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The nonlinear growth of Rayleigh-Taylor (R-T) instabilities in magnetic fluids is studied with two and three dimensional magnetohydrodynamical simulations. The growth of the instability from a multiple wavelength perturbation tends to be enhanced in the presence of a normal magnetic field because the flow is collimated along the field lines. The tangential field in the growth of multiple wavelength has dual effects (stabilizing and destabilizing) depending on the strength of the initial magnetic field. These effects are interpreted in terms of the nonlinear interactions between the R-T fingers and the amplified field lines. As the instability grows, the field is amplified by stretching. It is found that the magnetic field is amplified more efficiently at small scales and 3D simulations produce higher magnetic energy than in 2D (about 3.4\% of kinetic energy at the end of simulation). The amplified magnetic field is a sensitive function of numerical resolution since the numerical diffusivity is dependent on the resolution. The final structures are found to depend on the initial magnetic field (strength and direction) sensitively. The field component along the gravity vector becomes the dominating factor, which may explain the radial field in young supernova remnants (SNR).
Having studied the basic physics of the instability, we then simulate R-T instabilities in the shell of a young SNR and attempt to explain some of the radio features in the shell.
