Skip to main content
SpringerLink
Log in

Large Deviations in Turbulence

  • Chapter
  • First Online:
Book cover Large Deviations in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 885))

Abstract

We give a survey of the use of the multifractal method, as a manifestation of the large deviation theory, to study the scaling behavior in fully developed turbulence. Particular emphasis is reserved to the phenomenon of intermittency, i.e., the most relevant manifestation of the break-down of mean field arguments in turbulence. To explain intermittency, the statistical role of fluctuations are explicitly accounted for by means of the multifractal formalism. Its application to the statistics of velocity gradients and acceleration will be discussed. A remark related to the use of large deviation theory in multifractal formalism will be emphasized. Also, the presentation of the famous Refined Similarity Hypothesis due to Kolmogorov and Obukhov in 1962 to account for the statistical role of fluctuations will be reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. G. Parisi, U. Frisch, in Turbulence and Predictability of Geophysical Fluid Dynamics, ed. by M. Ghil, R. Benzi, G. Parisi (Amsterdam, North-Holland, 1985), p. 84

    Google Scholar 

  2. R. Benzi, G. Paladin, G. Parisi, A. Vulpiani, J. Phys. A Math. Gen. 17, 3521 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  3. U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  4. D. Harte, Multifractals: Theory and Applications (CRC, New York, 2001)

    Book  Google Scholar 

  5. A.N. Kolmogorov, J. Fluid Mech. 13, 82 (1962)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. E.A. Novikov, R.W. Stewart, Izv. Akad. Nauk SSSR Geofiz. 3, 408 (1964)

    Google Scholar 

  7. B.B. Mandelbrot, J. Fluid Mech. 62, 331 (1974)

    Article  ADS  MATH  Google Scholar 

  8. P.K. Kundu, I.M. Cohen, D.R. Dowling, Fluid Mechanics (Academic, Waltham, 2012)

    Google Scholar 

  9. O.A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow (Gordon and Breach, New York, 1969)

    MATH  Google Scholar 

  10. J. Bricmont, A. Kupiainen, R. Lefevere, Commun. Math. Phys. 230, 87 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. M. Hairer, J.C. Mattingly, Ann. Math. 164, 993 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. T. Bohr, M.H. Jensen, G. Paladin, A. Vulpiani, Dynamical Systems Approach to Turbulence (Cambridge University Press, Cambridge, 1998)

    Book  MATH  Google Scholar 

  13. A.N. Kolmogorov, Dokl. Akad. Nauk. SSSR, 30, 299 (1941); reprinted in A.N. Kolmogorov, Proc. R. Soc. Lond. A 434 9 (1991)

    Google Scholar 

  14. A. Monin, A. Yaglom, Statistical Fluid Dynamics (MIT, Cambridge, 1975)

    Google Scholar 

  15. L.F. Richardson, Weather Prediction by Numerical Processes (Cambridge University Press, Cambridge, 1922)

    Google Scholar 

  16. G.I. Taylor, Proc. R. Soc. Lond. A 151, 421 (1935)

    Article  ADS  MATH  Google Scholar 

  17. F. Anselmet, Y. Gagne, E.J. Hopfinger, R.A. Antonia, J. Fluid Mech. 140, 63 (1984)

    Article  ADS  Google Scholar 

  18. G. Paladin, A. Vulpiani, Phys. Rep. 156, 147 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  19. G. Boffetta, A. Mazzino, A. Vulpiani, J. Phys. A Math. Theor. 41, 363001 (2008)

    Article  MathSciNet  Google Scholar 

  20. U. Frisch, M.M. Afonso, A. Mazzino, V. Yakhot, J. Fluid Mech. 542, 97 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  21. C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (Springer, New York, 1999)

    Book  MATH  Google Scholar 

  22. C. Meneveau, K.R. Sreenivasan, Phys. Lett. A 137, 103 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  23. W. van de Water, P. Schram, Phys. Rev. A 37, 3118 (1988)

    Article  ADS  Google Scholar 

  24. U. Frisch, M. Vergassola, Europhys. Lett. 14, 439 (1991)

    Article  ADS  Google Scholar 

  25. U. Frisch, Z.S. She, Fluid Dyn. Res. 8, 139 (1991)

    Article  ADS  Google Scholar 

  26. B. Castaing, Y. Gagne, E.J. Hopfinger, Physica D 46, 177 (1990)

    Article  ADS  MATH  Google Scholar 

  27. A. Vincent, M. Meneguzzi, J. Fluid Mech. 225, 1 (1991)

    Article  ADS  MATH  Google Scholar 

  28. A. La Porta, G.A. Voth, A.M. Crawford, J. Alexander, E. Bodenschatz, Nature 409, 1017 (2001)

    Article  ADS  Google Scholar 

  29. L. Biferale, G. Boffetta, A. Celani, B.J. Devenish, A. Lanotte, F. Toschi, Phys. Rev. Lett. 93, 064502 (2004)

    Article  ADS  Google Scholar 

  30. Z.S. She, E. Lévêque, Phys. Rev. Lett. 72, 336 (1994)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica and INFN, University of Torino, via P. Giuria 1, Torino, I-10125, Italy

    Guido Boffetta

  2. INFN and CINFAI Consortium, DICCA – University of Genova, Via Montallegro 1, Genova, I-16146, Italy

    Andrea Mazzino

Authors
  1. Guido Boffetta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Mazzino
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guido Boffetta .

Editor information

Editors and Affiliations

  1. Dipartimento di Fisica, Università di Roma Sapienza, Roma, Italy

    Angelo Vulpiani

  2. Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, Roma, Italy

    Fabio Cecconi

  3. Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, Roma, Italy

    Massimo Cencini

  4. Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, Roma, Italy

    Andrea Puglisi

  5. Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Roma, Italy

    Davide Vergni

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Boffetta, G., Mazzino, A. (2014). Large Deviations in Turbulence. In: Vulpiani, A., Cecconi, F., Cencini, M., Puglisi, A., Vergni, D. (eds) Large Deviations in Physics. Lecture Notes in Physics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54251-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54251-0_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54250-3

  • Online ISBN: 978-3-642-54251-0

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation