Skip to main content
SpringerLink
Log in

Anisotropic turbulence in relativistic plasmas

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Signs of turbulence have been observed at the relativistic heavy ion collision at high collision energies. We study the signatures of turbulence in this system and find that there are significant departures from isotropic turbulence in the initial and the pre-equilibrium stages of the collision. As the anisotropic fluctuations are subleading to the isotropic fluctuations, the Kolmogorov spectrum can usually be obtained even for the initial stages. However, the energy spectrum and the temperature fluctuations indicate deviations from isotropic turbulence. Since a strong momentum anisotropy exists between the transverse and the longitudinal plane, we study the energy density spectrum in these two planes by slicing the sphere into different planes. The geometrical anisotropy is reflected in the anisotropic turbulence generated in the rotating plasma and we find that the scaling exponent is different in the two planes. We also obtain the temperature spectrum in the pre-equilibrium stages. The spectrum deviates from the Gaussian spectra expected for an isotropic turbulence. All these seem to indicate that the large scale momentum anisotropy persists in the smaller length scales for the relativistic heavy ion collisions.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability Statement

No Data associated in the manuscript

References

  1. J. Adams et al., STAR collaboration. Nucl. Phys. A 757, 102 (2005)

    Article  ADS  Google Scholar 

  2. K. Adcox et al., PHENIX collaboration. Nucl. Phys. A 757, 184 (2005)

    Article  ADS  Google Scholar 

  3. B. Back et al., PHOBOS collaboration. Nucl. Phys. A 757, 28 (2005)

    Article  ADS  Google Scholar 

  4. A. Arsence et al., BRAHMS collaboration. Nucl. Phys. A 757, 1 (2005)

    ADS  Google Scholar 

  5. K. Aamodt et al., The alice collaboration. Phys. Rev. Lett. 106, 032301 (2011)

    Article  ADS  Google Scholar 

  6. F. Becattini et al., Eur. Phys. J. C 75, 406 (2015)

    Article  ADS  Google Scholar 

  7. B. Schenke, S. Jeon, C. Gale, Phys. Rev. Lett. 106, 042301 (2011)

    Article  ADS  Google Scholar 

  8. P. Bozek, Phys. Rev. C 85, 034901 (2012)

    Article  ADS  Google Scholar 

  9. U. Heinz, R. Snellings, Ann. Rev. Nucl. Part. Sci. 63, 123 (2013)

    Article  ADS  Google Scholar 

  10. C. Gale, S. Jeon, B. Schenke, Int. J. Mod. Phys. A 28, 1340011 (2013)

    Article  ADS  Google Scholar 

  11. H. Song, U.W. Heinz, Phys. Rev. C 81, 024905 (2010)

    Article  ADS  Google Scholar 

  12. M. Luzum, Phys. Rev. C 83, 044911 (2011)

    Article  ADS  Google Scholar 

  13. P. Huovinen, P.F. Kolb, U.W. Heinz, P.V. Ruuskanen, S.A. Voloshin, Phys. Lett. B 503, 58 (2001)

    Article  ADS  Google Scholar 

  14. P.F. Kolb, U.W. Heinz, P. Huovinen, K.J. Eskola, K. Tuominen, Nucl. Phys. A 696, 197 (2001)

    Article  ADS  Google Scholar 

  15. T. Hirano, K. Tsuda, Phys. Rev. C 66, 054905 (2002)

    Article  ADS  Google Scholar 

  16. P.F. Kolb, R. Rapp, Phys. Rev. C 67, 044903 (2003)

    Article  ADS  Google Scholar 

  17. P. Romatschke, U. Romatschke, Phys. Rev. Lett. 99, 172301 (2007)

