an:05131656
Zbl 1115.76034
Gkioulekas, Eleftherios
On the elimination of the sweeping interactions from theories of hydrodynamic turbulence
EN
Physica D 226, No. 2, 151-172 (2007).
00193128
2007
j
76F05
local homogeneity; quasi-Lagrangian statistical theory; global homogeneity
Summary: We revisit the claim that the Eulerian and quasi-Lagrangian time correlation tensors are equal. This statement allows us to transform the results of an MSR [\textit{P. Martin, E. Siggia} and \textit{H.Rose}, Phys. Rev. A 8, 423--437 (1973)] 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.