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利用corner transport upwind和constrained transport算法求解非理想磁流体动力学方程组, 对匀强平行磁场作用下, 黏性各向异性等离子体自由剪切层中的Kelvin-Helmholtz不稳定性进行了数值模拟. 从流动结构、涡结构演化、磁场分布、横向磁压力、抗弯磁张力等角度对各向同性和各向异性黏性算例结果进行了讨论, 分析了黏性各向异性对Kelvin-Helmholtz不稳定性的影响. 结果表明, 黏性各向异性比黏性各向同性更利于流动的稳定. 其稳定性作用是由于磁感线方向上剪切速率降低导致界面卷起程度和圈数的降低, 并使卷起结构中小涡产生增殖、合并, 破坏了涡的常规增长, 从而导致流动的稳定. 黏性各向异性对横向磁压力的影响比对抗弯磁张力更大.
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关键词:
- 磁流体动力学 /
- 开尔文-亥姆霍兹不稳定性 /
- 黏性各向异性 /
- 涡
Kelvin-Helmholtz instability in anisotropic viscous fluid with uniform density in the presence of magnetic field is simulated through solving the non-ideal magnetohydrodynamic equations. The magnetic field is uniform and parallel to the stream. The magnetohydrodynamic equations are solved by corner transport upwind algorithm and constrained transport algorithm. In this paper, the influence of viscous anisotropy on Kelvin-Helmholtz instability is studied. The viscous anisotropy is embodied in the direction of the magnetic field, that is, viscosity parallel to the direction of the magnetic field line is much larger than that in the other directions. The results in the isotropic and the anisotropic viscous cases are compared from the aspects of flow structure, vortex evolution, and magnetic field distribution. It shows that the viscous anisotropy is more advantageous to the stability in a magnetized shear layer than the viscous isotropy. The flow structure evolves similarly in large scales but vortices evolve differently in small scales. Due to the decrease of the shear rate in the direction of the magnetic field lines, the rolling-up degree of interface and the number of laps decrease; the multiplication and merging of small vortices in the rolled-up structure destroy the regular growth of the vortex, which contributes to the stability of the flow. The increase of the magnetic energy at the sheared interface slows down effectively by the viscous anisotropy, which weakens the growth of the transverse magnetic pressure and anti-bending magnetic tension. However, viscous anisotropy shows much greater influence on the transverse magnetic pressure than on the anti-bending magnetic tension. The total enstrophy decreases slowly in viscous isotropy and anisotropy case. It increases quickly in late time in the former case, but is heavily suppressed in the latter case.-
Keywords:
- magnetohydrodynamics /
- Kelvin-Helmholtz instability /
- viscous anisotropy /
- vortex
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图 2 不同时刻自由剪切层示踪剂浓度场 (a)各向同性黏性(Re = 105); (b) 各向异性黏性(Re0 = 105, Re|| = 100)
Fig. 2. Tracer concentration field at different times: (a) Isotropic viscous case (Re = 105); (b) anisotropic viscous case (Re0 = 105, Re|| = 100).
图 3 不同时刻, 各向同性黏性(Re = 105)算例涡结构云图及流线 (a) t = 5.5; (b) t = 7.0; (c) t = 7.5; (d) t = 8.0; (e) t = 9.0; (f) t = 10
Fig. 3. Rortex field with streamlines at different times in isotropic viscous fluid (Re = 105): (a) t = 5.5; (b) t = 7.0; (c) t = 7.5; (d) t = 8.0; (e) t = 9.0; (f) t = 10.
图 4 不同时刻各向异性黏性(Re0 = 105, Re|| = 100)算例涡结构云图及流线 (a) t = 5.5; (b) t = 7.0; (c) t = 7.5; (d) t = 8.0; (e) t = 9.0; (f) t = 10
Fig. 4. Rortex field with streamlines at different times in anisotropic viscous fluid (Re0 =105, Re|| = 100): (a) t = 5.5; (b) t = 7.0; (c) t = 7.5; (d) t = 8.0; (e) t = 9.0; (f) t = 10.
