multifractal acceleration statistics in turbulence benjamin devenish met office, university of rome...
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![Page 1: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/1.jpg)
Multifractal acceleration statistics in turbulence
Benjamin Devenish
Met Office, University of Rome
L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F. Toschi
![Page 2: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/2.jpg)
Intermittency
K41
• Kolmogorov (1941)• Landau’s objection
- fluctuating energy dissipation
• Kolmogorov’s refined hypothesis (1962)
• Random beta model• Multifractal model
Eulerian velocity structure function
![Page 3: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/3.jpg)
Multifractal formalism (1)
Frisch (1995)
![Page 4: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/4.jpg)
Multifractal formalism (2)
• Eulerian reference frame
• Lagrangian reference frame
- time scale of eddy of scale r
- velocity difference at scale r
vur
Fractal dimension
Superposition of contributions from eddies of all sizes
Contributions from eddies smaller than scale r are uncorrelated
Fluctuatingur r /
h
r L
ruu
00 0Lr )(hD
),( maxmin hhhUniversal
![Page 5: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/5.jpg)
Acceleration in multifractal framework
• Acceleration
• Fluctuating Kolmogorov scale
![Page 6: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/6.jpg)
Acceleration pdf (1)
• Pdf of acceleration
• Probabililty of observing h in
• Pdf of large scale velocity 0v
0000 )()|(),|( dhdvvvhvha PPP
![Page 7: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/7.jpg)
Acceleration pdf (2)
• Multifractal
• K41 (h=1/3, D(h) = 3)
dhRaRaaP hzhhyhDh
)(3/)1(2)(3/))(5( ~2
1exp~)~(
Ra 2aaa /~ 14.1
No additional free parameters D(h) derived from She-Leveque model
![Page 8: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/8.jpg)
Direct numerical simulation
• Homogeneous isotropic turbulence• cubic lattice• Taylor-scale Reynolds number • Two million Lagrangian particles• Sampling rate 07.0
31024
280R
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Acceleration pdf (3)
K41prediction
Multifractal prediction
![Page 10: Multifractal acceleration statistics in turbulence Benjamin Devenish Met Office, University of Rome L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F](https://reader033.vdocuments.net/reader033/viewer/2022051516/56649d6a5503460f94a4827d/html5/thumbnails/10.jpg)
Conditional acceleration variance
Acceleration variance conditional on velocity
Lagrangian stochastic models
57.400
2 | vva 1
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Conditional acceleration variance
Multifractal prediction
B.L. Sawford et al., Phys. Fluids 15, 3478 (2003).
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Lagrangian structure functions
)( p
L
L
T
Multifractal prediction for the Lagrangian structure functions
whereSame D(h) as in Eulerian model
LT
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Lagrangian structure functions
P=8
P=6
P=4
Plotted using Extended Self Similarity
Bottleneck at
2.72
2.16
1.71
Multifractal Lagrangianexponents
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Conclusions
• Acceleration exhibits fluctuations up to • Multifractal formalism captures this behaviour
with no additional free parameters• Conditional acceleration variance• Velocity structure functions only for • Read more in Physical Review Letters vol. 93,
no.6 p.064502-1
a80
10t
57.400
2 | vva