Skip to main content
SpringerLink
Log in

Random Shear Flows and Correlations

  • Chapter
  • First Online:
Chaotic Flows

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 10))

  • 1025 Accesses

Abstract

Lagrangian velocity correlations are certain quantities in turbulent diffusion because of Taylor’s relation, which expresses the mean square displacements of fluid particles as a double integral over time of two-time Lagrangian velocity correlations. Taylor’s relation also has important physical consequences for anomalous transport. Indeed, long-range correlations are responsible for anomalous transport.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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. D. Ben-Avraham, S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, 1996)

    Google Scholar 

  2. A. Dreizin Yu, A.M. Dykhne, Sov. Phys. J. Exp. Theor. Phys. 36, 127 (1973)

    ADS  Google Scholar 

  3. O.G. Bakunin, Chaos Solitons & Fractals 23, 1703 (2005)

    ADS  MATH  Google Scholar 

  4. P. Resibois, M. Leener, De Classical Kinetic Theory (Wiley, New York, 1977)

    Google Scholar 

  5. B. Berne, J. Chem. Phys. 56, 2164 (1972)

    Article  ADS  Google Scholar 

  6. G. Matheron, G. De Marsily, Water Resour. Res. 16, 901 (1980)

    Article  ADS  Google Scholar 

  7. I.D. Howells, J. Fluid Mech. 9, 104 (1960)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. M. Avellaneda, A. Majda, J. Phys. Fluids 4, 41 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. O.G. Bakunin, T. Schep, J. Phys. Lett. A 322, 105 (2004)

    Article  ADS  MATH  Google Scholar 

  10. S. Redner, Physica D 38, 287 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  11. J.-P. Bouchaud, A. Georges, Phys. Rev. Let. 64, 2503 (1990)

    Article  ADS  Google Scholar 

  12. D.L. Koch, J.F. Brady, Phys. Fluids A 1, 47 (1990)

    Article  ADS  Google Scholar 

  13. A.J. Majda, A.L. Bertozzi, Vorticity and Incompressible Flow (Cambridge University Press, Cambridge, 2002)

    MATH  Google Scholar 

  14. E. Ben-Naim, S. Redner, Phys. Rev. A 45, 7207 (1992)

    Article  ADS  Google Scholar 

  15. M.E. Fisher, J. Chem. Phys. 44, 616 (1966)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Plasma Physics Department, “Kurchatov Institute”, Kurchatova Square 1, 123182, Moscow, Russia

    Oleg G. Bakunin

Authors
  1. Oleg G. Bakunin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oleg G. Bakunin .

Further Reading

Further Reading

1.1 Random Shear Flows and Transport

  • G.P. Bouchaud, A. Georges, Phys. Rep. 195, 132–292 (1990)

  • J. Cardy et al., Non-Equilibrium Mechanics and Turbulence (Cambridge University Press, Cambridge, 2008)

  • P. Castiglione et al., Chaos and Coarse Graining in Statistical Mechanics (Cambridge University Press, Cambridge, 2008)

  • W.C. Conner, J. Fraisserd, Fluid Transport in Nanoporous Materials (Springer, Berlin, 2006)

  • A. Crisanti, M. Falcioni, A. Vulpiani, Rivista Del Nuovo Cimento 14, 1–80 (1991)

  • J.W. Haus, K.W. Kehr, Phys. Rep. 150, 263 (1987)

  • M.B. Isichenko, Rev. Mod. Phys. 64, 961 (1992)

  • R. Klages, G. Radons, I. Sokolov (eds.), Anomalous Transport, Foundations and Applications (Wiley, New York, 2008)

  • A. Majda, P. Kramer, Phys. Rep. 314, 237–574 (1999)

  • R.M. Mazo, Brownian Motion, Fluctuations, Dynamics and Applications (Clarendon Press, Oxford, 2002)

  • A. Scott, Nonlinear Science (Oxford University Press, Oxford, 2003)

  • D. Sornette, Critical Phenomena in Natural Sciences (Springer, Berlin, 2006)

  • G.H. Weiss, Aspects and Applications of the Random Walk (Elsevier, Amsterdam, 1994)

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bakunin, O.G. (2011). Random Shear Flows and Correlations. In: Chaotic Flows. Springer Series in Synergetics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20350-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20350-3_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20349-7

  • Online ISBN: 978-3-642-20350-3

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

Publish with us

Policies and ethics

Search

Navigation