Skip to main content
SpringerLink
Log in

Some Aspects of Lagrangian Dynamics of Turbulence

  • Chapter
  • First Online:
Mixing and Dispersion in Flows Dominated by Rotation and Buoyancy

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 580))

  • 767 Accesses

Abstract

This chapter is dedicated to fundamental properties of Lagrangian transport in turbulence, emphasizing the role of anisotropy and 2D turbulence which are relevant for geophysical considerations. The focus is on three main aspects of Lagrangian turbulence: (i) the role of small-scale anisotropy on the Lagrangian energy spectrum, (ii) the role of Lagrangian intermittency and (iii) the relative dispersion of tracer particles.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Notes

  1. 1.

    These relations together with Eq. (14) show that the ballistic approximation previously discussed holds as long as \(t'_k\ll \left| S_2(D_k)/S_{au}(D_k)\right| = S_2(D_k)/2\epsilon \), which according to relation (9) requires \(\alpha \ll 1\). This justifies the choice of the smallest relevant persistence parameter.

References

  • F. Anselmet, Y. Gagne, E.J. Hopfinger, R.A. Antonia, High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89 (1984)

    Article  Google Scholar 

  • A. Arneodo, C. Baudet, F. Belin, R. Benzi, B. Castaing, B. Chabaud, R. Chavarria, S. Ciliberto, R. Camussi, F. Chillà, B. Dubrulle, Y. Gagne, B. Hebral, J. Herweijer, M. Marchaud, J. Maurer, J.F. Muzy, A. Naert, A. Noullez, J. peinke, F. Roux, P. Tabeling, W. van de Water, H. Willaime, Structure functions in turbulence, in various flow configurations, at Reynolds numbers between 30 and 5000, using extended self-similarity. Europhys. Lett. 34(6), 411–416 (1996)

    Google Scholar 

  • G.K. Batchelor, The theory of axisymmetric turbulence. Proc. R. Soc. Lond. Series A Math. Phys. Sci. 186(1007), 480–502 (1946)

    Google Scholar 

  • G.K. Batchelor, The application of the similarity theory of turbulence to atmospheric diffusion. Quart. J. R. Meteorol. Soc. 76(328), 133–146 (1950)

    Article  Google Scholar 

  • J. Berg, B. Lüthi, J. Mann, S. Ott, Backwards and forwards relative dispersion in turbulent flow: an experimental investigation. Phys. Rev. E 74(1), 016304 (2006)

    Article  Google Scholar 

  • L. Biferale, I. Procaccia, Anisotropy in turbulent flows and in turbulent transport. Phys. Rep. 414(2–3), 43–164 (2005)

    Article  MathSciNet  Google Scholar 

  • R. Bitane, H. Homann, J. Bec, Time scales of turbulent relative dispersion. Phys. Rev. E 86(4), 045302 (2012)

    Article  Google Scholar 

  • G. Boffetta, I. Sokolov, Relative dispersion in fully developed turbulence: the Richardson’s law and intermittency corrections. Phys. Rev. Lett. 88(9), 094501 (2002)

    Article  Google Scholar 

  • G. Boffetta, I. Sokolov, Statistics of two-particle dispersion in two-dimensional turbulence. Phys. Fluids 14(9), 3224–3232 (2002)

    Article  MATH  Google Scholar 

  • G. Boffetta, R.E. Ecke, Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427–451 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  • M. Bourgoin, N.T. Ouellette, H. Xu, J. Berg, E. Bodenschatz, The role of pair dispersion in turbulent flow. Science 311(5762), 835–838 (2006)

    Article  Google Scholar 

  • M. Bourgoin, J.-F. Pinton, R. Volk, Lagrangian methods in experimental fluid mechanics. in Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations, ed. By T. von Larcher, P.D. Williams (Wiley, Inc., 2014), p. 360

    Google Scholar 

  • M. Bourgoin, H. Xu, Focus on dynamics of particles in turbulence. New J. Phys. 16(8), 085010 (2014)

    Article  Google Scholar 

  • M. Bourgoin, Turbulent pair dispersion as a ballistic cascade phenomenology. J. Fluid Mech. 772, 678–704 (2015)

