Intermittency and Anomalous scaling in turbulence - Victor S. L'vov ...
Intermittency and Anomalous scaling in turbulence - Victor S. L'vov ...
Intermittency and Anomalous scaling in turbulence - Victor S. L'vov ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Kolmogorov-41 fixed po<strong>in</strong>t<br />
¯vn =<br />
1<br />
[2(a − c)] 1/3 λ n/3<br />
is unstable, giv<strong>in</strong>g<br />
a r<strong>and</strong>om evolution<br />
of the “shell velocities” ⇒<br />
ζ p<br />
<strong>Anomalous</strong> exponents <strong>in</strong><br />
2.5<br />
⇓ Sabra shell model ⇓<br />
2<br />
1.5<br />
1<br />
0.5<br />
0<br />
Shell model<br />
p/3<br />
0 1 2 3 4 5 6 7<br />
p<br />
|u 11 |/ <br />
8.0<br />
6.0<br />
4.0<br />
2.0<br />
0.0<br />
0.0e+00 2.0e+06 4.0e+06 6.0e+06 8.0e+06 1.0e+07<br />
timesteps<br />
<br />
<br />
Let S3(kn) ≡ Im un−1unun+1∗ . Exact:<br />
S3(kn) =<br />
1<br />
2kn(a − c)<br />
S2p(kn) ≡ <br />
|un| 2p<br />
<br />
− ɛ + δ( c<br />
a )n , ζ3 = 1 .<br />
∝ k −ζ2p<br />
n<br />
.<br />
8
Change language