On some mathematical aspects of the direct-interaction approximation in turbulence theory

    Authors

    B. K. Shivamoggi; M. D. Taylor;S. Kida

    Comments

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    Abbreviated Journal Title

    J. Math. Anal. Appl.

    Keywords

    SPHERICAL MODEL; Mathematics, Applied; Mathematics

    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 DLA solution to the perturbative solution is discussed within the framework of a continued-fraction representation. (C) 1999 Academic Press.

    Journal Title

    Journal of Mathematical Analysis and Applications

    Volume

    229

    Issue/Number

    2

    Publication Date

    1-1-1999

    Document Type

    Article

    Language

    English

    First Page

    639

    Last Page

    658

    WOS Identifier

    WOS:000078119400017

    ISSN

    0022-247X

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