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Renormalization Group Analysis of Models of Advection of a Vector Admixture and a Tracer Field by a Compressible Turbulent Flow

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Abstract

Using a quantum field theory renormalization group, we consider models of advection of a vector field and a tracer field by a compressible turbulent flow. Both advected fields are considered passive, i.e., they do not have a backward influence on the fluid dynamics. The velocity field is generated by the stochastic Navier-Stokes equation. We consider the model in the vicinity of the special space dimension d = 4. Analysis of the model in the vicinity of this dimension allows constructing a double expansion in the parameters y (related to the correlator of the random force for the velocity field) and ε = 4 − d. We show that in the framework of the one-loop approximation, the two models have similar scaling behavior, i.e., similar behavior of the correlation and structure functions in the inertial range. We calculate all critical dimensions, in particular, of tensor composite operators, in the leading order of the double expansion in y and ε.

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References

  1. A.N. Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics [in Russian], Petersburg Inst. Nucl. Phys. Press, St. Petersburg (1998); English transl., CRC, Boca Raton, Fla. (2004).

    Google Scholar 

  2. U. Täuber, Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior, Cambridge Univ. Press, New York (2014).

    Google Scholar 

  3. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford Univ. Press, Oxford (2002).

    Book  MATH  Google Scholar 

  4. U. Frisch, Turbulence: The legacy of A. N. Kolmogorov, Cambridge Univ. Press, Cambridge (1995).

    Book  MATH  Google Scholar 

  5. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics [in Russian] (Part 2), Nauka, Moscow (1967); English transl.: Statistical Fluid Mechanics: Mechanics of Turbulence, Dover, New York (2007).

    Google Scholar 

  6. P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers, Oxford Univ. Press, Oxford (2015).

    Book  MATH  Google Scholar 

  7. G. Falkovich, K. Gawȩdzki, and M. Vergassola, “Particles and fields in fluid turbulence,” Rev. Modern Phys., 73, 913–975 (2001).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. D. Biskamp, Magnetohydrodynamic Turbulence, Cambridge Univ. Press, Cambridge (2003).

    Book  MATH  Google Scholar 

  9. S. N. Shore, Astrophysical Hydrodynamics: An Introduction, Wiley-VCH, Weinheim (2007).

    Book  Google Scholar 

  10. E. Priest, Magnetohydrodynamics of the Sun, Cambridge Univ. Press, Cambridge (2014).

    Google Scholar 

  11. A. Pouquet, U. Frisch, and J. Léorat, “Strong MHD helical turbulence and the nonlinear dynamo effect,” J. Fluid Mech., 77, 321–354 (1976).

    Article  ADS  MATH  Google Scholar 

  12. C.-Y. Tu and E. Marsch, “MHD structures, waves, and turbulence in the solar wind: Observations and theories,” Space Sci. Rev., 73, 1–210 (1995).

    Article  ADS  Google Scholar 

  13. S. A. Balbus and J. F. Hawley, “Instability, turbulence, and enhanced transport in accretion disks,” Rev. Modern Phys., 70, 1–53 (1998).

    Article  ADS  Google Scholar 

  14. G. Chabrier, “Galactic stellar and substellar initial mass function,” Publ. Astron. Soc. Pac., 115, 763–795 (2003).

    Article  ADS  Google Scholar 

  15. B. G. Elemegreen and J. Scalo, “Interstellar turbulence I: Observations and processes,” Ann. Rev. Astron. Astrophys., 42, 211–273 (2004).

    Article  ADS  Google Scholar 

  16. C. Federrath, “On the universality of supersonic turbulence,” Mon. Not. R. Astron. Soc., 436, 1245–1257 (2013); arXiv:1306.3989v4 [astro-ph.SR] (2013).

    Article  ADS  Google Scholar 

  17. N. V. Antonov, “Renormalization group, operator product expansion, and anomalous scaling in models of turbulent advection,” J. Phys. A: Math. Gen., 39, 7825–7865 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids, Cambridge Univ. Press, Cambridge (1978).

