  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. 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 outlin of Tycho's supernova
remnant, we include clumping in the ejecta. 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 56Ni 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 54Fe. The large radial
distance of the X-ray emitting Si and S ejecta from the remnant center
indicates that they were initially in clumps.
