Sub-grid-scale model for studying Hall effects on macroscopic aspects of magnetohydrodynamic turbulence. (English) Zbl 1537.76051
Summary: A new sub-grid-scale model is developed for studying influences of the Hall term on macroscopic aspects of magnetohydrodynamic turbulence. Although the Hall term makes numerical simulations extremely expensive by exciting high-wave-number coefficients and makes magnetohydrodynamic equations stiff, studying macroscopic aspects of magnetohydrodynamic turbulence together with the Hall term is meaningful since this term often influences not only sub-ion-scales but also macroscopic scales. Our new sub-ion-scale sub-grid-scale model for large eddy simulations of Hall magnetohydrodynamic turbulence is developed in order to overcome the difficulties. Large eddy simulations by the use of the new model successfully reproduce statistical signatures such as the energies and probability density functions of the vorticity and current density, keeping some signatures intrinsic to Hall magnetohydrodynamic turbulence. Our new sub-grid-scale model enables numerical simulations of homogeneous and isotropic Hall magnetohydrodynamic turbulence with a small computational cost, improving the effective resolution of an LES from that carried out with earlier models, and retaining the ion-electron separation effects by the Hall term in the grid scales.
MSC:
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
References:
| [1] | Iroshnikov, P. S., Sov. Astron., 7, 566-571 (1964) |
| [2] | Kraichnan, R. H., Phys. Fluids, 8, 1385 (1965) |
| [3] | Sridhar, S.; Goldreich, P., Astrophys. J., 432, 612 (1994) |
| [4] | Goldreich, P.; Sridhar, S., Astrophys. J., 435, 680 (1997) |
| [5] | Stawicki, O.; Peter, G.; Li, Hui, J. Geophys. Res., 106 (2001), A8273-8281 |
| [6] | Cho, J.; Lazarian, A.; Vishniac, E. T., Astrophys. J., 566, L49 (2002) |
| [7] | Bale, S. D.; Kellogg, P. J.; Mozer, F. S.; Horbury, T. S.; Reme, H., Phys. Rev. Lett., 94, Article 215002 pp. (2002) |
| [8] | Biskamp, D., Magnetohydrodynamic Turbulence (2003), Cambridge University Press · Zbl 1145.76300 |
| [9] | Horbury, T. S.; Forman, M.; Oughton, S., Phys. Rev. Lett., 101, Article 175005 pp. (2008) |
| [10] | Alexandrova, O.; Saur, J.; Lacombe, C.; Mangeney, A.; Mitchell, J.; Schwartz, S. J.; Robert, P., Phys. Rev. Lett., 103, Article 165003 pp. (2009) |
| [11] | Kiyani, K. H.; Chapman, S. C.; Khotyaintsev, Yu. V.; Dunlop, M. W.; Sahraoui, F., Phys. Rev. Lett., 103, Article 075006 pp. (2009) |
| [12] | Servidio, S.; Matthaeus, W. H.; Shay, M. A.; Cassak, P. A.; Dmitruk, P., Phys. Rev. Lett., 102, Article 115003 pp. (2009) |
| [13] | Davidson, P. A., Turbulence in Rotating, Stratified and Electrically Conducting Fluids (2013), Cambridge University Press · Zbl 1282.76001 |
| [14] | Bruno, R.; Carbone, V., Turbulence in the Solar Wind (2016), Springer International Publishing: Springer International Publishing Switzerland |
| [15] | Mahajan, S. M.; Yoshida, Z., Phys. Plasmas, 7, 635 (2000) |
| [16] | Matthaeus, W. H.; Dmitruk, P.; Smith, D.; Ghosh, S.; Oughton, S., Geophys. Res. Lett., 30, Article GL017949 pp. (2003) |
| [17] | Smith, D.; Ghosh, S.; Dmitruk, P.; Matthaeus, W. H., Hall and turbulence effects on magnetic reconnection, Geophys. Res. Lett., 31, Article L02805 pp. (2004) |
| [18] | Ren, Y.; Yamada, M.; Gerhardt, S.; Ji, H.; Kulsrud, R.; Kuristyin, A., Phys. Rev. Lett., 95, Article 055003 pp. (2005) |
| [19] | Dmitruk, P.; Matthaeus, W. H., Phys. Plasmas, 13, Article 042307 pp. (2006) |