    Google Scholar 

  19. J. D. Fournier, P. L. Sulem, and A. Pouquet, “Infrared properties of forced magnetohydrodynamic turbulence,” J. Phys. A: Math. Gen., 15, 1393–1420 (1982).

    Article  ADS  MATH  Google Scholar 

  20. L. Ts. Adzhemyan, A. N. Vasil’ev, and M. Gnatich, “Renormalization-group approach to the theory of turbulence: Inclusion of a passive admixture,” Theor. Math. Phys., 58, 47–51 (1984).

    Article  MATH  Google Scholar 

  21. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics [in Russian], Vol. 6, Fluid Mechanics, Nauka, Moscow (1986); English transl. prev. ed., Pergamon, Oxford (1959).

    Google Scholar 

  22. P. Sagaut and C. Cambon, Homogeneous Turbulence Dynamics, Cambridge Univ. Press, Cambridge (2008).

    Book  MATH  Google Scholar 

  23. J. Kim and D. Ryu, “Density power spectrum of compressible hydrodynamic turbulent flows,” Astrophys. J., 630, L45–L48 (2005); arXiv:astro-ph/0507591v1 (2005).

    Article  ADS  Google Scholar 

  24. V. Carbone, R. Marino, L. Sorriso-Valvo, A. Noullez, and R. Bruno, “Scaling laws of turbulence and heating of fast solar wind: The role of density fluctuations,” Phys. Rev. Lett., 103, 061102 (2009).

    Article  ADS  Google Scholar 

  25. F. Sahraoui, M. L. Goldstein, P. Robert, and Yu. V. Khotyainstsev, “Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale,” Phys.Rev.Lett., 102, 231102 (2009).

    Article  ADS  Google Scholar 

  26. H. Aluie and G. L. Eyink, “Scale locality of magnetohydrodynamic turbulence,” Phys.Rev.Lett., 104, 081101 (2010); arXiv:0912.3752v1 [astro-ph.SR] (2009).

    Article  ADS  Google Scholar 

  27. S. Galtier and S. Banerjee, “Exact relation for correlation functions in compressible isothermal turbulence,” Phys. Rev. Lett., 107, 134501 (2011); arXiv:1108.4529v1 [astro-ph.SR] (2011).

    Article  ADS  Google Scholar 

  28. S. Banerjee and S. Galtier, “Exact relation with two-point correlation functions and phenomenological approach for compressible magnetohydrodynamic turbulence,” Phys.Rev.E, 87, 013019 (2013); arXiv:1301.2470v1 [physics.flu-dyn] (2013).

    Article  ADS  Google Scholar 

  29. S. Banerjee, L. Z. Hadid, F. Sahraoui, and S. Galtier, “Scaling of compressible magnetohydrodynamic turbulence in the fast solar wind,” Astrophys. J. Lett., 829, L27 (2016).

    Article  ADS  Google Scholar 

  30. L. Z. Hadid, F. Sahraoui, and S. Galtier, “Energy cascade rate in compressible fast and slow solar wind turbulence,” Astrophys. J., 838, 9 (2017); arXiv:1612.02150v1 [astro-ph.SR] (2016).

    Article  ADS  Google Scholar 

  31. P. S. Iroshnikov, “Turbulence of a conducting fluid in a strong magnetic field,” Sov. Astron., 7, 566 (1964).

    ADS  MathSciNet  Google Scholar 

  32. N. V. Antonov and N. M. Gulitskiy, “Two-loop calculation of the anomalous exponents in the Kazantsev-Kraichnan model of magnetic hydrodynamics,” in: Mathematical Modeling and Computational Science: MMCP 2011 (Lect. Notes Computer Sci., Vol. 7125, G. Adam, J. Busa, and M. Hnatič, eds.), Springer, Berlin (2012), pp. 128–135.

    Chapter  Google Scholar 

  33. N. V. Antonov and N. M. Gulitskiy, “Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev-Kraichnan kinematic model,” Phys. Rev. E, 85, 065301 (2012); arXiv:1202.5992v3 [cond-mat.stat-mech] (2012).

