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# Accession Number:

## AD0607934

# Title:

## FORMULATION OF THE THEORY OF TURBULENCE IN AN INCOMPRESSIBLE FLUID,

# Descriptive Note:

# Corporate Author:

## TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF

# Report Date:

## 1961-01-01

# Pagination or Media Count:

##
45.0

# Abstract:

## The theory of turbulence in an incompressible fluid is formulated using methods similar to those of quantum field theory. A systematic perturbation theory is set up, and the terms in the perturbation series are shown to be in one to one correspondence with certain diagrams analogous to Feynman diagrams. From a study of the diagrams it is shown that the perturbation series can be rearranged and partially summed in such a way as to reduce the problem to the solution of three simultaneous integral equations for three functions, one of which is the second order velocity correlation function. The equations have the form of infinite power series integral equations, and the first few terms in the power series are derived from an analysis of the diagrams to sixth order. Truncation of the integral equations at the lowest nontrivial order yields Chandrasekhars equation, and truncation at a higher order yields the equations discussed by Kraichnan. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#