Investigations of the Richtmyer-Meshkov Instability with Ideal Magnetohydrodynamics and Ideal Two-Fluid Plasma Models

  • Yuan Li

Student thesis: Doctoral Thesis


The Richtmyer-Meshkov instability (RMI) in the convergent geometry is numerically studied in the framework of ideal magnetohydrodynamics (MHD) and two-fluid plasma in this thesis. The converging RMI usually occurs along with the Rayleigh-Taylor instability (RTI) due to the non-uniform motion or continuous acceleration of the interface. First, we investigate the interaction between a converging cylindrical shock and double density interfaces in the presence of a saddle magnetic field with ideal MHD model. We show that the RMI is suppressed by the magnetic field . However, the extent of the suppression varies on the interface which leads to non-axisymmetric growth of the perturbations. The degree of asymmetry increases when the seed field strength increases. The perturbation amplitude is affected by the competition mechanism between RMI and RTI. It increases when RMI dominates RTI while decreases when RTI dominates. Then, we research the two-fluid plasma RMI of a cylindrical density interface without an initial magnetic field. Varying the Debye length scale, we examine the effects of the coupling between the electron and ion fluids. The charge separation is responsible for the self-generated electromagnetic fields. We show that the Biermann battery effect dominates the generation of magnetic field when the coupling effect is weak. In addition to the RT stabilization effect during flow deceleration, the interfaces are accelerated by the induced Lorentz force. As a consequence, the perturbations develop into the RTI, leading to an enhancement of the perturbation amplitude compared with the hydrodynamic case. Finally, we investigate the linear evolution of two-fluid plasma RMI. We show that the increase of perturbation amplitude is almost contributed by the ion shock-interface interaction. We also examine the effect of magnetic field in the streamwise direction. For a short duration after the ion shock-interface interaction, the growth rate is similar for different initial magnetic field strengths. As time progresses the suppression of the instability due to the magnetic field is observed. The growth rate shows oscillations with a frequency that is related to the ion or electron cyclotron frequency. The instability is suppressed due to the vorticity being transported away from the interface.
Date of AwardAug 2021
Original languageEnglish (US)
Awarding Institution
  • Physical Science and Engineering
SupervisorRavi Samtaney (Supervisor)


  • Richtmyer-Meshkov instability
  • Magnetohydrodynamics
  • Two-fluid plasma

Cite this