    Article  ADS  Google Scholar 

  34. N. V. Antonov and N. M. Gulitskiy, “Erratum: Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: two-loop renormalization-group analysis of the Kazantsev-Kraichnan kinematic model,” Phys. Rev. E, 87, 039902 (2013).

    Article  ADS  Google Scholar 

  35. E. Jurčišinova and M. Jurčišin, “Anomalous scaling of the magnetic field in the Kazantsev-Kraichnan model,” J. Phys. A: Math. Theor., 45, 485501 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  36. E. Jurčišinova and M. Jurčišin, “Anomalous scaling of a passive scalar advected by a turbulent velocity field with finite correlation time and uniaxial small-scale anisotropy,” Phys. Rev. E, 77, 016306 (2008); arXiv:nlin/0703063v1 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  37. E. Jurčišinova, M. Jurcišin, and R. Remecký, “Influence of anisotropy on anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field,” Phys. Rev. E, 80, 046302 (2009).

    Article  ADS  MATH  Google Scholar 

  38. N. V. Antonov and N. M. Gulitskiy, “Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field,” Phys. Rev. E, 91, 013002 (2015); arXiv:1406.3808v2 [cond-mat.stat-mech] (2014).

    Article  ADS  Google Scholar 

  39. N. V. Antonov and N. M. Gulitskiy, “Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling,” Phys. Rev. E, 92, 043018 (2015); arXiv:1506.05615v2 [cond-mat.stat-mech] (2015).

    Article  ADS  Google Scholar 

  40. N. V. Antonov and N. M. Gulitskiy, “Logarithmic violation of scaling in anisotropic kinematic dynamo model,” AIP Conf. Proc, 1701, 100006 (2016).

    Article  Google Scholar 

  41. N. V. Antonov and N. M. Gulitskiy, “Anisotropic turbulent advection of a passive vector field: Effects of the finite correlation time,” EPJ Web Conf., 108, 02008 (2016).

    Article  Google Scholar 

  42. L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil’ev, Renormalization Group Method in the Theory of Developed Turbulence [in Russian], St. Petersburg Univ. Press, St. Petersburg (1998); English transl.: The Field Theoretic Renormalization Group in Fully Developed Turbulence, Gordon and Breach, London (1999).

    Google Scholar 

  43. R. H. Kraichnan, “Small-scale structure of a scalar field convected by turbulence,” Phys. Fluids, 11, 945–953 (1968).

    Article  ADS  MATH  Google Scholar 

  44. K. Gawȩdzki and A. Kupiainen, “Anomalous scaling of the passive scalar,” Phys. Rev. Lett., 75, 3834–3837 (1995)

    Article  ADS  Google Scholar 

  45. D. Bernard, K. Gawȩdzki, and A. Kupiainen, “Anomalous scaling in the N-point functions of a passive scalar,” Phys. Rev. E, 54, 2564–2572 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  46. M. Chertkov and G. Falkovich, “Anomalous scaling exponents of a white-advected passive scalar,” Phys. Rev. Lett., 76, 2706–2709 (1996).

    Article  ADS  Google Scholar 

  47. L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil’ev, “Renormalization group, operator product expansion, and anomalous scaling in a model of advected passive scalar,” Phys. Rev. E, 58, 1823–1835 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  48. N. V. Antonov, “Anomalous scaling regimes of a passive scalar advected by the synthetic velocity field,” Phys. Rev. E, 60, 6691–6707 (1999).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. E. Jurčišinova and M. Jurčišin, “Anomalous scaling of the magnetic field in the helical Kazantsev-Kraichnan model,” Phys. Rev. E, 91, 063009 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. N. V. Antonov, A. Lanotte, and A. Mazzino, “Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence,” Phys. Rev. E, 61, 6586–6605 (2000); arXiv:nlin/0001039v1 (2000)

    Article  ADS  Google Scholar 

  51. N. V. Antonov and N. M. Gulitskii, “Anomalous scaling in statistical models of passively advected vector fields,” Theor. Math. Phys., 176, 851–860 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  52. H. Arponen, “Anomalous scaling and anisotropy in models of passively advected vector fields,” Phys. Rev. E, 79, 056303 (2009); arXiv:0811.0510v2 [nlin.CD] (2008).

