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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. [ABSTRACT FROM AUTHOR]

A unified and analytical model is developed to study the effects of an inclined magnetic field on magneto-Rayleigh–Taylor (MRT) and magneto-Richtmyer–Meshkov (MRM) instabilities in ideal magnetohydrodynamics. Unlike either a horizontal or a vertical magnetic field is present, the decay modes possess decaying and oscillation behaviors together. The vorticity transportation is analyzed. The dispersion relations are derived, and some interesting phenomena are observed. For a small R that represents the ratio of the magnetic field strength, or equivalently, the inclination θ, the growth rate of MRT instabilities resembles the case when a vertical magnetic field is present. For a large R, the growth rate resembles to the case when a horizontal magnetic field exists. The maximum growth rate becomes strongly dependent on At instead of on R. Furthermore, analytical expression is obtained for the MRM instability by using the impulsive accelerated model. The decaying and oscillating rates of the perturbed amplitude are explicitly related to θ. For two limiting cases, with either the vertical or the horizontal magnetic field existing, our results retrieve previous one of the theoretical analyses and numerical simulations. Generally, the asymptotic amplitude becomes independent of the wave number of the initial perturbation in the MRM instability. These findings regarding magneto-hydrodynamic interfacial instabilities in an inclined magnetic field could provide physical insights for magnetically driven targets and astrophysical observations. This analytical model is easily expanded to investigate the effects of finite thickness of magnetic slab and sheared magnetic field in relevant to high-energy-density physics and to astrophysics. [ABSTRACT FROM AUTHOR]

An exact theoretical analysis is presented, mainly concerning linearly elastic Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities at spherical interfaces by using the decomposition method. A stability analysis is performed to investigate the growth rates of instability with the degree of spherical harmonics n, dimensionless radius Br, Atwood number At, and elastic ratio T. Generally, spherical RT and RM instabilities resemble their planar counterparts when Br or n is large. However, low mode perturbations behave quite differently from planar ones, which is also observed in experiments in inertial confinement fusion and in theoretical analysis in geophysics. An analytical expression is obtained to study the dependence of the cutoff radius. There exist two kinds of it: a small one at which the most-active mode cannot be activated and a larger one that is similar to the planar one. In addition, the elastic parameter strongly affects the evolution of a mode with a lower number. The method is extended to study the RT instability at the interface between an elastic solid and a viscous fluid, which is relevant to some situations encountered experimentally. Finally, RM instability in elastic solids is also investigated, in particular, with regard to the evolution of RM instability with low-mode asymmetries. This method is able to provide guidelines for further studying spherical RT and RM instabilities in complex situations, including the finite thickness effects, elastoplastic properties, and Bell–Plesset effects. [ABSTRACT FROM AUTHOR]

We first derive the exact dispersion relation for viscous Rayleigh-Taylor instability in the presence of a horizontal magnetic field using a decomposition method, and we find that the horizontal magnetic field contributes to the generation of vorticity inside the flow, thereby further distorting the velocity field. This differs from the previous view of the horizontal magnetic field behaving as a surface-tension-like force that does not produce any vorticity in inviscid flow. Vorticity transport is also investigated. The well-known approximate dispersion relation yields growth rates based on an irrotational approximation with a maximum error of 19% in comparison with the exact rates. Furthermore, we investigate the physics of the viscous Richtmyer-Meshkov instability in the presence of a magnetic field, and we find that the presence of the magnetic field leads to the generation of more eigenvalues, thereby modifying the motion of the interface. Comparisons confirm that the viscosity and magnetic field both play fundamental roles in interface behavior, and it is clarified that the behaviors of the interface for viscous Richtmyer-Meshkov instability become in agreement with the numerical simulations. The dependences of the eigenvalues on the viscosities and densities of the fluids, as well as on the magnetic field, are also discussed. Finally, we analyze the evolution of the decay modes to investigate the rotationality of the velocity fields. [ABSTRACT FROM AUTHOR]

The impulsively accelerated Richtmyer-Meshkov instability (RMI) of a fluid-solid interface is theoretically studied with a decomposition method, and the least stable mode is shown to oscillate but decay due to the combined effects of elasticity and viscosity. The dispersion relation of RMI in viscous fluids is obtained as well, and the predicted interface amplitude agrees with numerical simulations better than the previous linear and weakly nonlinear theories. As time tends to infinity, the asymptotic amplitude of the disturbed interface is found to be inversely proportional to the wave number in viscous fluids but to be independent of the wave number for the interface between elastic solids. [ABSTRACT FROM AUTHOR]