Title

On The Elimination Of The Sweeping Interactions From Theories Of Hydrodynamic Turbulence

Keywords

Local homogeneity; Quasi-Lagrangian; Sweeping interactions; Turbulence

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. © 2006 Elsevier Ltd. All rights reserved.

Publication Date

2-15-2007

Publication Title

Physica D: Nonlinear Phenomena

Volume

226

Issue

2

Number of Pages

151-172

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.physd.2006.11.012

Socpus ID

33846614451 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33846614451

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