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Acceleration of Lagrangian particles in shell models of turbulence

Lorenzo Piro1,*, Massimo Cencini2,3, and Roberto Benzi4,1

  • *Contact author: lorenzo.piro@roma2.infn.it
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Phys. Rev. Fluids 10, L092601 – Published 10 September, 2025

DOI: https://doi.org/10.1103/lltk-vsrb

Abstract

Lagrangian acceleration has been investigated both experimentally and numerically in the past, and it has been shown to exhibit extreme fluctuations, which have been rationalized as events in which tracer particles get trapped into vortical structures such as vortex tubes or filaments. Here, we consider the statistics of acceleration within the multifractal framework, as in Biferale et al., Phys. Rev. Lett. 93, 064502 (2004), and investigate the statistics of Lagrangian acceleration using shell models of turbulence, as in Boffetta et al., Phys. Rev. E 66, 066307 (2002), that—by construction—do not contain vortical structures. Our analysis reveals that, despite not accounting for specific coherent vortex structures, the multifractal model accurately captures the extreme intermittent fluctuations observed in the acceleration, with predictions that remain robust across a wide range of Reynolds numbers.

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References (37)

  1. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk. SSSR 30, 299 (1941).
  2. U. Frisch, Turbulence: The legacy of AN Kolmogorov (Cambridge University Press, Cambridge, 1995).
  3. 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. Marchand, J. Maurer, J. F. Muzy, A. Naert, A. Noullez, J. Peinke et al., Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity, Europhys. Lett. 34, 411 (1996).
  4. F. Anselmet, R. Antonia, and L. Danaila, Turbulent flows and intermittency in laboratory experiments, Planet. Space Sci. 49, 1177 (2001).
  5. R. H. Kraichnan, Small-scale structure of a scalar field convected by turbulence, Phys. Fluids 11, 945 (1968).
  6. K. Gawędzki and A. Kupiainen, Anomalous scaling of the passive scalar, Phys. Rev. Lett. 75, 3834 (1995).
  7. M. Chertkov and G. Falkovich, Anomalous scaling exponents of a white-advected passive scalar, Phys. Rev. Lett. 76, 2706 (1996).
  8. B. I. Shraiman and E. D. Siggia, Symmetry and scaling of turbulent mixing, Phys. Rev. Lett. 77, 2463 (1996).
  9. U. Frisch, A. Mazzino, A. Noullez, and M. Vergassola, Lagrangian method for multiple correlations in passive scalar advection, Phys. Fluids 11, 2178 (1999).
  10. B. I. Shraiman and E. D. Siggia, Scalar turbulence, Nature (London) 405, 639 (2000).
  11. G. Falkovich, K. Gawedzki, and M. Vergassola, Particles and fields in fluid turbulence, Rev. Mod. Phys. 73, 913 (2001).
  12. G. Parisi and U. Frisch, On the singularity structure of fully developed turbulence, in Turbulence and Predictability of Geophysical Fluid Dynamics, edited by M. Ghil, G. Parisi, and R. Benzi (North-Holland, Amsterdam, 1985), p. 84.
  13. N. Mordant, P. Metz, O. Michel, and J.-F. Pinton, Measurement of Lagrangian velocity in fully developed turbulence, Phys. Rev. Lett. 87, 214501 (2001).
  14. G. Boffetta, F. De Lillo, and S. Musacchio, Lagrangian statistics and temporal intermittency in a shell model of turbulence, Phys. Rev. E 66, 066307 (2002).
  15. A. Arnéodo et al., Universal intermittent properties of particle trajectories in highly turbulent flows, Phys. Rev. Lett. 100, 254504 (2008).
  16. A. La Porta, G. A. Voth, A. M. Crawford, J. Alexander, and E. Bodenschatz, Fluid particle accelerations in fully developed turbulence, Nature (London) 409, 1017 (2001).
