  The evolution of Type Ia supernovae in the surrounding medium is studied
using 2-dimensional numerical hydrodynamic simulations. The ejecta are assumed
to be described by an exponential density profile, following the work of
Dwarkadas & Chevalier (1998). The case of a circumstellar (CS) region formed by
mass loss from the progenitor or a companion star is also considered. The
decelerating contact discontinuity is found to be Rayleigh-Taylor (R-T)
unstable, as expected, and the nature of the instability is studied in detail
for 2 cases: 1) a constant density ambient medium, and 2) a CS medium whose
density goes as r^{-2}. The nature of the instability is found to be different
in both cases. In the case of a CS medium the instability is much better
resolved, and a fractal-like structure is seen. In the case of a constant
density medium the extent of growth is less, and the R-T fingers are found to
be limited by the presence of Kelvin-Helmholtz mushroom caps at the tips of the
fingers. The unstable region is far enough away from the reverse shock that the
latter is not affected by the mixing taking place in the interaction region. In
contrast the reverse shock in the case of a CS medium is found to be rippled
due to the formation of instabilities. In neither case is the outer shock front
affected. These results are consistent with similar studies of power-law ejecta
profiles conducted by Chevalier, Blondin & Emmering (1992). Our results are
then applied to Tycho's supernova remnant.