    Article  ADS  MathSciNet  Google Scholar 

  53. E. Jurčišinova, M. Jurčišin, and M. Menkyna, “Anomalous scaling in the Kazantsev-Kraichnan model with finite time correlations: Two-loop renormalization group analysis of relevant composite operators,” Eur. Phys. J. B, 91, 313 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  54. M. Hnatič, J. Honkonen, and T. Lučivjanský, “Advanced field-theoretical methods in stochastic dynamics and theory of developed turbulence,” Acta Phys. Slovaca, 66, 69–264 (2016); arXiv:1611.06741v1 [cond-mat.statmech] (2016).

    Google Scholar 

  55. L. Ts. Adzhemyan, N. V. Antonov, J. Honkonen, and T. L. Kim, “Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: Two-loop approximation,” Phys. Rev. E, 71, 016303 (2005); arXiv:nlin/0408057v1 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  56. N. V. Antonov, “Scaling behavior in a stochastic self-gravitating system,” Phys. Rev. Lett., 92, 161101 (2004); arXiv:astro-ph/0308369v1 (2003).

    Article  ADS  Google Scholar 

  57. N. V. Antonov, N. M. Gulitskiy, and A. V. Malyshev, “Stochastic Navier-Stokes equation with colored noise: Renormalization group analysis,” EPJ Web Conf., 126, 04019 (2016).

    Article  Google Scholar 

  58. E. Jurčišinova, M. Jurčišin, and R. Remecký, “Turbulent Prandtl number in the A model of passive vector admixture,” Phys. Rev. E, 93, 033106 (2016).

    Article  ADS  Google Scholar 

  59. E. Jurčišinova, M. Jurčišin, and M. Menkyna, “Simultaneous influence of helicity and compressibility on anomalous scaling of the magnetic field in the Kazantsev-Kraichnan model,” Phys. Rev. E, 95, 053210 (2017).

    Article  ADS  Google Scholar 

  60. M. Vergassola and A. Mazzino, “Structures and intermittency in a passive scalar model,” Phys. Rev. Lett., 79, 1849–1852 (1997).

    Article  ADS  Google Scholar 

  61. A. Celani, A. Lanotte, and A. Mazzino, “Passive scalar intermittency in compressible flow,” Phys. Rev. E, 60, R1138–R1141 (1999).

    Article  ADS  Google Scholar 

  62. M. Chertkov, I. Kolokolov, and M. Vergassola, “Inverse cascade and intermittency of passive scalar in one-dimensional smooth flow,” Phys. Rev. E., 56, 5483–5499 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  63. L. Ts. Adzhemyan and N. V. Antonov, “Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow,” Phys. Rev. E, 58 part A, 7381–7396 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  64. N. V. Antonov, M. Yu. Nalimov, and A. A. Udalov, “Renormalization group in the problem of the fully developed turbulence of a compresible fluid,” Theor. Math. Phys., 110, 305–315 (1997).

    Article  MATH  Google Scholar 

  65. N. V. Antonov and M. M. Kostenko, “Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy,” Phys. Rev. E, 90, 063016 (2014); arXiv:1410.1262v1 [cond-mat.stat-mech] (2014).

    Article  ADS  Google Scholar 

  66. N. V. Antonov and M. M. Kostenko, “Anomalous scaling in magnetohydrodynamic turbulence: Effects of anisotropy and compressibility in the kinematic approximation,” Phys. Rev. E, 92, 053013 (2015); arXiv: 1507.08516v1 [cond-mat.stat-mech] (2015).

