Title

On Some Mathematical Aspects Of The Direct-Interaction Approximation In Turbulence Theory

Abstract

The purpose of this paper is to clarify some mathematical issues associated with the direct-interaction approximation (DIA) given by Kraichnan [Phys. Rev. 109 (1958), 1407; J. Fluid Mech. 5 (1959), 497; Phys. Fluids 7 (1964), 1723; 8 (1965), 575; 9 (1966), 1728] via its application to Kraichnan's [J. Math. Phys. 2 (1961), 124] model equation. The latter process is shown to lead to a functional equation; the basic properties and construction of the solution of this equation are addressed. The relation of the DIA solution to the perturbative solution is discussed within the framework of a continued-fraction representation. © 1999 Academic Press.

Publication Date

1-15-1999

Publication Title

Journal of Mathematical Analysis and Applications

Volume

229

Issue

2

Number of Pages

639-658

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1006/jmaa.1998.6191

Socpus ID

0343215876 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0343215876

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