for inhomogeneous flow which are of simplicity comparable to the directinteraction equations for homogeneous flow. The new approximation presupposes a representation of the turbulent fields by expansion in some appropriate set of orthonormal functions which obey the boundary cpmditions. The covariances which are offdiagonal in the chosen representation, as well as the triple correlations, were approximated in terms of diagonal covariances and diagonal average response functions by a procedure resembling the directinteraction scheme. The final equations involve only the meanfield amplitudes and the diagonal covariance and response functions. The approximation was illustrated by applying it to infinitePrandtlnumber Boussinesq convection between infinite horizontal planes. The range of applicability and the limitations of the approximation were discussed. (Author)
Descriptors : (*FLUID FLOW, TURBULENCE), (*TURBULENCE, STATISTICAL ANALYSIS), (*STOCHASTIC PROCESSES, MATHEMATICAL MODELS), (*MATRICES(MATHEMATICS), NUMERICAL ANALYSIS), CONVECTION, EQUATIONS, MOTION, STATISTICAL DISTRIBUTIONS, FOURIER ANALYSIS, FUNCTIONS(MATHEMATICS), POWER SERIES, DIFFERENTIAL GEOMETRY, VELOCITY, TEMPERATURE
Distribution Statement : APPROVED FOR PUBLIC RELEASE