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@roma2.infn.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.

CORRELATION BETWEEN LAGRANGIAN AND EULERIAN MEASUREMENTS. INTERMITTENCY OF VELOCITY INCREMENTS --STRUCTURE FUNCTIONS. HIGH RESOLUTION DNS AND EXPERIMENTAL DATA. INERTIAL RANGE AND VISCOUS RANGE.

LINK EULERIAN- LAGRANGIAN K41 NOT ENOUGH !

INTERMITTENCY INTERMITTENCY 2048^3 16 Mega particles 3==Gaussian [ DNS Rel = 600; R. Benzi, L.B. R. Fischer, D. Lamb,L. Kadanoff, F. Toschi] PRL 100, 234503 2008. 2048^3 16 Mega particles 3==Gaussian

IN LOG-LOG ALL COWS ARE BLACK! DEF MAGNIFYING GLASS IN LOG-LOG ALL COWS ARE BLACK!

EULERIAN STATISTICS: LONGITUDINAL VS TRANSVERSE DEF DEF LOCAL SLOPES: LONGITUDINAL AND TRANSVERSE: [ DNS Rel = 600 2048^3 R. Benzi, L.B. R. Fischer, L. Kadanoff, F. Toschi] PRL 100, 234503 2008. good agreement with data from Gotoh (PoF 2002)

INERTIAL RANGE : LONGITUDINAL VS TRANSVERSE LOCAL SLOPES: LONGITUDINAL AND TRANSVERSE: [ DNS Rel = 600 2048^3 R. Benzi, L.B. R. Fischer, L. Kadanoff, F. Toschi] PRL 100, 234503 2008. good agreement with data from Gotoh (PoF 2002)

1st MESSAGE: LONGITUDINAL AND TRANSVERSE SCALE DIFFERENTLY P=10 K41=10/3

EULERIAN USE TWO DIFFERENT MULTIFRACTAL D(H) TO FIT SEPARATELY LONGITUDINAL AND TRANSVERSE EULERIAN SCALING Parisi & Frisch (1983)

going Lagrangian

LINK EUL-LAG SAME!!!!!

(i) INTERMITTENCY; (ii) UNIVERSALITY; (iii) ANISOTROPY WE LEARN ABOUT: 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

(i) INTERMITTENCY; (ii) UNIVERSALITY; (iii) ANISOTROPY 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

(v) ROLE OF VORTEX FILAMENTS WE LEARN ABOUT: 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

CHECK THE LINK EUL-LAG TO HIGHER LAGRANGIAN STATISTICS. INERTIAL RANGE: . p=8 p=10 [ DNS Rel = 600 2048^3; 16MParticles; R. Benzi, L.B. R. Fischer, L. Kadanoff, F. Toschi] PRL 100, 234503 2008. p=6 p=4

LAGRANGIAN SCALING AS PREDICTED FROM THE EULERIAN D(H)’s LINK EUL-LAG

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 Kaneda’s 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 p=10, 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.

http://cfd.cineca.it 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.