Anomalous scaling in the kazantsev-kraichnan model with finite time correlations: two-loop renormalization group analysis of relevant composite operators. (English) Zbl 1515.82118
Summary: The field theoretic renormalization group technique together with the operator product expansion in the second order of the perturbation theory (in the two-loop approximation) is used for the investigation of the influence of the finite time correlations of the velocity field on the anomalous dimensions of the leading set of composite operators, which drive the anomalous scaling of correlation functions of a weak magnetic field in the framework of the kinematic Kazantsev-Kraichnan model in the presence of a large scale anisotropy. The system of possible scaling regimes of the model is found and two important special limits of the model are briefly discussed. The general two-loop expressions for the anomalous and critical dimensions of the leading composite operators are found as functions of the spatial dimension \(d\) and of the renormalization group fixed point value of the parameter \(u\), which drives the presence of the finite time correlations of the velocity field in the model. The anisotropic hierarchies among various anomalous dimensions are investigated and it is shown that, regardless of the fixed point value of the parameter \(u\) as well as regardless of the spatial dimension of the system, the leading role in the anomalous scaling properties of the model is played by the anomalous dimensions of the composite operators near the isotropic shell, in accordance with the Kolmogorov’s local isotropy restoration hypothesis. The properties of the anomalous dimensions of the leading composite operators in the Kazantsev-Kraichnan model with finite time correlations of the velocity field are compared to the properties of the corresponding anomalous dimensions of the composite operators relevant in the framework of the Kraichnan model of passively advected scalar field with finite time correlations. It is shown that, regardless of the fixed point value of the parameter \(u\), the two-loop corrections to the anomalous dimensions are much more important in the framework of the Kazantsev-Kraichnan vector model than in the Kraichnan model of a passive scalar advection. At the same time, again regardless of the strength of time correlations, the two-loop values of the leading anomalous dimensions in the Kazantsev-Kraichnan model of the passive magnetic field are significantly more negative than the corresponding two-loop values of the relevant anomalous dimensions in the framework of the Kraichnan model. It means that the anomalous scaling of the correlation functions of the passive magnetic field, deep inside the inertial interval of the turbulent environment with finite time correlations of the velocity field, must be much more pronounced than in the case of the correlation functions of the passively advected scalar field.
MSC:
| 82C28 | Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics |
Keywords:
statistical and nonlinear physicsReferences:
| [1] | Kolmogorov, A. N., No article title, Dokl. Akad. Nauk SSSR, 30, 301 (1941) |
| [2] | Kolmogorov, A. N., No article title, Dokl. Akad. Nauk SSSR, 31, 538 (1941) |
| [3] | Kolmogorov, A. N., No article title, Dokl. Akad. Nauk SSSR, 32, 16 (1941) |
| [4] | A.S. Monin, A.M. Yaglom, in Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. 2 |
| [5] | W.D. McComb, The Physics of Fluid Turbulence (Clarendon, Oxford, 1990) · Zbl 0748.76005 |
| [6] | U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995) · Zbl 0832.76001 |
| [7] | Sreenivasan, K. R.; Antonia, R. A., No article title, Ann. Rev. Fluid Mech., 29, 435 (1997) · doi:10.1146/annurev.fluid.29.1.435 |
| [8] | Falkovich, G.; Gawȩdzki, K.; Vergassola, M., No article title, Rev. Mod. Phys., 73, 913 (2001) · Zbl 1205.76133 · doi:10.1103/RevModPhys.73.913 |
| [9] | L.Ts. Adzhemyan, N.V. Antonov, A.N. Vasil’ev, The Field Theoretic Renormalization Group in Fully Developed Turbulence (Gordon & Breach, London, 1999) · Zbl 0956.76002 |
| [10] | Antonia, R. A.; Satyaprakash, B. R.; Hussain, A. K.F., No article title, J. Fluid Mech., 119, 55 (1982) · doi:10.1017/S0022112082001268 |
| [11] | Anselmet, F.; Gagne, Y.; Hopfinger, E.; Antonia, R. A., No article title, J. Fluid Mech., 140, 63 (1984) · doi:10.1017/S0022112084000513 |
| [12] | Meneveau, C.; Sreenivasan, K. R., No article title, Phys. Rev. A, 41, 2246 (1990) · doi:10.1103/PhysRevA.41.2246 |
| [13] | Borgas, M. S., No article title, Phys. Fluids A, 4, 2055 (1992) · Zbl 0762.76048 · doi:10.1063/1.858375 |
| [14] | V.R. Kuznetsov, V.A. Sabel’nikov, Turbulence and Combustion (Hemisphere Publishing, New York, 1990) · Zbl 0923.76064 |
| [15] | Antonov, N. V., No article title, J. Phys. A, 39, 7825 (2006) · Zbl 1117.76030 · doi:10.1088/0305-4470/39/25/S04 |
| [16] | Antonia, R. A.; Hopfinger, E. J.; Gagne, Y.; Anselmet, F., No article title, Phys. Rev. A, 30, 2704 (1984) · doi:10.1103/PhysRevA.30.2704 |
| [17] | Sreenivasan, K. R., No article title, Proc. R. Soc. Lond., Ser. A, 434, 165 (1991) · Zbl 0726.76050 · doi:10.1098/rspa.1991.0087 |
| [18] | Holzer, M.; Siggia, E. D., No article title, Phys. Fluids, 6, 1820 (1994) · Zbl 0866.76034 · doi:10.1063/1.868243 |
| [19] | Pumir, A., No article title, Phys. Fluids, 6, 2118 (1994) · Zbl 0834.76040 · doi:10.1063/1.868216 |
| [20] | Tong, C.; Warhaft, Z., No article title, Phys. Fluids, 6, 2165 (1994) · doi:10.1063/1.868219 |
| [21] | Elperin, T.; Kleeorin, N.; Rogachevskii, I., No article title, Phys. Rev. E, 52, 2617 (1995) · doi:10.1103/PhysRevE.52.2617 |
| [22] | Elperin, T.; Kleeorin, N.; Rogachevskii, I., No article title, Phys. Rev. Lett., 76, 224 (1996) · doi:10.1103/PhysRevLett.76.224 |
| [23] | Elperin, T.; Kleeorin, N.; Rogachevskii, I., No article title, Phys. Rev. E, 53, 3431 (1996) · doi:10.1103/PhysRevE.53.3431 |
