[1] MOREAU R.Magnetohydrodynamics[M].London:Kluwer Academic Publisher,1990.
[2] VOROBEV A,ZIKANOV O.Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field[J].Journal of Fluid Mechanics,2007,574(574):131-154.
[3] HARTMANN J. Hg-Dynamics I:Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field[J].Kongelige Danske Videnskabernes Selskab,Matematisk-Fysiske Meddelelser,1937,15(6):1-28.
[4] HARTMANN J,LAZARUS F.Hg-Dynamics Ⅱ:Experimental investigations on the flow of mercury in a homogeneous magnetic field[M].Kongelige Danske Videnskabernes Selskab,Matematisk-Fysiske Meddelelser,1937,15(7):1-45.
[5] SHERCLIFF J A.Steady motion of conducting fluids in pipes under transverse magnetic fields[J].Mathematical Proceedings of the Cambridge Philosophical Society,1953,49(1):136-144.
[6] KINET M,KNAEPEN B,MOLOKOV S.Instabilities and transition in magnetohydrodynamic flows in ducts with electrically conducting walls[J].Physical Review Letters,2009,103(15):154501.
[7] DAVIDSON P A.Magnetohydrodynamics in materials processing[J].Annual Review of Fluid Mechanics,1999,31(1):273-300.
[8] 王宝峰,李建超.电磁搅拌技术在连铸生产中的应用[J].鞍钢技术,2009(1):1-5.
[9] MORLEY N B,SMOLENTSEV S,BARLEON L,et al.Liquid magnetohydrodynamics-recent progress and future directions for fusion[J].Fusion Engineering and Design,2000,51:701-713.
[10] SMOLENTSEV S,MOREAU R,BÜHLER L,et al.MHD thermofluid issues of liquid-metal blankets:phenomena and advances[J].Fusion Engineering and Design,2010,85:1196-1205.
[11] BRANOVER H.Magnetohydrodynamic flow in ducts[M].New York:John Wiley,1978.
[12] CHOWDHURY V,BÜHLER L,MISTRANGELO C,et al.Experimental study of instabilities in magnetohydrodynamic boundary layers[J].Fusion Engineering and Design,2015,98:1751-1754.
[13] JIANMEI W,JIANFENG K,YANJUAN Z,et al.Viscosity monitoring and control on oil-filmbearing lubrication with Ferro fluids[J].Tribology International,2014,75(5):61-68.
[14] AL-SHAIKHLI A K,H FATIMA K O,A FADHIL J L.The magnetic field study of a finite solenoid[J].Circuits and Systems,2013,4(3):316-322.
[15] MURGATROYD W.Experiments on magneto-hydrodynamic channel flow[J].Philosophical Magazine,1953,44(359):1348-1354.
[16] LYKOUDIS P S.Transition from laminar to turbulent flow in magneto-fluid mechanic channels[J].Reviews of Modern Physics,1960,32(4):796-798.
[17] BRANOVER G G.Resistance of magnetohydrodynamic channels[J].Magnetohydrodynamics,1967,3(4):1-11.
[18] MORESCO P,ALBOUSSIÉRET.Experimental study of the instability of the Hartmann layer[J].Journal of Fluid Mechanics,2004,504(1):167-181.
[19] CHOWDHURY V,BÜHLER L,MISTRANGELO C,et al.Experimental study of instabilities in magnetohydrodynamic boundary layers[J].Fusion Engineering and Design,2015,98:1751-1754.
[20] SHATROV V,GERBETH G.Marginal turbulent magne-tohydrodynamic flow in a square duct[J].Physics of Fluids,2010,22(8):585-591.
[21] ZHAO Y,ZIKANOV O.Instabilities and turbulence in magnetohydrodynamic flow in a toroidal duct prior to transition in Hartmann layers[J].Journal of Fluid Mechanics,2012,692:288-316.
[22] ZIKANOV O,KRASNOV D,BOECK T,et al.Laminar-turbulent transition in magnetohydrodynamic duct,pipe,and channel flows[J].Applied Mechanics Reviews,2014,66(3):030802.
[23] 杨小龙,符松.直接数值模拟/大涡模拟中数值误差影响的研究[J].应用数学和力学,2008,29(7):790-798.
