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

Li Yuan; Samtaney Ravi; Wheatley Vincent

doi:10.1016/j.mre.2018.01.003

Volume 3 Issue 4

Jul. 2018

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Li Yuan, Samtaney Ravi, Wheatley Vincent. The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics[J]. Matter and Radiation at Extremes, 2018, 3(4). doi: 10.1016/j.mre.2018.01.003

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Li Yuan, Samtaney Ravi, Wheatley Vincent. The Richtmyer-Meshkov instability of a double-layer interface in convergent geometry with magnetohydrodynamics[J]. Matter and Radiation at Extremes, 2018, 3(4). doi: 10.1016/j.mre.2018.01.003

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

doi: 10.1016/j.mre.2018.01.003

1.
aMechanical Engineering, King Abdullah University of Science and Technology, Saudi Arabia
2.
bMechanical and Mining Engineering, The University of Queensland, Australia

More Information

Corresponding author: *Corresponding author. ravi.samtaney@kaust.edu.sa (R. Samtaney).
Received Date: 2017-11-08
Accepted Date: 2018-01-18
Publish Date: 2018-07-15

Abstract

Abstract

The interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field is numerically investigated within the framework of ideal magnetohydrodynamics. Three fluids of differing densities are initially separated by the two perturbed cylindrical interfaces. The initial incident converging shock is generated from a Riemann problem upstream of the first interface. The effect of the magnetic field on the instabilities is studied through varying the field strength. It shows that the Richtmyer-Meshkov and Rayleigh-Taylor instabilities are mitigated by the field, however, the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations. The degree of asymmetry of the interfacial growth rate is increased when the seed field strength is increased.
- Magnetohydrodynamics,
- Double density interfaces,
- Converging shock,
- Richtmyer-Meshkov instability

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References(29)

References

[1]	R.D. Richtmyer, Taylor instability in shock acceleration of compressible fluids, Commun. Pure Appl. Math. 13 (2) (1960) 297–319.10.1002/cpa.3160130207
[2]	E.E. Meshkov, Instability of the interface of two gases accelerated by a shock wave, Fluid Dynam. 4 (5) (1969) 101–104.10.1007/bf01015969
[3]	D. Arnett, The role of mixing in astrophysics, Astrophys. J. Suppl. Series 127 (2) (2000) 213.10.1086/313364
[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) 323–339.10.1016/s0010-2180(98)00076-5
[5]	J. Yang, T. Kubota, E.E. Zukoski, Applications of shock-induced mixing to supersonic combustion, AIAA J. 31 (5) (1993) 854–862.10.2514/3.11696
[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) 3933–4024.10.1063/1.871025
[7]	P.Y. Chang, G. Fiksel, M. Hohenberger, J.P. Knauer, et al., et al., Fusion yield enhancement in magnetized laser-driven implosions, Phys. Rev. Lett. 107 (3) (2011) 035006.10.1103/physrevlett.107.035006
[8]	M.H. ohenberger, 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) 056306.10.1063/1.3696032
[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) 072708.10.1063/1.4816813
[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) 8.10.1112/plms/s1-14.1.170
[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–L56.10.1063/1.1591188
[13]	V. Wheatley, D.I. Pullin, R. Samtaney, Stability of an impulsively accelerated density interface in magnetohydrodynamics, Phys. Rev. Lett. 95 (12) (2005) 125002.10.1103/physrevlett.95.125002
[14]	V. Wheatley, R. Samtaney, D.I. Pullin, The Richtmyer-Meshkov instability in magnetohydrodynamics, Phys. Fluids 21 (8) (2009) 082102.10.1063/1.3194303
[15]	V. Wheatley, R. Samtaney, D.I. Pullin, R.M. Gehre, The transverse field Richtmyer-Meshkov instability in magnetohydrodynamics, Phys. Fluids 26 (1) (2014) 016102.10.1063/1.4851255
[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) 6773–6783.10.1016/j.jcp.2009.05.042
[18]	A. Bakhsh, S. Gao, R. Samtaney, V. Wheatley, Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics, Phys. Fluids 28 (3) (2016) 034106.10.1063/1.4943162
[19]	A. Bakhsh, R. Samtaney, Linear analysis of converging Richtmyer–Meshkov instability in the presence of an azimuthal magnetic field, J. Fluids Eng. 140 (5) (2018) 050901.10.1115/1.4038487
[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) 104102.10.1063/1.4932110
[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) 013701.10.1103/physrevfluids.2.013701
[22]	K.O. Mikaelian, Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells, Phys. Rev. A 42 (6) (1990) 3400.10.1103/physreva.42.3400
[23]	K.O. Mikaelian, Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified cylindrical shells, Phys. Fluids 17 (9) (2005) 094105.10.1063/1.2046712
[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 ∇B on the numerical solution of the magnetohydrodynamic equations, J. Comput. Phys. 35 (3) (1980) 426–430.10.1016/0021-9991(80)90079-0
[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 16. IOP Publishing, 2005, p. 40.10.1088/1742-6596/16/1/005
[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) 126102.10.1063/1.4902432
[29]	M. Lombardini, D.I. Pullin, Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer-Meshkov instability, Phys. Fluids 21 (11) (2009) 114103.10.1063/1.3258668