| [24] | Warhaft, Z., No article title, Ann. Rev. Fluid Mech., 32, 203 (2000) · Zbl 0988.76042 · doi:10.1146/annurev.fluid.32.1.203 |
| [25] | Shraiman, B. I.; Siggia, E., No article title, Nature, 405, 639 (2000) · doi:10.1038/35015000 |
| [26] | Moisy, F.; Willaime, H.; Andersen, J. S.; Tabeling, P., No article title, Phys. Rev. Lett., 86, 4827 (2001) · doi:10.1103/PhysRevLett.86.4827 |
| [27] | Arnèodo, A., No article title, Phys. Rev. Lett., 100, 254504 (2008) · doi:10.1103/PhysRevLett.100.254504 |
| [28] | Vergassola, M., No article title, Phys. Rev. E, 53, r3021 (1996) · doi:10.1103/PhysRevE.53.R3021 |
| [29] | Gawȩdzki, K.; Kupiainen, A., No article title, Phys. Rev. Lett., 75, 3834 (1995) · doi:10.1103/PhysRevLett.75.3834 |
| [30] | Bernard, D.; Gawȩdzki, K.; Kupiainen, A., No article title, Phys. Rev. E, 54, 2564 (1996) · doi:10.1103/PhysRevE.54.2564 |
| [31] | Chertkov, M.; Falkovich, G.; Kolokolov, I.; Lebedev, V., No article title, Phys. Rev. E, 52, 4924 (1995) · doi:10.1103/PhysRevE.52.4924 |
| [32] | Chertkov, M.; Falkovich, G., No article title, Phys. Rev. Lett., 76, 2706 (1996) · doi:10.1103/PhysRevLett.76.2706 |
| [33] | Avellaneda, M.; Majda, A., No article title, Commun. Math. Phys., 131, 381 (1990) · Zbl 0703.76042 · doi:10.1007/BF02161420 |
| [34] | Avellaneda, M.; Majda, A., No article title, Commun. Math. Phys., 146, 139 (1992) · Zbl 0754.76046 · doi:10.1007/BF02099212 |
| [35] | Majda, A., No article title, J. Stat. Phys., 73, 515 (1993) · Zbl 1102.82328 · doi:10.1007/BF01054338 |
| [36] | Horntrop, D.; Majda, A., No article title, J. Math. Sci. Univ. Tokyo, 1, 23 (1994) · Zbl 0813.76073 |
| [37] | Zhang, Q.; Glimm, J., No article title, Commun. Math. Phys., 146, 217 (1992) · Zbl 0749.76031 · doi:10.1007/BF02102625 |
| [38] | Kraichnan, R. H., No article title, Phys. Rev. Lett., 72, 1016 (1994) · doi:10.1103/PhysRevLett.72.1016 |
| [39] | Kraichnan, R. H.; Yakhot, V.; Chen, S., No article title, Phys. Rev. Lett., 75, 240 (1995) · doi:10.1103/PhysRevLett.75.240 |
| [40] | Shraiman, B. I.; Siggia, E. D., No article title, Phys. Rev. Lett., 77, 2463 (1996) · doi:10.1103/PhysRevLett.77.2463 |
| [41] | Pumir, A.; Shraiman, B. I.; Siggia, E. D., No article title, Phys. Rev. E, 55, r1263 (1997) · doi:10.1103/PhysRevE.55.R1263 |
| [42] | Pumir, A., No article title, Europhys. Lett., 34, 25 (1996) · doi:10.1209/epl/i1996-00410-4 |
| [43] | Pumir, A., No article title, Europhys. Lett., 37, 529 (1997) · doi:10.1209/epl/i1997-00186-5 |
| [44] | Pumir, A., No article title, Phys. Rev. E, 57, 2914 (1998) · doi:10.1103/PhysRevE.57.2914 |
| [45] | Rogachevskii, I.; Kleeorin, N., No article title, Phys. Rev. E, 56, 417 (1997) · doi:10.1103/PhysRevE.56.417 |
| [46] | Lanotte, A.; Mazzino, A., No article title, Phys. Rev. E, 60, r3483 (1999) · doi:10.1103/PhysRevE.60.R3483 |
| [47] | Arad, I.; Biferale, L.; Procaccia, I., No article title, Phys. Rev. E, 61, 2654 (2000) · doi:10.1103/PhysRevE.61.2654 |