  17. N. Mordant, A. M. Crawford, and E. Bodenschatz, Three-dimensional structure of the Lagrangian acceleration in turbulent flows, Phys. Rev. Lett. 93, 214501 (2004).
  18. L. Biferale, G. Boffetta, A. Celani, B. J. Devenish, A. S. Lanotte, and F. Toschi, Multifractal statistics of Lagrangian velocity and acceleration in turbulence, Phys. Rev. Lett. 93, 064502 (2004).
  19. D. Buaria and K. R. Sreenivasan, Scaling of acceleration statistics in high Reynolds number turbulence, Phys. Rev. Lett. 128, 234502 (2022).
  20. L. Biferale, G. Boffetta, A. Celani, A. Lanotte, and F. Toschi, Particle trapping in three-dimensional fully developed turbulence, Phys. Fluids 17, 021701 (2005).
  21. U. Frisch and M. Vergassola, A prediction of the multifractal model: The intermediate dissipation range, Europhys. Lett. 14, 439 (1991).
  22. L. Biferale, M. Cencini, D. Vergni, and A. Vulpiani, Exit time of turbulent signals: A way to detect the intermediate dissipative range, Phys. Rev. E 60, R6295 (1999).
  23. G. Boffetta, A. Mazzino, and A. Vulpiani, Twenty-five years of multifractals in fully developed turbulence: A tribute to giovanni paladin, J. Phys. A 41, 363001 (2008).
  24. L. Biferale, Shell models of energy cascade in turbulence, Annu. Rev. Fluid Mech. 35, 441 (2003).
  25. T. Bohr, M. H. Jensen, G. Paladin, and A. Vulpiani, Dynamical Systems Approach to Turbulence (Cambridge University Press, 2005).
  26. V. S. L'vov, E. Podivilov, A. Pomyalov, I. Procaccia, and D. Vandembroucq, Improved shell model of turbulence, Phys. Rev. E 58, 1811 (1998).
  27. R. Benzi and F. Toschi, Lectures on turbulence, Phys. Rep. 1021, 1 (2023).
  28. Z.-S. She and E. Leveque, Universal scaling laws in fully developed turbulence, Phys. Rev. Lett. 72, 336 (1994).
  29. M. De Pietro, L. Biferale, G. Boffetta, and M. Cencini, Time irreversibility in reversible shell models of turbulence, Eur. Phys. J. E 41, 48 (2018).
  30. L. Biferale, E. Bodenschatz, M. Cencini, A. S. Lanotte, N. T. Ouellette, F. Toschi, and H. Xu, Lagrangian structure functions in turbulence: A quantitative comparison between experiment and direct numerical simulation, Phys. Fluids 20, 065103 (2008).
  31. R. Benzi, L. Biferale, R. Fisher, D. Lamb, and F. Toschi, Inertial range Eulerian and Lagrangian statistics from numerical simulations of isotropic turbulence, J. Fluid Mech. 653, 221 (2010).
  32. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, Extended self-similarity in turbulent flows, Phys. Rev. E 48, R29 (1993).
  33. J. Bec, L. Biferale, M. Cencini, A. S. Lanotte, and F. Toschi, Effects of vortex filaments on the velocity of tracers and heavy particles in turbulence, Phys. Fluids 18, 081702 (2006).
  34. L. Chevillard, S. G. Roux, E. Lévêque, N. Mordant, J.-F. Pinton, and A. Arnéodo, Lagrangian velocity statistics in turbulent flows: Effects of dissipation, Phys. Rev. Lett. 91, 214502 (2003).
  35. A. Corbetta, V. Menkovski, R. Benzi, and F. Toschi, Deep learning velocity signals allow quantifying turbulence intensity, Sci. Adv. 7, eaba7281 (2021).
  36. T. Dombre and J.-L. Gilson, Intermittency, chaos and singular fluctuations in the mixed Obukhov-Novikov shell model of turbulence, Physica D 111, 265 (1998).
  37. A. A. Mailybaev, Blowup as a driving mechanism of turbulence in shell models, Phys. Rev. E 87, 053011 (2013).

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Phys. Rev. Fluids 10, L092601– Published 10 September, 2025
  • Received 11 June 2025
  • Accepted 11 August 2025
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