Wheatley, Vincent (2005) On the Richtmyer-Meshkov instability in magnetohydrodynamics. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05272005-145538
The Richtmyer-Meshkov instability is important in applications including inertial confinement fusion and astrophysical phenomena. In some applications, the fluids involved are plasmas and can be affected by magnetic fields. For one configuration, it has been numerically demonstrated that the growth of the instability is suppressed in the presence of a magnetic field. Here, the nature of this suppression is theoretically and numerically investigated. In ideal incompressible magnetohydrodynamics, we examine the stability of an impulsively accelerated perturbed density interface in the presence of a magnetic field initially parallel to the acceleration. This is accomplished by analytically solving the linearized initial value problem, which is a model for the Richtmyer-Meshkov instability. We find that the initial growth rate of the interface is unaffected by the magnetic field, but the interface amplitude then asymptotes to a constant value. Thus the instability is suppressed. The interface behavior from the model is compared to the results of compressible simulations. We then consider regular shock refraction at an oblique planar density interface in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal magnetohydrodynamic simulations indicate that the presence of the magnetic field inhibits the deposition of vorticity on the shocked contact, which leads to the suppression of the Richtmyer-Meshkov instability. We show that the shock refraction process produces a system of five to seven plane waves that intersect at a point. In all solutions, the shocked contact is vorticity free. These solutions are not unique, but differ in the type of waves that participate. The equations governing the structure of these multiple-wave solutions are obtained and a numerical method of solution is described. Solutions are compared to the results of simulations. The limit of vanishing magnetic field is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular wedge whose angle scales with the applied field magnitude. The shock-induced shear across the wedge is supported by slow-mode expansion fans within it, leaving the shocked contact vorticity free. To verify these findings, an approximate leading order asymptotic solution was computed.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Subject Keywords:||impulse model; instability suppression; linear stability; MHD; MHD shock refraction; Richtmyer-Meshkov instability; singular limit|
|Degree Grantor:||California Institute of Technology|
|Division:||Engineering and Applied Science|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||17 May 2005|
|Author Email:||vincent.wheatley (AT) gmail.com|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||31 May 2005|
|Last Modified:||26 Dec 2012 02:47|
- Final Version
See Usage Policy.
Repository Staff Only: item control page