Intermittency and Anomalous scaling in turbulence - Victor S. L'vov ...

Belinicher-L’vov-Pomyalov-Procaccia-98: Standard Gaussian decomposi-
tion, like F4 ⇒ F 2 2 , destroys Euler rescaling symmetry and fixes h = 1 3 ,
(K41). Suggested h-invariant decompositions, like F4 ⇒ F 2 3 /F2, preserve
the rescaling symmetry, leave h free, and demonstrate multiscaling in an
analytical, NS based theory (in the BL-87 sweeping-free representation)
L’vov-Procaccia-2000 Analytic calculation of anomalous exps. ζn in NS
turbulence: Using the (LP-96) fusing rules to flush out a small parameter
δ = ζ2− 2 3 0.03 in “4–eddy interaction amplitude” in the ladder diagrams
for exps. ⇒ ζn = n − 3)
− δn(n 1 + 2 δ b(n − 2)
3 2
, δ n < 1 , n ≤ 12 .
Benzi-Bifferale-Sbragaglia-Toschi-03: Anomalous scaling in shell models:
Using Fusion Rules and “time-dependent random multiplicative process”
for closure of correlation function ⇒ calculation (without free parameters)
of the anomalous scaling exps. in shell models.
T O BE CON T IN UED