EULERIAN AND LAGRANGIAN STATISTICS FROM HIGH RESOLUTION DNS

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EULERIAN AND LAGRANGIAN STATISTICS FROM HIGH
RESOLUTION DNS
LUCA BIFERALE Dept. of Physics, INFN and CNISM.
University of Tor Vergata, Rome. biferale_at_roma2.in
fn.it
ICTR Collaboration
Thanks to M. Cencini, A.S. Lanotte, F. Toschi,
J. Bec, R. Benzi, E. Bodenschatz, G. Boffetta, E.
Calzavarini, A. Celani, B. Devenish, R. Fisher,
T. Gotoh, L. Kadanoff, D. Lamb, S. Musacchio, N.
Ouellette, H. Xu.
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• CORRELATION BETWEEN LAGRANGIAN AND EULERIAN
  MEASUREMENTS.
• INTERMITTENCY OF VELOCITY INCREMENTS --STRUCTURE
  FUNCTIONS.
• HIGH RESOLUTION DNS AND EXPERIMENTAL DATA.
• INERTIAL RANGE AND VISCOUS RANGE.

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EULERIAN
LAGRANGIAN
LINK EULERIAN- LAGRANGIAN
K41 NOT ENOUGH !
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INTERMITTENCY
INTERMITTENCY
DNS Rel 600 R. Benzi, L.B. R. Fischer, D.
Lamb,L. Kadanoff, F. Toschi PRL 100, 234503 2008.
20483 16 Mega particles
3Gaussian
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DEF
MAGNIFYING GLASS
IN LOG-LOG ALL COWS ARE BLACK!
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EULERIAN STATISTICS LONGITUDINAL VS TRANSVERSE
DEF
DEF
LOCAL SLOPES LONGITUDINAL AND TRANSVERSE
DNS Rel 600 20483 R. Benzi, L.B. R. Fischer,
L. Kadanoff, F. Toschi PRL 100, 234503 2008.
good agreement with data from Gotoh (PoF 2002)
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INERTIAL RANGE LONGITUDINAL VS TRANSVERSE
LOCAL SLOPES LONGITUDINAL AND TRANSVERSE
DNS Rel 600 20483 R. Benzi, L.B. R. Fischer,
L. Kadanoff, F. Toschi PRL 100, 234503 2008.
good agreement with data from Gotoh (PoF 2002)
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1st MESSAGE LONGITUDINAL AND TRANSVERSE SCALE
DIFFERENTLY
P10
K4110/3
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EULERIAN USE TWO DIFFERENT MULTIFRACTAL D(H) TO
FIT SEPARATELY LONGITUDINAL AND TRANSVERSE
EULERIAN SCALING
Parisi Frisch (1983)
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going Lagrangian
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LINK EUL-LAG
SAME!!!!!
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K41
PRL 100, 254504 (2008), ICTR
WE LEARN ABOUT (i) INTERMITTENCY (ii)
UNIVERSALITY (iii) ANISOTROPY
WE LEARN ABOUT (i) INTERMITTENCY (ii)
UNIVERSALITY (iii) ANISOTROPY
see also L.B. E. Bodenschatz, M. Cencini, A.
Lanotte, N. Ouellette, F. Toschi and H. Xu, PoF
2008
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K41
PRL 100, 254504 (2008), ICTR
WE LEARN ABOUT (iv) MULTIFRACTALITY
WE LEARN ABOUT (i) INTERMITTENCY (ii)
UNIVERSALITY (iii) ANISOTROPY
LINK EUL-LAG
see also L.B. E. Bodenschatz, M. Cencini, A.
Lanotte, N. Ouellette, F. Toschi and H. Xu, PoF
2008
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K41
PRL 100, 254504 (2008), ICTR
WE LEARN ABOUT (v) ROLE OF VORTEX FILAMENTS
WE LEARN ABOUT (i) INTERMITTENCY (ii)
UNIVERSALITY (iii) ANISOTROPY
see also J. Bec, L.B. M. Cencini, A.S. Lanotte
and F. Toschi, PoF 2006
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LAGRANGIAN CHECK THE LINK EUL-LAG TO HIGHER
LAGRANGIAN STATISTICS.
INERTIAL RANGE .
p8
p10
DNS Rel 600 20483 16MParticles R. Benzi,
L.B. R. Fischer, L. Kadanoff, F. Toschi PRL
100, 234503 2008.
p6
p4
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LAGRANGIAN SCALING AS PREDICTED FROM THE
EULERIAN D(H)s
LINK EUL-LAG
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• take-home messages
• Eulerian homogeneous and isotropic statistics
  longitudinal and transverse scaling differ at
  high moments. Is this true also at higher
  Reynolds? (waiting from Kanedas data) Is this a
  problem for theory? (see also L.B. and I.
  Procaccia, Phys. Rep 2005)
• dimensional Eulerian-Lagrangian link, extended to
  Multifractal phenomenology, gives a prediction
  for Lagrangian statistics once given the Eulerian
  one (and --to some extent-- viceversa).
• Prediction is satisfactory, WITHIN ERROR BARS,
  up to p10, hints that at even higher orders
  things can change (wait and see).
• Universality of Lagrangian statistics good
  overlap between DNS and EXP, WITHIN ERROR BARS.

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Thanks to M. Cencini, A.S. Lanotte, F.
Toschi J. Bec, R. Benzi, E. Bodenschatz, G.
Boffetta, E. Calzavarini, A. Celani, B. Devenish,
R. Fisher, T. Gotoh, L. Kadanoff, D. Lamb, S.
Musacchio, N. Ouellette, H. Xu.
http//cfd.cineca.it
see Toschi Bodenschatz, ARFM 2009 for a review.