    Article  ADS  Google Scholar 

  18. H. Song, U.W. Heinz, Phys. Letts. B. 658(5), 279–283 (2008)

    Article  ADS  Google Scholar 

  19. Z.W. Lin, S. Pal, C.M. Ko, B.A. Li, B. Zhang, Phys. Rev. C 64, 011902(R) (2001)

    Article  ADS  Google Scholar 

  20. B. Zhang, C.M. Ko, M. Gyulassy, Phys. Lett. B 455, 45 (1999)

    Article  ADS  Google Scholar 

  21. C. Chattopadhyay, Rajeev S. Bhalerao, Jean-Yves. Ollitrault, S. Pal, Phys. Rev. C 97, 034915 (2018)

    Article  ADS  Google Scholar 

  22. K. Paech, A. Dumitru, Phys. Lett. B 623, 200–207 (2005)

    Article  ADS  Google Scholar 

  23. T. Abe, K. Niu, J. Phys. Soc. Jpn. 49, 717 (1980)

    Article  ADS  Google Scholar 

  24. P. Romatschke, M. Strickland, Phys. Rev. D 68, 036004 (2003)

    Article  ADS  Google Scholar 

  25. S. Mrowczynski, Phys. Lett. B 214, 587 (1988)

    Article  ADS  Google Scholar 

  26. M. Asakawa, S.A. Bass, B. Müller, Phys. Rev. Lett. 96, 252301 (2006)

    Article  ADS  Google Scholar 

  27. M. Asakawa, S.A. Bass, B. Müller, Prog. Theor. Phys. 116, 725 (2007)

    Article  ADS  Google Scholar 

  28. S. Floerchinger, U.A. Wiedemann, JHEP 11, 100 (2011)

    Article  ADS  Google Scholar 

  29. Y. Jiang, J.Z.-W. Lin, J. Liao, Phys. Rev. C 94, 044910 (2016)

    Article  ADS  Google Scholar 

  30. A. Saha, S. Sanyal, Int. J. Mod. Phys. E (2020)

  31. X. Deng, X. Huang, Y. Ma, S. Zhang, Phys. Rev. C 101, 064908 (2020)

    Article  ADS  Google Scholar 

  32. L.P. Csernai, V.K. Magas, D.J. Wang, Phys. Rev. C 87, 034906 (2013)

    Article  ADS  Google Scholar 

  33. R. Micha, I. Tkachev, Phys. Rev. D 70, 043538 (2003)

    Article  ADS  Google Scholar 

  34. J. Berges, A. Rothkopf, J. Schmidt, Phys. Rev. Lett. 101, 041603 (2008)

    Article  ADS  Google Scholar 

  35. J. Berges, G. Hoffmeister, Nucl. Phys. B 813, 383 (2009)

    Article  ADS  Google Scholar 

  36. J. Berges, D. Sexty, Phys. Rev. D 83, 085004 (2011)

    Article  ADS  Google Scholar 

  37. A.H. Mueller, A.I. Shoshi, S.M.H. Wong, Nucl. Phys. B 760, 145 (2007)

    Article  ADS  Google Scholar 

  38. P. Arnold, G.D. Moore, Phys. Rev. D 73, 025006 (2006)

    Article  ADS  Google Scholar 

  39. J. Berges, S. Scheffler, D. Sexty, Phys. Lett. B 681, 362 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  40. K. Fukushima, Phys. Rev. C 89, 024907 (2014)

    Article  ADS  Google Scholar 

  41. K. Fukushima, F. Gelis, Nucl. Phys. A 874, 108 (2012)

    Article  ADS  Google Scholar 

  42. M.E. Carrington, A. Rebhan, Eur. Phys. J. C 71, 1787 (2011)

    Article  ADS  Google Scholar 

  43. M.J. Tannenbaum, Rept. Prog. Phys. 69, 2005 (2006)

    Article  ADS  Google Scholar 

  44. E. Calzetta, Phys. Rev. D 103, 056018 (2021)

    Article  ADS  Google Scholar 

  45. I. Fouxon, Y. Oz, Phys. Lett. B 694(3), 261 (2010)

    Article  ADS  Google Scholar 

  46. G.L. Eyink, T.D. Drivas, Phys. Rev. X 8, 011023 (2018)

    Google Scholar 

  47. A. Saha, S. Sanyal, Int. J. Mod. Phys. E 29(01), 2050001 (2020)

    Article  ADS  Google Scholar 

  48. S. Corrsin, J. Appl. Phys. 22, 469 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  49. Z. Lin, C.M. Ko, B. Li, B. Zhang, S. Pal, Phys. Rev. C 72, 064901 (2005)

    Article  ADS  Google Scholar 

  50. X.N. Wang, M. Gyulassy, Phys. Rev. D 44, 3501 (1991)

    Article  ADS  Google Scholar 

  51. B. Zhang, Comput. Phys. Commun. 109, 193 (1998)

    Article  ADS  Google Scholar 

  52. J. Xu, C.M. Ko, Phys. Rev. C 84, 014903 (2011)

    Article  ADS  Google Scholar 

  53. Fluid Mechanics, Pijush K. Kundu, Ira M. Cohen and David R. Dowling, Elsevier Inc, https://doi.org/10.1016/C2009-0-63410-3; Trinh Khanh Tuoc, arXiv:0910.2072 [physics.flu-dyn]

  54. A.K. Kolmogorov, Dokl. Akad. Nauk SSSR 31, 538 (1941)

    Google Scholar 

  55. V. Zakharov, V. L’vov, G. Falkovich, Kolmogorov Spectra of Turbulence (Wave Turbulence Springer-Verlag, Berlin, 1992)

    Book  MATH  Google Scholar 

  56. V. L’vov, Wave Turbulence Under Parametric Exitation (Springer-Verlag, Berlin, 1994)

    Book  Google Scholar 

  57. U. Frisch, Turbulence Cambridge University Press (England, Cambridge, 1995)

    Google Scholar 

  58. M. Baggioli, V. Brazhkin, K. Trachenko arXiv:2003.13506v2 [hep-th]

  59. B. McInnes, Nucl Phys. B 921, 39–58 (2017)

    Article  ADS  Google Scholar 

  60. X. An, G. Baçar, M. Stephanov, H.U. Yee, Phys. Rev. C 100, 024910 (2019)

    Article  ADS  Google Scholar 

  61. P.K. Kundu, I.M. Cohen, D.R. Dowling, Fluid Mechanics, 5th edn. (Elsevier Academic Press, San Diego, CA, USA, 2012)

    MATH  Google Scholar 

  62. W. Busza, K. Rajagopal, W. van der Schee, Ann. Rev. Nucl. Part. Sci. 68, 1–49 (2018)

    Article  Google Scholar 

  63. R.S. Bhalerao, Pramana 25, 247–257 (2010)

    Article  ADS  Google Scholar 

  64. U. Heinz, Annu. Rev. Nucl. Part. Sci. 63 123-151 (2013)

  65. A. Saha, S. Sanyal, Mod. Phys. Lett. A 36(22), 2150152 (2021)

    Article  ADS  Google Scholar 

  66. Á. Mócsy, P. Sorensen, Nucl. Phys. A 855(1), 241–244 (2011)

    Article  ADS  Google Scholar 

  67. S. Basu et al., Phys. Rev. C 94, 044901 (2016)

    Article  ADS  Google Scholar 

  68. A. A. Budini, Phys. Rev. E 91, 052113 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  69. T. Abe, K. Niu, J. Phys. Soc. Jpn. 49, 725 (1980)

    Article  ADS  Google Scholar 

  70. S. Mrowczynski, Phys. Lett. 314, 118 (1993)

    Article  Google Scholar 

  71. P. Arnold, G.D. Moore, Phys. Rev. D 73, 025013 (2006)

    Article  ADS  Google Scholar 

  72. Y. Ogura, J. Meteorol. 539 (1958)

Download references

Acknowledgements

For computational infrastructure, we acknowledge the Center for Modeling, Simulation and Design (CMSD) at the University of Hyderabad, where part of the simulations was carried out. A.S is supported by INSPIRE Fellowship of the Department of Science and Technology (DST) Govt. of India, through Grant no: IF170627. The authors would like to thank the referees for their constructive comments which has improved the paper to a large extent.

Author information

Authors and Affiliations

  1. School of Physics, University of Hyderabad, Gachibowli, Hyderabad, 500046, India

    Abhisek Saha & Soma Sanyal

Authors
  1. Abhisek Saha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Soma Sanyal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Soma Sanyal.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saha, A., Sanyal, S. Anisotropic turbulence in relativistic plasmas. Eur. Phys. J. Plus 137, 1074 (2022). https://doi.org/10.1140/epjp/s13360-022-03242-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-03242-0

Search

Navigation