[24] KOBAYASHI H.Large eddy simulation of magnetohydrod-ynamic turbulent duct flows[J].Physics of Fluids,2008,20(1):015102.
[25] KOBAYASHI H.Large eddy simulation of magnetohydrod-ynamic turbulent channel flows with local subgrid-scale model based on coherent structures[J].Physics of Fluids,2006,18(4):045107.
[26] VOROBEV A,ZIKANOV O.Smagorinsky constant in LES modeling of anisotropic MHD turbulence[J].Theoretical and Computational Fluid Dynamics,2008,22(3):317-325.
[27] ROBERTS P H.An introduction to magnetohydrodynamics[M].London:Longmans,GreenCo,1967.
[28] LUNDQUIST Stig.Studies in magnetohydrodynamics[J].Arkiv für Fysik,1952,5(4):297-347.
[29] LOCK R C.The stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field[J].Proceedings of the Royal Society A:Mathematical Physical & Engineering Sciences,1955,233(1192):105-125.
[30] TAKASHIMA M. The stability of the modified plane Poiseuille flow in the presence of a transverse magnetic field[J].Fluid Dynamics Research,1996,17(6):293-310.
[31] TAKASHIMA M.The stability of the modified plane Couette flow in the presence of a transverse magnetic field[J].Fluid Dynamics Research,1998,22(2):105-121.
[32] LINGWOOD R J,ALBOUSSI?RE T.On the stability of the Hartmann layer[J].Physics of Fluids,1999,11(8):2058-2068.
[33] SCHMID P J,HENNINGSON D S.Stability and transition in shear flows[M].New York:Springer-Verlag,2001.
[34] GERARD-VARET,D.Amplification of small perturbations in a Hartmann layer[J].Physics of Fluids,2002,14(4):1458-1467.
[35] AIRIAU C,CASTETS M.On the amplification of small disturbances in a channel flow with a normal magnetic field[J].Physics of Fluids,2004,16(8):2991-3005.
[36] KRASNOV D S,ZIENICKE E,ZIKANOV O,et al. Numerical study of the instability of the Hartmann layer[J]. Journal of Fluid Mechanics,2004,504:183-211.
[37] ZIENICKE E,KRASNOV D.Parametric study of streak breakdown mechanism in Hartmann flow[J].Physics of Fluids,2005,17(11):114101.
[38] 董帅,林殿吉,吕玉坤.哈特曼边界层的初级稳定性分析[J].力学学报,2016,48(2):327-335.
[39] ZAKIR HUSSAIN.磁场作用下金属流体线性稳定性分析[D].北京:中国科学院大学,2012.
[40] ZAKIR HUSSAIN,刘婵,倪明玖,等.平行平板间导电流体的磁流体动力学稳定性[J].中国科学院研究生院学报,2013,30(3):304-310.
[41] BÜHLER L.Instabilities in quasi-two-dimensional magnet-ohydrodyamic flows[J].Journal of Fluid Mechanics,1996,326:125-150.
[42] 董帅,刘立帅,叶学民.磁场作用下壁面导电率对导电流体流动稳定性的影响[J].华北电力大学学报(自然科学版),2017,(1):103-110.
[43] BOECK T,KRASNOV D,ROSSI M,et al.Transition to turbulence in MHD channel flow with spanwise magnetic field[C]//Proceedings of the Summer Program,2006:363-374.
[44] KRASNOV D,ROSSI M,ZIKANOV O,et al.Optimal growth and transition to turbulence in channel flow with spanwise magnetic field[J].Journal of Fluid Mechanics,2008,596:73-101.
[45] KRASNOV D,PAREPALLI P,ZIKANOV O,et al.Effect of wall conductivity on turbulent channel flow under spanwise magnetic field[J].Proceedings in Applied Mathematics and Mechanics,2010,10(1):515-516.
[46] 董帅,李本文.平行磁场作用下的低雷诺数平板流研究[J].东北大学学报(自然科学版),2012,33(8):1154-1157.
[47] DONG S,KRASNOV D,LI B W,et al.Instability of streaks in channel flow with a streamwise magnetic field[J].Magnetohydrodynamics,2012,48(1):57-67.