| [48] | Antonov, N. V.; Lanotte, A.; Mazzino, A., No article title, Phys. Rev. E, 61, 6586 (2000) · doi:10.1103/PhysRevE.61.6586 |
| [49] | Antonov, N. V.; Honkonen, J.; Mazzino, A.; Muratore-Ginanneschi, P., No article title, Phys. Rev. E, 62, r5891 (2000) · doi:10.1103/PhysRevE.62.R5891 |
| [50] | Antonov, N. V.; Hnatich, M.; Honkonen, J.; Jurčišin, M., No article title, Phys. Rev. E, 68, 046306 (2003) · doi:10.1103/PhysRevE.68.046306 |
| [51] | Chaves, M.; Gawȩdzki, K.; Horvai, P.; Kupiainen, A.; Vergassola, M., No article title, J. Stat. Phys., 113, 643 (2003) · Zbl 1137.76388 · doi:10.1023/A:1027348316456 |
| [52] | Arponen, H., No article title, Phys. Rev. E, 81, 036325 (2010) · doi:10.1103/PhysRevE.81.036325 |
| [53] | Kraichnan, R. H., No article title, Phys. Fluids, 11, 945 (1968) · Zbl 0164.28904 · doi:10.1063/1.1692063 |
| [54] | Kazantsev, A. P., No article title, Sov. Phys. JETP, 26, 1031 (1968) |
| [55] | D.J. Amit, Field Theory, Renormalization Group, and Critical Phenomena (McGraw-Hill, New York, 1978) |
| [56] | J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon, Oxford, 1989) · Zbl 1033.81006 |
| [57] | A.N. Vasil’ev, Quantum-Field Renormalization Group in the Theory of Critical Phenomena and Stochastic Dynamics (Chapman & Hall/CRC, Boca Raton, 2004) · Zbl 1140.82019 |
| [58] | D.J. Amit, V. Martin-Mayor, Field Theory, Renormalization Group, and Critical Phenomena. Graphs to Computers, 3rd edn. (World Scientific, Singapore, 2005) · Zbl 1088.81001 |
| [59] | Adzhemyan, L. Ts.; Antonov, N. V.; Vasil’ev, A. N., No article title, Phys. Rev. E, 58, 1823 (1998) · doi:10.1103/PhysRevE.58.1823 |
| [60] | Adzhemyan, L. Ts.; Antonov, N. V.; Vasil’ev, A. N., No article title, Theor. Math. Phys., 120, 1074 (1999) · Zbl 0966.76033 · doi:10.1007/BF02557413 |
| [61] | Adzhemyan, L. Ts.; Antonov, N. V.; Barinov, V. A.; Kabrits, Yu. S.; Vasil’ev, A. N., No article title, Phys. Rev. E, 63, 025303 (2001) · doi:10.1103/PhysRevE.63.025303 |
| [62] | Adzhemyan, L. Ts.; Antonov, N. V.; Barinov, V. A.; Kabrits, Yu. S.; Vasil’ev, A. N., No article title, Phys. Rev. E, 64, 056306 (2001) · doi:10.1103/PhysRevE.64.056306 |
| [63] | Adzhemyan, L. Ts.; Antonov, N. V.; Hnatich, M.; Novikov, S. V., No article title, Phys. Rev. E, 63, 016309 (2000) · doi:10.1103/PhysRevE.63.016309 |
| [64] | Jurčišinová, E.; Jurčišin, M.; Remecký, R.; Scholtz, M., No article title, Int. J. Mod. Phys. B, 22, 3589 (2008) · Zbl 1149.76630 · doi:10.1142/S0217979208048565 |
| [65] | Jurčišinová, E.; Jurčišin, M., No article title, Phys. Rev. E, 77, 016306 (2008) · doi:10.1103/PhysRevE.77.016306 |
| [66] | Antonov, N. V., No article title, Phys. Rev. E, 60, 6691 (1999) · Zbl 1062.76512 · doi:10.1103/PhysRevE.60.6691 |
| [67] | Adzhemyan, L. Ts.; Antonov, N. V.; Honkonen, J., No article title, Phys. Rev. E, 66, 036313 (2002) · doi:10.1103/PhysRevE.66.036313 |
| [68] | Adzhemyan, L. Ts.; Antonov, N. V., No article title, Phys. Rev. E, 58, 7381 (1998) · doi:10.1103/PhysRevE.58.7381 |