    Article  ADS  MathSciNet  Google Scholar 

  67. M. Hnatich, E. Jurčišinova, M. Jurčišin, and M. Repašan, “Compressible advection of a passive scalar: Two-loop scaling regimes,” J. Phys. A: Math. Gen., 39, 8007–8021 (2006).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  68. V. S. L’vov and A. V. Mikhailov, “Toward a nonlinear theory of sonic and hydrodynamic turbulence of a compressible liquid [in Russian],” Preprint No. 54, Institute of Automation and Electrometry, Novosibirsk (1977).

    Google Scholar 

  69. I. Staroselsky, V. Yakhot, S. Kida, and S. A. Orszag, “Long-time, large-scale properties of a randomly stirred compressible fluid,” Phys. Rev. Lett., 65, 171–174 (1990).

    Article  ADS  Google Scholar 

  70. S. S. Moiseev, A. V. Tur, and V. V. Yanovskii, “Spectra and excitation methods of turbulence in a compressible fluid,” Sov. Phys. JETP, 44, 556–561 (1976).

    ADS  Google Scholar 

  71. J. Honkonen and M. Yu. Nalimov, “Two-parameter expansion in the renormalization-group analysis of turbulence,” Z. Phys. B, 99, 297–303 (1996).

    Article  ADS  Google Scholar 

  72. L. Ts. Adzhemyan, J. Honkonen, M. V. Kompaniets, and A. N. Vasil’ev, “Improved ε expansion for three-dimensional turbulence: Two-loop renormalization near two dimensions,” Phys. Rev. E, 71, 036305 (2005); arXiv:nlin/0407067v1 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  73. L. Ts. Adzhemyan, M. Hnatich, and J. Honkonen, “Improved ε expansion in the theory of turbulence: Summation of nearest singularities by inclusion of an infrared irrelevant operator,” Eur. Phys. J B, 73, 275–285 (2010).

    Article  ADS  MATH  Google Scholar 

  74. A. Z. Patashinskii and V. L. Pokrovskii, Fluctuation Theory of Phase Transitions [in Russian], Nauka, Moscow (1982); English transl. prev. ed., Pergamon, Oxford (1979).

    Google Scholar 

  75. D. Forster, D. R. Nelson, and M. J. Stephen, “Large-distance and long-time properties of a randomly stirred fluid,” Phys. Rev. A, 16, 732–740 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  76. L. Ts. Adzhemyan, N. V. Antonov, and A. N. Vasil’ev, “Infrared divergences and the renormalization group in the theory of fully developed turbulence,” Sov. Phys. JETP, 68, 742 (1989).

    Google Scholar 

  77. N. V. Antonov, N. M. Gulitskiy, M. M. Kostenko, and T. Lučivjanskš, “Turbulent compressible fluid: Renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields,” Phys. Rev. E, 95, 033120 (2017); arXiv:1611.00327v2 [cond-mat.stat-mech] (2016).

    Article  ADS  Google Scholar 

  78. N. V. Antonov, N. M. Gulitskiy, M. M. Kostenko, and T. Lučivjanský, “Renormalization group analysis of a turbulent compressible fluid near d = 4: Crossover between local and non-local scaling regimes,” EPJ Web Conf., 125, 05006 (2016).

    Article  Google Scholar 

  79. N. V. Antonov, N. M. Gulitskiy, M. M. Kostenko, and T. Lučivjanský, “Advection of a passive scalar field by turbulent compressible fluid: Renormalization group analysis near d = 4,” EPJ Web Conf., 137, 10003 (2017).

    Article  Google Scholar 

  80. N. V. Antonov, N. M. Gulitskiy, M. M. Kostenko, and T. Lučivjanský, “Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization near d = 4,” EPJ Web Conf., 164, 07044 (2017).

    Article  Google Scholar 

  81. N. V. Antonov, A. Lanotte, and A. Mazzino, “Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence,” Phys. Rev. E, 61, 6586–6605 (2000); arXiv:nlin/0001039v1 (2000).