[48] DONG S,KRASNOV D,BOECK T.Secondary energy growth and turbulence suppression in conducting channel flow with streamwise magnetic field[J].Physics of Fluids(1994-present),2012,24(7):074101.
[49] MÜLLER U,BÜHLER L.Magnetofluiddynamics in channels and containers[M].Berlin:Springer,2001.
[50] POTHÉRAT A.Quasi-two-dimensional perturbations in duct flows under transverse magnetic field[J].Physics of Fluids(1994-present),2007,19(7):074104.
[51] BIAU D,SOUEID H,BOTTARO A.Transition to turbulence in duct flow[J].Journal of Fluid Mechanics,2008,596:133-142.
[52] KRASNOV D,ZIKANOV O,ROSSI M,et al.Optimal linear growth in magnetohydrodynamic duct flow[J].Journal of Fluid Mechanics,2010,653(1):273-299.
[53] 刘婵,倪明玖,胡军,等.绝缘方腔中MHD流体流动的线性稳定性分析[C]//中国力学学会、西安交通大学.中国力学大会——2013论文摘要集.西安:中国力学学会、西安交通大学,2013.
[54] BOECK T,KRASNOV D,THESS A,et al.Large-scale intermittency of liquid-metal channel flow in a magnetic field[J].Physical Review Letters,2008,101(24):244501.
[55] KRASNOV D,ZIKANOV O,THESS A,et al.Direct numerical simulation of transition in MHD duct flow[J].Proceedings in Applied Mathematics and Mechanics,2011,1(1):659-660.
[56] KRASNOV D,ZIKANOV O,BOECK T.Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers[J].Journal of Fluid Mechanics,2012,704:421-446.
[57] HU J,LIU C,ZHANG N M,et al.Optimal linear growth of MHD flow in a square duct[C]//Simos T E,Tsitouras C.AIP Conference Proceedings.AIP Publishing,2015,1648(1):030025.
[58] PRIEDE J,ALEKSANDROVA S,MOLOKOV S.Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct[J].Journal of Fluid Mechanics,2012,708:111-127.
[59] TATSUMI T,YOSHIMURA T.Stability of the laminar flow in a rectangular duct[J].Journal of Fluid Mechanics,1990,212:437-449.
[60] UHLMANN M,NAGATA M.Linear stability of flow in an internally heated rectangular duct[J].Journal of Fluid Mechanics,2006,551:387-404.
[61] HUNT J C R.Magnetohydrodynamic flow in rectangular ducts[J].ournal of Fluid Mechanics,1965,21(4):577-590.
[62] PRIEDE J,ALEKSANDROVA S,MOLOKOV S.Linear stability of Hunt's flow[J].Journal of Fluid Mechanics,2010,649:115-134.
[63] TING A L,WALKER J S,MOON T J,et al.Linear stability analysis for high-velocity boundary layers in liquid-metal magnetohydrodynamic flows[J].International Journal of Engineering Science,1991,29(8):939-948.
[64] BRAIDEN L,KRASNOV D,MOLOKOV S,et al.Transition to turbulence in Hunt's flow in a moderate magnetic field[J].Europhysics Letters,2016,115(4):44002.
[65] SMOLENTSEV S,MOREAU R,ABDOU M.Characteri-zation of key magnetohydrodynamic phenomena in PbLi flows for the US DCLL blanket[J].Fusion Engineering and Design,2008,83(5):771-783.
[66] VANTIEGHEM S,KNAEPEN B.Numerical simulation of magnetohydrodynamic flow in a toroidal duct of square cross-section[J].International Journal of Heat and Fluid Flow,2011,32(6):1120-1128.
[67] ROBERTS P H.Singularities of Hartmann Layers[J].Proceedings of the Royal Society A,1967,300(1460):94-107.
[68] ÅKERSTEDT H O.Damping of transient energy growth of three-dimensional perturbations in hydromagnetic pipe flow[J].Fluid Dynamics Research,1995,15(5):295-312.
[69] SATAKE S,KUNUGI T,SMOLENTSEV S. Direct numerical simulations of turbulent pipe flow in a transverse magnetic field[J].Journal of Turbulence.2002,3(20):1-12.
[70] MANNEVILLE P.Understanding the sub-critical transition to turbulence in wall flows[J].Pramana,2008,70(6):1009-1021. |