图 5 不同时刻剪切层中磁场云图和磁感线 (a)各向同性黏性(Re = 105); (b) 各向异性黏性(Re0 = 105, Re|| = 100)
Fig. 5. Magnetic field with field lines at different times: (a) Isotropic viscous case (Re = 105); (b) anisotropic viscous case (Re0 = 105, Re|| = 100)
图 7 平均磁能密度放大倍数随时间的变化
Fig. 7. Evolution of the amplification factor of average magnetic energy.
图 8 平均横向磁压力和抗弯磁张力随时间的变化 (a) 横向磁压力; (b) 抗弯磁张力
Fig. 8. Evolution of the average transverse magnetic pressure and anti-bending magnetic tension: (a) Transverse magnetic pressure; (b) anti-bending magnetic tension.
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[1] Michikoshi S, Inutsuka, S I 2006 Astrophys. J. 641 1131
Google Scholar
[2] Latter H N, Papaloizou J 2018 Mon. Not. R. Astron. Soc. 474 3110
Google Scholar
[3] Masson A, Nykyri K 2018 Space Sci. Rev. 214 71
Google Scholar
[4] Faganello M, Califano F 2017 J. Plasma Phys. 83 535830601
Google Scholar
[5] Ma X Y, Otto A, Delamere P A 2014 J. Geophys. Res.: Space 119 781
Google Scholar
[6] Srinivasan B, Tang X Z 2013 Phys. Plasmas 20 056307
Google Scholar
[7] Wang L F, Ye W H, He X T, et al 2017 Sci. China: Phys. Mech. Astron. 60 055201
Google Scholar
[8] Zhou Y 2017 Phys. Rep. 720-722 1
Google Scholar
[9] Rao P A, Fuelberg H E 2000 Mon. Weather Rev. 128 3437
Google Scholar
[10] Soloviev A V, Lukas R, Donelan M A, Haus B K, Ginis I 2017 J. Geophys. Res.: Oceans 122 10174
Google Scholar
[11] Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Clarendon Press)
[12] Ho C M, Huerre P 1984 Annu. Rev. Fluid Mech. 16 365
Google Scholar
[13] Winant C D, Browand F K 1974 J. Fluid Mech. 63 237
Google Scholar
[14] Brown G L, Roshko A 1986 J. Fluid Mech. 170 499
Google Scholar
[15] 王立锋, 叶文华, 李英骏 2008 物理学报 57 3038
Google Scholar
Wang L F, Ye W H, Li Y J 2008 Acta Phys. Sin. 57 3038
Google Scholar
[16] 王立锋, 叶文华, 范征锋, 孙彦乾, 郑炳松, 李英骏 2009 物理学报 58 6381
Google Scholar
Wang L F, Ye W H, Fan Z F, Sun Y Q, Zheng B S, Li Y J 2009 Acta Phys. Sin. 58 6381
Google Scholar
[17] Talwar S P 1965 Phys. Fluids 8 1295
Google Scholar
[18] Duhau S, Gratton J 1975 J. Plasma Phys. 13 451
Google Scholar
[19] Srivastava K M, Vyas D N 1979 Astrophys. Space Sci. 62 353
Google Scholar
[20] Choudhury S R, Patel V L 1985 Phys. Fluids 28 3292
Google Scholar
[21] Choudhury S R 1986 Phys. Fluids 29 1509
Google Scholar
[22] Ruderman M S, Verwichte E, Erdélyi R, Goossens M 1996 J. Plasma Phys. 56 285
Google Scholar
[23] Brown K G, Choudhury S R 2002 Q. Appl. Math. 60 601
Google Scholar
[24] Prajapati R P, Chhajlani R K 2010 Phys. Plasmas 17 112108
Google Scholar
[25] Gardiner T A, Stone J M 2008 J. Comput. Phys. 227 4123
Google Scholar
[26] Liu C Q, Wang Y Q, Yang Y, Duan Z W 2016 Sci. China: Phys. Mech. Astron. 59 684711
Google Scholar
[27] Liu Y, Chen Z H, Zhang H H, Lin Z Y 2018 Phys. Fluids 30 044102
Google Scholar
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