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Relative Dispersion in Direct Cascades of Generalized Two-Dimensional Turbulence

  • Alexis Foussard
  • Stefano BertiEmail author
  • Xavier Perrot
  • Guillaume Lapeyre
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 26)

Abstract

The statistical features of turbulent flows depend on the locality properties of energy transfers among scales. The latter, in turn, may have consequences for the relative dispersion of passive particles. We consider a class of two-dimensional flows of geophysical interest, namely \(\alpha \)-turbulence models, possessing different locality properties. We numerically study relative dispersion in such flows using both fixed-time and fixed-scale indicators. The results are compared with predictions based on phenomenological arguments to explore the relation between the locality of the turbulent cascade and that of relative dispersion. We find that dispersion behaviors agree with expectations from local theories, for small enough values of the parameter \(\alpha \) (dynamics close to surface quasi geostrophy) and for sufficiently small initial pair separations. Non-local dispersion is instead observed for the largest \(\alpha \) considered (quasi-geostrophic model).

Notes

Acknowledgements

This work was supported by TOSCA/CNES as a contribution to the SWOT project. Figures are adapted from [20] (reproduced with permission).

References

  1. 1.
    Kraichnan, R.H.: Phys. Fluids 10, 1417 (1967)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Boffetta, G., Ecke, R.E.: Annu. Rev. Fluid Mech. 44, 427 (2012)CrossRefGoogle Scholar
  3. 3.
    Morel, P., Larcheveque, M.: J. Atmos. Sci. 31, 2189 (1974)CrossRefGoogle Scholar
  4. 4.
    Bennett, A.F.: J. Atmos. Sci. 41, 1881 (1984)CrossRefGoogle Scholar
  5. 5.
    LaCasce, J.H.: Prog. Oceanogr. 77, 1 (2008)CrossRefGoogle Scholar
  6. 6.
    Berti, S., dos Santos, F., Lacorata, G., Vulpiani, A.: J. Phys. Oceanogr. 41, 1659 (2011)CrossRefGoogle Scholar
  7. 7.
    Er-El, J., Peskin, R.L.: J. Atmos. Sci. 38, 2264 (1981)CrossRefGoogle Scholar
  8. 8.
    Lacorata, G., Aurell, E., Legras, B., Vulpiani, A.: J. Atmos. Sci. 61, 2936 (2004)CrossRefGoogle Scholar
  9. 9.
    Jullien, M.-C.: Phys. Fluids 15, 2228 (2003)CrossRefGoogle Scholar
  10. 10.
    Rivera, M.K., Ecke, R.E.: Phys. Rev. Lett. 95, 194503 (2005)CrossRefGoogle Scholar
  11. 11.
    Babiano, A., Basdevant, C., Le Roy, P., Sadourny, R.: J. Fluid Mech. 214, 535 (1990)CrossRefGoogle Scholar
  12. 12.
    Boffetta, G., Sokolov, I.: Phys. Fluids 14, 3224 (2002)CrossRefGoogle Scholar
  13. 13.
    Nicolleau, F., Yu, G.: Phys. Fluids 16, 2309 (2004)CrossRefGoogle Scholar
  14. 14.
    Pierrehumbert, R.T., Held, I.M., Swanson, K.L.: Chaos. Solitons and Fractals 4, 1111 (1994)CrossRefGoogle Scholar
  15. 15.
    Lapeyre, G.: Fluids 2, 7 (2017)CrossRefGoogle Scholar
  16. 16.
    Klein, P., Lapeyre, G., Roullet, G., Le Gentil, S., Sasaki, H.: Geophys. Astrophys. Fluid Dyn. 105, 421 (2011)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Salazar, J.P.L.C., Collins, L.R.: Annu. Rev. Fluid Mech. 41, 405 (2009)CrossRefGoogle Scholar
  18. 18.
    Batchelor, G.K., Meteorol, Q.J.R.: Soc. 551, 133 (1950)Google Scholar
  19. 19.
    Bourgoin, M., Ouellette, N.T., Xu, H., Berg, J., Bodenschatz, E.: Science 311, 835 (2006)CrossRefGoogle Scholar
  20. 20.
    Foussard, A., Berti, S., Perrot, X., Lapeyre, G.: J. Fluid Mech. 821, 358 (2017)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Aurell, E., Boffetta, G., Crisanti, A., Paladin, G., Vulpiani, A.: J. Rev. A 30, 1 (1997)Google Scholar
  22. 22.
    Özgökmen, T.M., Poje, A.C., Fischer, P.F., Childs, H., Krishnan, H., Garth, C., Haza, A.C., Ryan, E.: Ocean Model. 52, 16 (2012)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexis Foussard
    • 1
  • Stefano Berti
    • 2
    Email author
  • Xavier Perrot
    • 1
  • Guillaume Lapeyre
    • 1
  1. 1.LMD/IPSLCNRS/ENSParisFrance
  2. 2.Université de LilleUnité de Mécanique de Lille, UML EA 7512LilleFrance

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