    Article  ADS  Google Scholar 

  82. Y. Zhou, “Renormalization group theory for fluid and plasma turbulence,” Phys. Rep., 448, 1–49 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  83. M. K. Nandy and J. K. Bhattacharjee, “Renormalization-group analysis for the infrared properties of a randomly stirred binary fluid,” J. Phys. A: Math. Gen., 31, 2621–2637 (1998).

    Article  ADS  MATH  Google Scholar 

  84. N. V. Antonov, “Anomalous scaling of a passive scalar advected by the synthetic compressible flow,” Phys. D, 144, 370–386 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  85. D. Yu. Volchenckov and M. Yu. Nalimov, “The corrections to fully developed turbulent spectra due to the compressibility of fluid,” Theor. Math. Phys., 106, 307–318 (1996).

    Article  MATH  Google Scholar 

  86. H. K. Janssen, “On a Lagrangean for classical field dynamics and renormalization group calculations of dynamical critical properties,” Z. Phys. B, 23, 377–380 (1976).

    Article  ADS  Google Scholar 

  87. C. De Dominicis, “FrTechniques de renormalisation de la theorie des champs et dynamique des phenomenes critiques,” J. Phys. Colloq. France, 37, C1–247–C1–253 (1976).

    Article  ADS  Google Scholar 

  88. H. K. Janssen, “Field-theoretic method applied to critical dynamics,” in: Dynamical Critical Phenomena and Related Topics (Lect. Notes Phys., Vol. 104, C. P. Enz, ed.), Springer, Heidelberg (1979), pp. 25–47.

    Chapter  Google Scholar 

  89. L. Ts. Adzhemyan, M. Yu. Nalimov, and M. M. Stepanova, “Renormalization-group approach to the problem of the effect of compressibility on the spectral properties of developed turbulence,” Theor. Math. Phys., 104, 971–979 (1995).

    Article  MATH  Google Scholar 

  90. N. V. Antonov, M. Hnatich, J. Honkonen, and M. Jurčišin, “Turbulence with pressure: Anomalous scaling of a passive vector field,” Phys. Rev. E, 68, 046306 (2003); arXiv:nlin/0305024v1 (2003).

    Article  ADS  Google Scholar 

  91. B. Duplantier and A. Ludwig, “Multifractals, operator-product expansion, and field theory,” Phys. Rev. Lett., 66, 247–251 (1991).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  92. G. L. Eyink, “Lagrangian field theory, multifractals, and universal scaling in turbulence,” Phys. Lett. A, 172, 355–360 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  93. N. V. Antonov, N. M. Gulitskiy, M. M. Kostenko, and A. V. Malyshev, “Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models,” Phys. Rev. E, 97, 033101 (2018); arXiv:1710.04992v2 [cond-mat.stat-mech] (2017).

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    N. V. Antonov, N. M. Gulitskiy & M. M. Kostenko

  2. Pavol Jozef Šafárik University in Košice, Košice, Slovakia

    T. Lučivjanský

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  1. N. V. Antonov
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  2. N. M. Gulitskiy
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  3. M. M. Kostenko
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  4. T. Lučivjanský
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Correspondence to N. V. Antonov or N. M. Gulitskiy.

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The authors declare no conflicts of interest.

This research was supported in part by the Russian Foundation for Basic Research (Grant No. 18-32-00238, all results concerning magnetohydrodynamics and vector admixture) and the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS.”

The research of N. M. Gulitskiy was supported by the St. Petersburg Committee of Science and Higher Schools and St. Petersburg University (Travel Grant No. 37722050).

The research of T. Lučivjanský was supported by VEGA (Grant No. 1/0345/17 of the Ministry of Education, Science, Research, and Sport of the Slovak Republic) and the Slovak Research and Development Agency (a grant under Contract No. APVV-16-0186).

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 200, No. 3, pp. 429–451, September, 2019.

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Antonov, N.V., Gulitskiy, N.M., Kostenko, M.M. et al. Renormalization Group Analysis of Models of Advection of a Vector Admixture and a Tracer Field by a Compressible Turbulent Flow. Theor Math Phys 200, 1294–1312 (2019). https://doi.org/10.1134/S0040577919090046

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