Theoretical And Numerical Research On Interface Instabilities In Magnetohydrodynamics

When an interface separating two fluids with different densities is accelerated by external force, the small initial perturbation on the interface may grow with time, resulting in interface instabilities eventually. Two typical interface instabilities are considered in this thesis, Rayleigh-Taylor (RT) instability and Richtmyer-Meshkov (RM) instability. When the heavy fluid is accelerated by the light fluid, RT instability will occur on the interface, while RM instability will happen after a shock wave hits on the disturbed interface. Since RT and RM instabilities play an important role in engineering and scientific fields, such as the inertial confinement fusion, the supersonic combustion, the formation of stars and the compressible turbulent flow, a great attention is attracted by these two instabilities and a large number of theoretical, numerical and experimental investigations have been conducted all over the world. The effect of magnetic field on the RT and RM instabilities also has been widely discussed because the subject in the inertial confinement fusion and the astronomical phenomena is plasma. Based on these, the interface instabilities in magnetohydrodynamics have been investigated with numerical and theoretical methods in this thesis.The3rd WENO scheme and mixed GLM method are employed in the numerical part to simulate the interaction between a planar shock wave (Ma=10) and a2D rectangular cloud (the ratio of the density of the cloud to the ambient gas is10) in different initial orientations and strengths for the magnetic field. With qualitative and quantitative discussion of the evolution of interface, the statistical variables of the cloud, the mixing rate of the cloud and the magnetic field, it is found that magnetic field will decrease the vorticity deposited on the interface and reduce the growth of interface instabilities; magnetic field will influence the evolution of cloud and the configuration of the cloud will be different with different orientations of the initial field; the field will influence the acceleration and the mixing rate of the cloud, generally, the stronger the field strength, the lower the mixing rate of the cloud; and the field will be greatly amplified in some regions behind the shock when the cloud is presented. In theoretical part, a non-ideal magnetohydrodynamical potential flow model considering the influences of magnetic field, fluid viscosity and surface tension is constructed in a plane perpendicular to the magnetic field based on the potential flow model. The effects of magnetic field, fluid viscosity and surface tension on the growth of bubble and spike are then analyzed in details with this new model, resulting in the influences of these factors to the RT and RM instabilities. The results show that the influence of magnetic field on the RT and RM instabilities is caused by its nonlinear part, and whether the RT and RM instabilities can be suppressed or enhanced depends on the direction of the nonlinear part of magnetic field; it is also observed that the velocity and amplitude of bubble and spike generally will be reduced by viscosity and surface tension, which indicates that viscosity and surface tension can suppress RT and RM instabilities, what’s more, the bubble and spike will oscillate if surface tension is strong enough.