Date post: | 21-Dec-2015 |
Category: |
Documents |
View: | 218 times |
Download: | 1 times |
Multifractal acceleration statistics in turbulence
Benjamin Devenish
Met Office, University of Rome
L. Biferale, G. Boffetta, A. Celani, A.Lanotte, F. Toschi
Intermittency
K41
• Kolmogorov (1941)• Landau’s objection
- fluctuating energy dissipation
• Kolmogorov’s refined hypothesis (1962)
• Random beta model• Multifractal model
Eulerian velocity structure function
Multifractal formalism (1)
Frisch (1995)
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
Acceleration in multifractal framework
• Acceleration
• Fluctuating Kolmogorov scale
Acceleration pdf (1)
• Pdf of acceleration
• Probabililty of observing h in
• Pdf of large scale velocity 0v
0000 )()|(),|( dhdvvvhvha PPP
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
Direct numerical simulation
• Homogeneous isotropic turbulence• cubic lattice• Taylor-scale Reynolds number • Two million Lagrangian particles• Sampling rate 07.0
31024
280R
Acceleration pdf (3)
K41prediction
Multifractal prediction
Conditional acceleration variance
Acceleration variance conditional on velocity
Lagrangian stochastic models
57.400
2 | vva 1
Conditional acceleration variance
Multifractal prediction
B.L. Sawford et al., Phys. Fluids 15, 3478 (2003).
Lagrangian structure functions
)( p
L
L
T
Multifractal prediction for the Lagrangian structure functions
whereSame D(h) as in Eulerian model
LT
Lagrangian structure functions
P=8
P=6
P=4
Plotted using Extended Self Similarity
Bottleneck at
2.72
2.16
1.71
Multifractal Lagrangianexponents
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