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

• Exact “Dissipative-bridge” relationships, (L’vov-Procaccia-96)
NSE:
∂v
+ (v · ∇)v + ∇p = ν ∆v
∂t
⇒
∂v
∂t + P
(v · ∇)v
= ν ∆v
P: transversal projector, Wr: r-separated velocity increment.
NSE for Wr schematically :
Wr ∂Wr
∂t + Wr P
(Wr · ∇)Wr
∂Wr
∂t + P
(Wr · ∇)Wr
= ν ∆Wr ⇒
= Wrν ∆Wr ⇒ −ν(∇Wr) ·(∇Wr) −ε(r) .
Thus, inside of the average operator, 〈. . .〉, the viscous range object ε(r)
can be evaluated as the inertial range object Wr P
(Wr · ∇)Wr
ε(r) ⇒ W3 r
r
W 3 r /r:
⇒ µn = n − ζ3n ⇒ µ2 = 2 − ζ6 0.3 ÷ 0.4
Exact “dissipative-bridge” relations µn = n − ζ3n
are known in liter-
ature as a consequence of Kolmogorov “Refined Similarity” hypothesis.
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