On the elimination of the sweeping interactions from theories of hydrodynamic turbulence
Abbreviated Journal Title
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
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.
Physica D-Nonlinear Phenomena
"On the elimination of the sweeping interactions from theories of hydrodynamic turbulence" (2007). Faculty Bibliography 2000s. 7162.