    Article  Google Scholar 

  • A.D. Bragg, P.J. Ireland, L.R. Collins, Forward and backward in time dispersion of fluid and inertial particles in isotropic turbulence. Phys. Fluids 28(1), 013305 (2016)

    Article  Google Scholar 

  • S. Chandrasekhar, The theory of axisymmetric turbulence. Proc. R. Soc. Lond. Series A Math. Phys. Sci. 242(855), 557–577 (1950)

    MATH  MathSciNet  Google Scholar 

  • S.Y. Chen, B. Dhruva, S. Kurien, K.R. Sreenivasan, M.A. Taylor, Anomalous scaling of low-order structure functions of turbulent velocity. J. Fluid Mech. 533, 183–192 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • M. Chertkov, A. Pumir, B.I. Shraiman, Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11(8), 2394–2410 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • P.A. Davidson, B.R. Pearson, Identifying turbulent energy distributions in real, rather than Fourier, space. Phys. Rev. Lett. 95(21), 214501 (2005)

    Article  Google Scholar 

  • T. Faber, J.C. Vassilicos, Turbulent pair separation due to multiscale stagnation point structure and its time asymmetry in two-dimensional turbulence. Phys. Fluids 21(1), 015106 (2009)

    Article  MATH  Google Scholar 

  • G. Falkovich, K. Gawedski, M. Vergassola, Particles and fields in fluid turbulence. Rev. Mod. Phys. 73(4), 913–975 (2001)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • S. Garg, Z. Warhaft, On the small scale structure of simple shear flows. Phys. Fluids 10(3), 662–673 (1998)

    Article  Google Scholar 

  • S.R. Hanna, Lagrangian and Eulerian time-scale relations in the daytime boundary-layer. J. Appl. Meteorol. 20(3), 242–249 (1981)

    Article  Google Scholar 

  • R.J. Hill, Opportunities for use of exact statistical equations. J. Turbul. 7, 43 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • J. Hinze, Turbulence (McGraw-Hill, 1959)

    Google Scholar 

  • J. Jucha, H. Xu, A. Pumir, E. Bodenschatz, Time-reversal-symmetry breaking in turbulence. Phys. Rev. Lett. 113(5), 054501 (2014)

    Article  Google Scholar 

  • M.C. Jullien, J. Paret, P. Tabeling, Richardson pair dispersion in two-dimensional turbulence. Phys. Rev. Lett. 82(14), 2872–2875 (1999)

    Article  Google Scholar 

  • A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305 (1941)

    MathSciNet  Google Scholar 

  • A.N. Kolmogorov, Refining the notions of the local structure of turbulence in an incompressible viscous fluid at high Reynolds numbers, in Mécanique de la Turbulence (CNRS, Paris, 1962), pp. 447–458

    Google Scholar 

  • R.C. Lien, E.A. D’Asaro, G.T. Dairiki, Lagrangian frequency spectra of vertical velocity and vorticity in high-Reynolds-number oceanic turbulence. J. Fluid Mech. 362, 177–198 (1998)

    Article  MATH  Google Scholar 

  • R.C. Lien, E.A. D’Asaro, The Kolmogorov constant for the Lagrangian velocity spectrum and structure function. Phys. Fluids 14(12), 4456–4459 (2002)

    Article  MATH  Google Scholar 

  • E. Lindborg, Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech. 388, 259–288 (1999)

    Article  MATH  Google Scholar 

  • J. Mann, S. Ott, J.S. Andersen, Experimental study of relative, turbulent diffusion. Technical Report Riso-R-1036 (EN), Risoe National Laboratory, Roskilde, Denmark, 1999

    Google Scholar 

  • N. Mordant, P. Metz, O. Michel, J.-F. Pinton, Measurements of Lagrangian velocity in fully developed turbulence. Phys. Rev. Lett. 87(21), 214501 (2001)

    Article  Google Scholar 

  • A.M. Obukhov, On the distribution of energy in the spectrum of a turbulent flow. Izv. Akad. Nauk SSSR 5, 453–466 (1941)

