  This study investigates the evolution of Rayleigh-Taylor (R-T) instabilities
in Type Ia supernova remnants that are associated with a low adiabatic index
gamma, where gamma < 5/3, which reflects the expected change in the supernova
shock structure as a result of cosmic-ray particle acceleration. Extreme cases,
such as the case with the maximum compression ratio that corresponds to
gamma=1.1, are examined. As gamma decreases, the shock compression ratio rises,
and an increasingly narrow inter shock region with a more pronounced initial
mixture of R-T unstable gas is produced. Consequently, the remnant outline may
be perturbed by small-amplitude, small-wavelength bumps. However, as the
instability decays over time, the extent of convective mixing in terms of the
ratio of the radius of the R-T fingers to the blast wave does not strongly
depend on the value of gamma for gamma >= 1.2. As a result of the age of the
remnant, the unstable gas cannot extend sufficiently far to form metal-enriched
filaments of ejecta material close to the periphery of Tycho's supernova
remnant. The consistency of the dynamic properties of Tycho's remnant with the
adiabatic model gamma=5/3 reveals that the injection of cosmic rays is too weak
to alter the shock structure. Even with very efficient acceleration of cosmic
rays at the shock, significantly enhanced mixing is not expected in Type Ia
supernova remnants.
