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

✍ Scribed by Eleftherios Gkioulekas

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 546 KB
• Volume: 226
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/j.physd.2006.11.012

✦ Synopsis

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.