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

Structure functions and experimental evidence for intermittency
– Velocity difference across
separation r gives velocity
of ”r-eddies:”
Longitudinal velocity structure functions S ℓ
n (r) = W ℓ n r
Wr = v(r, t) − v(0, t) ,
– Longitudinal velocity:
W ℓ r = Wr · r
r
∝ r ζn.
In particular: S2(r) – Energy of r-eddies,
S3(r) = − 4
ε r (Kolmogorov-41) – Energy flux on scale r,
5
. S4(r) − 3 S 2 2 (r) – Deviation from the Gaussian statistics,
...
S2n(r)/S n 2 (r) – Statistics of very rare events
S ℓ
n (r) = Cn εr n/3 r ζn−n/3 , L − renormalization length .
L
3