| [69] | Antonov, N. V.; Honkonen, J., No article title, Phys. Rev. E, 63, 036302 (2001) · doi:10.1103/PhysRevE.63.036302 |
| [70] | Chkhetiani, O. G.; Hnatich, M.; Jurčišinová, E.; Jurčišin, M.; Mazzino, A.; Repašan, M., No article title, Phys. Rev. E, 74, 036310 (2006) · doi:10.1103/PhysRevE.74.036310 |
| [71] | Chkhetiani, O. G.; Hnatich, M.; Jurčišinová, E.; Jurčišin, M.; Mazzino, A.; Repašan, M., No article title, J. Phys. A: Math. Gen., 39, 7913 (2006) · Zbl 1122.76040 · doi:10.1088/0305-4470/39/25/S08 |
| [72] | Chkhetiani, O. G.; Hnatich, M.; Jurčišinová, E.; Jurčišin, M.; Mazzino, A.; Repašan, M., No article title, Czech. J. Phys., 56, 827 (2006) · doi:10.1007/s10582-006-0134-2 |
| [73] | Adzhemyan, L. Ts.; Antonov, N. V.; Honkonen, J.; Kim, T. L., No article title, Phys. Rev. E, 71, 016303 (2005) · doi:10.1103/PhysRevE.71.016303 |
| [74] | Gladysheva, A. V.; Jurčišinová, E.; Jurčišin, M.; Remecký, R., No article title, Phys. Part. Nucl., 41, 1023 (2010) · doi:10.1134/S1063779610070099 |
| [75] | Jurčišinová, E.; Jurčišin, M.; Remecký, R., No article title, Phys. Rev. E, 80, 046302 (2009) · doi:10.1103/PhysRevE.80.046302 |
| [76] | Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V., No article title, Phys. Rev. E, 97, 033101 (2018) · doi:10.1103/PhysRevE.97.033101 |
| [77] | Adzhemyan, L. Ts.; Antonov, N. V.; Runov, A. V., No article title, Phys. Rev. E, 64, 046310 (2001) · doi:10.1103/PhysRevE.64.046310 |
| [78] | Hnatič, M.; Jurčišin, M.; Mazzino, A.; Šprinc, S., No article title, Acta Phys. Slov., 52, 559 (2002) |
| [79] | Novikov, S. V., No article title, J. Phys. A: Math. Gen., 39, 8133 (2006) · Zbl 1122.76046 · doi:10.1088/0305-4470/39/25/S23 |
| [80] | Jurčišinová, E.; Jurčišin, M.; Remecký, R.; Scholtz, M., No article title, Phys. Part. Nucl. Lett., 5, 219 (2008) · doi:10.1134/S1547477108030175 |
| [81] | Jurčišinová, E.; Jurčišin, M.; Remecký, R., No article title, J. Phys. A: Math. Theor., 42, 275501 (2009) · Zbl 1421.76058 · doi:10.1088/1751-8113/42/27/275501 |
| [82] | Antonov, N. V.; Gulitskiy, N. M., No article title, Theor. Math. Phys., 176, 851 (2013) · Zbl 1286.76136 · doi:10.1007/s11232-013-0072-7 |
| [83] | Adzhemyan, L. Ts.; Antonov, N. V.; Gol’din, P. B.; Kompaniets, M. V., No article title, J. Phys. A: Math. Theor., 46, 135002 (2013) · Zbl 1264.82054 · doi:10.1088/1751-8113/46/13/135002 |
| [84] | Antonov, N. V.; Gulitskiy, N. M., No article title, Phys. Rev. E, 91, 013002 (2015) · doi:10.1103/PhysRevE.91.013002 |
| [85] | Antonov, N. V.; Gulitskiy, N. M., No article title, Phys. Rev. E, 92, 043018 (2015) · doi:10.1103/PhysRevE.92.043018 |
| [86] | Antonov, N. V.; Kostenko, M. M., No article title, Phys. Rev. E, 92, 053013 (2015) · doi:10.1103/PhysRevE.92.053013 |
| [87] | Antonov, N. V.; Gulitskiy, N. M., No article title, EPJ Web Conf., 108, 02008 (2016) · doi:10.1051/epjconf/201610802008 |