    Google Scholar 

  • A.M. Obukhov, Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 77–81 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  • S. Ott, J. Mann, An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207–223 (2000)

    Article  MATH  Google Scholar 

  • N.T. Ouellette, H. Xu, M. Bourgoin, E. Bodenschatz, Small-scale anisotropy in Lagrangian turbulence. New J. Phys. 8(6), 102 (2006)

    Article  Google Scholar 

  • M. Ould-Rouiss, The axisymmetric equivalent of Kolmogorov’s equation. Eur. Phys. J. B 23(1), 107–120 (2001)

    Article  Google Scholar 

  • G. Parisi, U. Frisch, A multifractal model of intermittency, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, ed. By M. Ghil, R. Benzi, G. Parisi (Amsterdam, Eds. North Holland, 1985), pp. 84–87

    Google Scholar 

  • A. Pumir, B.I. Shraiman, Persistent small scale anisotropy in homogeneous shear flows. Phys. Rev. Lett. 75(17), 3114–3117 (1995)

    Article  Google Scholar 

  • L.F. Richardson, Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. Lond. Series A 110(756), 709–737 (1926)

    Article  Google Scholar 

  • H.C. Rodean, The universal constant for the Lagrangian structure-function. Phys. Fluids A 3(6), 1479–1480 (1991)

    Article  Google Scholar 

  • J.P.L.C. Salazar, L.R. Collins, Two-particle dispersion in isotropic turbulent flow. Annu. Rev. Fluid Mech. 41, 405–432 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  • B.L. Sawford, Reynolds number effects in Lagrangian stochastic models for turbulent dispersion. Phys. Fluids A 3(6), 1577–1586 (1991)

    Article  Google Scholar 

  • B. Sawford, Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289–317 (2001)

    Article  MATH  Google Scholar 

  • B.L. Sawford, P.K. Yeung, M.S. Borgas, Comparison of backwards and forwards relative dispersion in turbulence. Phys. Fluids 17(9), 095109 (2005)

    Article  MATH  Google Scholar 

  • K.R. Sreenivasan, On the universality of the Kolmogorov constant. Phys. Fluids 7(3), 2778–2784 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  • G.I. Taylor, Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212 (1922)

    Article  MATH  MathSciNet  Google Scholar 

  • H. Tennekes, Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67(3), 561–567 (1975)

    Article  MATH  Google Scholar 

  • K.A. Weinman, A.Y. Klimenko, Estimation of the Kolmogorov constant \(C_0\) by direct numerical simulation of a continuous scalar. Phys. Fluids 12(12), 3205–3220 (2000)

    Article  MATH  Google Scholar 

  • H. Xu, M. Bourgoin, N.T. Ouellette, E. Bodenschatz, High order Lagrangian velocity statistics in turbulence. Phys. Rev. Lett. 96(2), 024503 (2006)

    Article  Google Scholar 

  • P.K. Yeung, Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech. 34, 115–142 (2002)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Lyon, ENS Lyon, Université Claude Bernard – Lyon 1, CNRS, Laboratoire de Physique, 69342, Lyon, France

    Mickaël Bourgoin

Authors
  1. Mickaël Bourgoin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mickaël Bourgoin .

Editor information

Editors and Affiliations

  1. Department of Applied Physics, University of Technology Eindhoven Department of Applied Physics, Eindhoven, The Netherlands

    Herman J.H. Clercx

  2. University of Technology Eindhoven , Eindhoven, Noord-Brabant, The Netherlands

    GertJan F. Van Heijst

Rights and permissions

Reprints and permissions

Copyright information

© 2018 CISM International Centre for Mechanical Sciences

About this chapter

Cite this chapter

Bourgoin, M. (2018). Some Aspects of Lagrangian Dynamics of Turbulence. In: Clercx, H., Van Heijst, G. (eds) Mixing and Dispersion in Flows Dominated by Rotation and Buoyancy. CISM International Centre for Mechanical Sciences, vol 580. Springer, Cham. https://doi.org/10.1007/978-3-319-66887-1_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66887-1_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66886-4

  • Online ISBN: 978-3-319-66887-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation