Abstract
Using the field theoretic renormalization group technique and the operator product expansion, the kinematic MHD turbulence is investigated in the second order (two-loop) approximation of the corresponding perturbative expansion. The anomalous dimensions of the leading composite operators, which drive the anomalous scaling of the single-time two-point correlation functions of the passive magnetic field, are calculated. It is shown that the two-loop corrections to these anomalous dimensions are significant and lead to the more anomalous (more negative) values of the total two-loop anomalous dimensions. It also means that the anomalous scaling at the two-loop level of approximation is much more pronounced in the present model of passive vector advection than in the analogous model of passive scalar quantity advected by the turbulent velocity field driven by the stochastic Navier–Stokes equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. 2.
W. D. McComb, The Physics of Fluid Turbulence (Clarendon, Oxford, 1990).
U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
G. Falkovich, K. Gawedzki, and M. Vergassola, Rev. Mod. Phys. 73, 913–975 (2001).
R. H. Kraichnan, Phys. Fluids 11, 945–953 (1968).
N. V. Antonov, J. Phys. A 39, 7825–7865 (2006).
D. J. Amit, Field Theory, Renormalization Group, and Critical Phenomena (McGraw-Hill, New York, 1978).
J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon, Oxford, 1989).
A. N. Vasil’ev, Quantum-Field Renormalization Group in the Theory of Critical Phenomena and Stochastic Dynamics (Chapman & Hall/CRC, Boca Raton, 2004).
L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil’ev, Phys. Rev. E 58, 1823–1835 (1998).
L. Ts. Adzhemyan, N. V. Antonov, V. A. Barinov, Yu. S. Kabrits, and A. N. Vasil’ev, Phys. Rev. E 63, 025303(R) (2001);
L. Ts. Adzhemyan, N. V. Antonov, V. A. Barinov, Yu. S. Kabrits, and A. N. Vasil’ev, Phys. Rev. E 64, 056306 (2001).
L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil’ev, The Field Theoretic Renormalization Group in Fully Developed Turbulence (Gordon and Breach, London, 1999).
N. V. Antonov, Phys. Rev. E 60, 6691–6707 (1999).
N. V. Antonov, A. Lanotte, and A. Mazzino, Phys. Rev. E 61, 6586–6605 (2000).
L. Ts. Adzhemyan, N. V. Antonov, and A. V. Runov, Phys. Rev. E 64, 046310 (2001).
N. V. Antonov, M. Hnatic, J. Honkonen, and M. Jurcisin, Phys. Rev. E 68, 046306 (2003).
E. Jurčišinová, M. Jurčišin, R. Remecký, and M. Scholtz, Int. J. Mod. Phys. B 22, 3589–3617.
E. Jurčišinová and M. Jurčišin, Phys. Rev. E 77, 016306 (2008).
O. G. Chkhetiani, M. Hnatich, E. Jurčišinová, M. Jurčišin, A. Mazzino, M. Repašan, Phys. Rev. E 74, 036310 (2006).
E. Jurčišinová and M. Jurčišin, J. Phys. A 45, 485501 (2012).
N. V. Antonov and N. M. Gulitskiy, Phys. Rev. E 85, 065301(R) (2012).
E. Jurčišinová and M. Jurčišin, Phys. Rev. E 88, 011004(R) (2013).
E. Jurčišinová, M. Jurčišin, and M. Menkyna, Phys. Rev. E 95, 053210 (2017).
E. Jurčišinová, M. Jurčišin, and M. Menkyna, Eur. Phys. J. B 91, 313 (2018).
L. Ts. Adzhemyan, N. V. Antonov, J. Honkonen, and T. L. Kim, Phys. Rev. E 71, 016303 (2005).
E. Jurčišinová, M. Jurčišin, and R. Remecký, J. Phys. A: Math. Theor. 42, 275501 (2009).
E. Jurčišinová, M. Jurčišin, and R. Remecký, Phys. Rev. E 84, 046311 (2011).
L. Ts. Adzhemyan, N. V. Antonov, M. V. Kompaniets, and A. N. Vasil’ev, Int. J. Mod. Phys. B 17, 2137–2170.
FUNDING
The work was supported by grants VEGA nos. 2/0065/17 and 2/0058/19 of Slovak Academy of Sciences, and by grant APVV-17-0020.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Jurčišinová, E., Jurčišin, M. & Remecký, R. Anomalous Dimensions of Leading Composite Operators in the Kinematic MHD Turbulence: Two-Loop Renormalization Group Analysis. Phys. Part. Nuclei 51, 812–815 (2020). https://doi.org/10.1134/S1063779620040371
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779620040371