| [88] | Hnatich, M.; Honkonen, J.; Jurčišin, M.; Mazzino, A.; Šprinc, S., No article title, Phys. Rev. E, 71, 066312 (2005) · doi:10.1103/PhysRevE.71.066312 |
| [89] | Antonov, N. V.; Gulitskiy, N. M., No article title, Phys. Rev. E, 85, 065301 (2012) · doi:10.1103/PhysRevE.85.065301 |
| [90] | Antonov, N. V.; Gulitskiy, N. M., No article title, Lecture Notes Comput. Sci., 7125, 128 (2012) · doi:10.1007/978-3-642-28212-6_11 |
| [91] | Jurčišinová, E.; Jurčišin, M., No article title, J. Phys. A: Math. Theor., 45, 485501 (2012) · Zbl 1339.82003 · doi:10.1088/1751-8113/45/48/485501 |
| [92] | Jurčišinová, E.; Jurčišin, M., No article title, Phys. Rev. E, 88, 011004 (2013) · doi:10.1103/PhysRevE.88.011004 |
| [93] | Jurčišinová, E.; Jurčišin, M., No article title, Phys. Rev. E, 91, 063009 (2015) · doi:10.1103/PhysRevE.91.063009 |
| [94] | Jurčišinová, E.; Jurčišin, M.; Menkyna, M., No article title, Phys. Rev. E, 95, 053210 (2017) · doi:10.1103/PhysRevE.95.053210 |
| [95] | Chertkov, M.; Falkovich, G.; Lebedev, V., No article title, Phys. Rev. Lett., 76, 3707 (1996) · doi:10.1103/PhysRevLett.76.3707 |
| [96] | Eyink, G., No article title, Phys. Rev. E, 54, 1497 (1996) · doi:10.1103/PhysRevE.54.1497 |
| [97] | Bouchaud, J. P.; Comtet, A.; Georges, A.; Le Doussal, P., No article title, J. Phys. (Paris), 48, 1445 (1987) · doi:10.1051/jphys:019870048090144500 |
| [98] | Bouchaud, J. P.; Comtet, A.; Georges, A.; Le Doussal, P., No article title, J. Phys. (Paris), 49, 369 (1988) · doi:10.1051/jphys:01988004902036900 |
| [99] | Bouchaud, J. P.; Georges, A., No article title, Phys. Rep., 195, 127 (1990) · doi:10.1016/0370-1573(90)90099-N |
| [100] | Honkonen, J.; Karjalainen, E., No article title, J. Phys. A, 21, 4217 (1988) · doi:10.1088/0305-4470/21/22/023 |
| [101] | Honkonen, J.; Pis’mak, Yu. M.; Vasil’ev, A. N., No article title, J. Phys. A, 21, l835 (1989) · Zbl 0653.60110 · doi:10.1088/0305-4470/21/17/004 |
| [102] | Honkonen, J.; Pis’mak, Yu. M., No article title, J. Phys. A, 22, l899 (1989) · Zbl 0707.60104 · doi:10.1088/0305-4470/22/18/010 |
| [103] | Fournier, J. D.; Sulem, P. L.; Pouquet, A., No article title, J. Phys. A, 15, 1393 (1982) · Zbl 0498.76097 · doi:10.1088/0305-4470/15/4/037 |
| [104] | Adzhemyan, L. Ts.; Vasil’ev, A. N.; Gnatich, M., No article title, Theor. Math. Phys., 64, 777 (1985) · Zbl 0637.76049 · doi:10.1007/BF01017957 |
| [105] | Martin, P. C.; Siggia, E. D.; Rose, H. A., No article title, Phys. Rev. A, 8, 423 (1973) · doi:10.1103/PhysRevA.8.423 |
| [106] | De Dominicis, C., No article title, J. Phys. (Paris), Colloq., 37, c1-247 (1976) · doi:10.1051/jphyscol:1976138 |
| [107] | Janssen, H. K., No article title, Z. Phys. B, 23, 377 (1976) · doi:10.1007/BF01316547 |
| [108] | Bausch, R.; Janssen, H. K.; Wagner, H., No article title, Z. Phys. B, 24, 113 (1976) · doi:10.1007/BF01312880 |
| [109] | Jurčišinová, E.; Jurčišin, M., No article title, Phys. Part. Nucl., 44, 360 (2013) · doi:10.1134/S1063779613020184 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
