On the elimination of the sweeping interactions from theories of hydrodynamic turbulence

    Authors

    E. Gkioulekas

    Comments

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    Abbreviated Journal Title

    Physica D

    Keywords

    turbulence; local homogeneity; quasi-Lagrangian; sweeping interactions; SMALL-SCALE TURBULENCE; CLASSICAL STATISTICAL DYNAMICS; FULLY-DEVELOPED; TURBULENCE; HIDDEN BRS INVARIANCE; ISOTROPIC TURBULENCE; RENORMALIZATION-GROUP; ENERGY-DISSIPATION; EXACT RESUMMATIONS; FLUID; TURBULENCE; 1ST PRINCIPLES; Mathematics, Applied; Physics, Multidisciplinary; Physics, Mathematical

    Abstract

    In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between incremental homogeneity and global homogeneity. It is shown that both the elimination of the sweeping interactions and the derivation of the 4/5-law require a homogeneity assumption stronger than incremental homogeneity but weaker than global homogeneity. The quasi-Lagrangian transformation, on the other hand, requires an even stronger homogeneity assumption which is many-time rather than one-time but still weaker than many-time global homogeneity. We argue that it is possible to relax this stronger assumption and still preserve the conclusions derived from theoretical work based on the quasi-Lagrangian transformation. (c) 2006 Elsevier B.V All rights reserved.

    Journal Title

    Physica D-Nonlinear Phenomena

    Volume

    226

    Issue/Number

    2

    Publication Date

    1-1-2007

    Document Type

    Review

    Language

    English

    First Page

    151

    Last Page

    172

    WOS Identifier

    WOS:000244572500006

    ISSN

    0167-2789

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