| [20] | Galtier, S.; Buchlin, E., Astrophysics, 656, 560-566 (2007) |
| [21] | Mininni, P.; Alexakis, A.; Pouquet, A., J. Plasma Phys., 73, 377 (2007) |
| [22] | Galtier, S., Phys. Rev. E, 77, Article 015302 pp. (2008) |
| [23] | Hori, D.; Miura, H., Plasma Fusion Res., 3, Article S1053 pp. (2008) |
| [24] | Meyrand, R.; Galtier, S., Phys. Rev. Lett., 109, Article 194501 pp. (2012) |
| [25] | Miura, H.; Araki, K., Plasma Phys. Control. Fusion, 55, Article 014012 pp. (2013) |
| [26] | Miura, H.; Araki, K., Phys. Plasmas, 21, Article 072313 pp. (2014) |
| [27] | Miura, H., Fluids, 4, 46 (2019) |
| [28] | Huba, J. D., Phys. Plasmas, 3, 2523 (1996) |
| [29] | Winske, D., Phys. Plasmas, 3, 3966 (1996) |
| [30] | Zhu, P.; Schnack, D. D.; Ebrahimi, F.; Zweibel, E. G.; Suzuki, M.; Hegna, C. C.; Sovinec, C. R., Phys. Rev. Lett., 101, Article 085005 pp. (2008) |
| [31] | Goto, R.; Miura, H.; Ito, A.; Sato, M.; Hatori, T., Plasma Fusion Res., 9, Article 1403076 pp. (2014) |
| [32] | Goto, R.; Miura, H.; Ito, A.; Sato, M.; Hatori, T., Phys. Plasmas, 22, Article 032115 pp. (2015) |
| [33] | Umeda, T.; Wada, Y., Phys. Plasmas, 24, Article 072307 pp. (2017) |
| [34] | Park, W.; Velova, E. V.; Fu, G. Y.; Tang, X. Z., Phys. Plasmas, 6, 1796 (1999) |
| [35] | Sugiyama, L. E.; Park, W., Phys. Plasmas, 7, 4644 (2000) |
| [36] | Sovinec, C. R.; Glasser, A.; Gianakon, T. A.; Barnes, D. C.; Nebel, R. A.; Kruger, S. E.; Schnack, D. D.; Plimpton, S. J.; Tarditi, A.; Chu, M. S., J. Comput. Phys., 195, 355 (2004) · Zbl 1087.76070 |
| [37] | H. Miura, R. Goto, A. Ito, M. Sato, T. Hatori, in: 25th IAEA FEC, TH/P5-17, Oct. 13-18 2014, St. Petersburg, Russia. |
| [38] | Braginskii, S. I., Transport processes in a plasma, (Leontovich, M. A., Reviews of Plasma Physics, vol. 1 (1965), Consultants Bureau: Consultants Bureau New York), 205 |
| [39] | Hazeltine, R. D.; Meiss, J. D., Plasma Confinement (1991), Addison Wesley |
| [40] | Schnack, D. D.; Barnes, D. C.; Brennan, D. P.; Hegna, C. C.; Held, E.; Kim, C. C.; Kruger, S. E.; Pankin, A. Y.; Sovinec, C. R., Phys. Plasmas, 13, Article 058103 pp. (2006) |
| [41] | Durbin, P. A.; Pettersson Reif, B. A., Statistical Theory and Modeling for Turbulent Flows (2001), John Wiley & Sons · Zbl 1030.76001 |
| [42] | Garnier, E.; Adams, N.; Sagaut, P., Large Eddy Simulation for Compressible Flows (2009), Springer-Verlag · Zbl 1179.76005 |
| [43] | Kobayashi, H., Phys. Plasmas, 18, Article 045107 pp. (2006) |
| [44] | Chermyshov, A. A.; Karelsky, K. V.; Petrosyan, A. S., Phys. Plasmas, 13, Article 104501 pp. (2006) |
| [45] | Hamba, F.; Tsuchiya, M., Phys. Plasmas, 17, Article 012301 pp. (2010) |
| [46] | Sondak, D.; Oberai, A., Phys. Plasmas, 19, Article 102308 pp. (2012) |
| [47] | Chermyshov, A. A.; Karelsky, K. V.; Petrosyan, A. S., Phys. Usp., 57, 421 (2014) |
| [48] | Miesch, M.; Matthaeus, W.; Brandenburg, A.; Petrosyan, A.; Pouquet, A.; Cambon, C.; Jenko, F.; Uzdensky, D.; Stone, J.; Tobias, S.; Toomre, J.; Velli, M., Space Sci. Rev., 194, 97 (2015) |
| [49] | Miura, H.; Araki, K.; Hamba, F., J. Comput. Phys., 316, 385 (2016) · Zbl 1349.76130 |
| [50] | Miura, H.; Hamba, F.; Ito, A., Nucl. Fusion, 57, Article 076034 pp. (2017) |
| [51] | Camporeale, E.; Sorriso-Valvo, L.; Califano, F.; Retinó, A., Phys. Rev. Lett., 120, Article 125101 pp. (2018) |
| [52] | Pekurovsky, D., SIAM J. Sci. Comput., 34, C192-C209 (2012) · Zbl 1253.65205 |
| [53] | Yoshizawa, A.; Yokoi, N., Phys. Plasmas, 5, 2902 (1998) |
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.
