The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics

Yuan Li; Ravi Samtaney; Vincent Wheatley

doi:10.1016/j.mre.2018.01.003

[1] R.D. Richtmyer, Taylor instability in shock acceleration of compressible fluids, Commun. Pure Appl. Math. 13 (2) (1960) 297-319.

[2] E.E. Meshkov, Instability of the interface of two gases accelerated by a shock wave, Fluid Dynam. 4 (5) (1969) 101-104.

[3] D. Arnett, The role of mixing in astrophysics, Astrophys. J. Suppl. Series 127 (2) (2000) 213.

[4] A.M. Khokhlov, E.S. Oran, G.O. Thomas, Numerical simulation of deflagration-to-detonation transition: the role of shock-flame interactions in turbulent flames, Combust. Flame 117 (1) (1999) 323-339.

[5] J. Yang, T. Kubota, E.E. Zukoski, Applications of shock-induced mixing to supersonic combustion, AIAA J. 31 (5) (1993) 854-862.

[6] J. Lindl, Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain, Phys. Plasmas 2 (11) (1995) 3933-4024.

[7] P.Y. Chang, G. Fiksel, M. Hohenberger, J.P. Knauer, R. Betti, et al., Fusion yield enhancement in magnetized laser-driven implosions, Phys. Rev. Lett. 107 (3) (2011) 035006.

[8] M. Hohenberger, P.Y. Chang, G. Fiksel, J.P. Knauer, R. Betti, et al., Inertial confinement fusion implosions with imposed magnetic field compression using the OMEGA Laser, Phys. Plasmas 19 (5) (2012), 056306.

[9] L.J. Perkins, B.G. Logan, G.B. Zimmerman, C.J. Werner, Two-dimensional simulations of thermonuclear burn in ignition-scale inertial confinement fusion targets under compressed axial magnetic fields, Phys. Plasmas 20 (7) (2013), 072708.

[10] J.W. Strutt, L. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, Proc. London Math. Soc. 14 (1) (1883) 8.

[11] G. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes I, in: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 201, The Royal Society, 1950, pp. 192-196.

[12] R. Samtaney, Suppression of the Richtmyer-Meshkov instability in the presence of a magnetic field, Phys. Fluids 15 (8) (2003) L53-L56.

[13] V. Wheatley, D.I. Pullin, R. Samtaney, Stability of an impulsively accelerated density interface in magnetohydrodynamics, Phys. Rev. Lett. 95 (12) (2005), 125002.

[14] V. Wheatley, R. Samtaney, D.I. Pullin, The Richtmyer-Meshkov instability in magnetohydrodynamics, Phys. Fluids 21 (8) (2009), 082102.

[15] V. Wheatley, R. Samtaney, D.I. Pullin, R.M. Gehre, The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics, Phys. Fluids 26 (1) (2014), 016102.

[16] V. Wheatley, R.M. Gehre, R. Samtaney, D.I. Pullin, The magnetohydrodynamic Richtmyer-Meshkov instability: the oblique field case, in: 29th International Symposium on Shock Waves 2, Springer, 2015, pp. 1107-1112.

[17] R. Samtaney, A method to simulate linear stability of impulsively accelerated density interfaces in ideal-MHD and gas dynamics, J. Comput. Phys. 228 (18) (2009) 6773-6783.

[18] A. Bakhsh, S. Gao, R. Samtaney, V. Wheatley, Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics, Phys. Fluids 28 (3) (2016) 034106.

[19] A. Bakhsh, R. Samtaney, Linear analysis of converging RichtmyereMeshkov instability in the presence of an azimuthal magnetic field, J. Fluids Eng. 140 (5) (2018) 050901.

[20] W. Mostert, V. Wheatley, R. Samtaney, D.I. Pullin, Effects of magnetic fields on magnetohydrodynamic cylindrical and spherical Richtmyer- Meshkov instability, Phys. Fluids 27 (10) (2015) 104102.

[21] W. Mostert, D.I. Pullin, V. Wheatley, R. Samtaney, Magnetohydrodynamic implosion symmetry and suppression of Richtmyer-Meshkov instability in an octahedrally symmetric field, Phys. Rev. Fluids 2 (1) (2017) 013701.

[22] K.O. Mikaelian, Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells, Phys. Rev. A 42 (6) (1990) 3400.

[23] K.O. Mikaelian, Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells, Phys. Fluids 17 (9) (2005) 094105.

[24] J.P. Goedbloed, R. Keppens, S. Poedts, Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas, Cambridge University Press, 2010.

[25] J.U. Brackbill, D.C. Barnes, The effect of nonzero VB on the numerical solution of the magnetohydrodynamic equations, J. Comput. Phys. 35 (3) (1980) 426-430.

[26] R. Samtaney, P. Colella, T.J. Ligocki, D.F. Martin, S.C. Jardin, An adaptive mesh semi-implicit conservative unsplit method for resistive MHD, in: Journal of Physics: Conference Series, vol. 16, IOP Publishing, 2005, p. 40.

[27] M. Adams, P. Colella, D. T. Graves, J. N. Johnson, H. S. Johansen, et al., Chombo Software Package for AMR Applications Design Document.

[28] W. Mostert, V. Wheatley, R. Samtaney, D.I. Pullin, Effects of seed magnetic fields on magnetohydrodynamic implosion structure and dynamics, Phys. Fluids 26 (12) (2014) 126102.

[29] M. Lombardini, D.I. Pullin, Small-amplitude perturbations in the threedimensional cylindrical Richtmyer-Meshkov instability, Phys. Fluids 21 (11) (2009) 114103.