We present two-dimensional high-resolution hydrodynamical simulations in spherical polar coordinates of a Type Ia supernova interacting with a constant density interstellar medium. The ejecta are assumed to be freely expanding with an exponential density profile. The interaction gives rise to a double-shocked structure susceptible to hydrodynamic instabilities. The Rayleigh-Taylor instability initially grows, but the Kelvin-Helmholtz instability takes over, producing vortex rings. Provided the simulation is initiated early in the evolution with a perturbation � 1%, the instability reaches its fully developed nonlinear strength within 5 doubling times. The further nonlinear evolution does not depend on the initial conditions. Considering the small initial radii of Type Ia supernovae, they are likely to reach this fully developed phase. The nonlinear instability initially evolves toward longer wavelengths and eventually fades away when the reverse shock front is in the flatter part of the supernova density distribution. Based on observations of X-ray knots and the protrusion in the southeast outline of Tycho’s supernova remnant, we include clumping in the ejecta because these features cannot be explained by instabilities growing from small perturbations. The clump interaction with the reverse shock induces Rayleigh-Taylor and Kelvin-Helmholtz instabilities on the clump surface that facilitate fragmentation. In order to survive crushing and to have a bulging effect on the forward shock, the clump’s initial density ratio to the surrounding ejecta must be at least 100 for the conditions in Tycho’s remnant. The 56 Ni bubble effect may be important for the development of clumpiness in the ejecta. The observed presence of an Fe clump would then require a non-radioactive origin for this Fe, possibly 54 Fe. The large radial distance of the X-ray emitting Si and S ejecta from the remnant center indicates that they were initially in clumps. Subject headings: hydrodynamics —instability — supernova remnants — supernovae: general — supernovae: individual (SN 1572) – 2 – 1
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