A unified model to study the effects of elasticity, viscosity, and magnetic fields on linear Richtmyer-Meshkov instability

A unified analytical approach to study the effects of elasticity, viscosity, and magnetic fields on the Richtmyer-Meshkov (RM) instability by using the impulsively accelerated model is presented. This model clarifies the discontinuity in the oscillation periods and yields the asymptotic decaying rate in elastic solids. It reveals that the complex eigenvalues produce better results compared with the numerical simulations for RM instability in viscous fluids and resolves the standing controversy between the analytical theory and numerical simulations at a vacuum/fluid interface. At last, it easily retrieves the results when the normal or tangential magnetic field is present. Those good agreements, between numerical simulations and theoretical analysis, would enable the model to be valuable in more complex situations such as in the elastic-plastic slabs with or without the presence of magnetic fields, as well as in the nonlinear regime.