  Core-collapse supernova (SN) explosions may occur in the highly inhomogeneous
molecular clouds (MCs) in which their progenitors were born. We perform a
series of 3-dimensional hydrodynamic simulations to model the interaction
between an individual supernova remnant (SNR) and a turbulent MC medium, in
order to investigate possible observational evidence for the turbulent
structure of MCs. We find that the properties of SNRs are mainly controlled by
the mean density of the surrounding medium, while a SNR in a more turbulent
medium with higher supersonic turbulent Mach number shows lower interior
temperature, lower radial momentum, and dimmer X-ray emission compared to one
in a less turbulent medium with the same mean density. We compare our
simulations to observed SNRs, in particular, to W44, W28 and IC 443. We
estimate that the mean density of the ambient medium is $\sim 10\,$cm$^{-3}$
for W44 and W28. The MC in front of IC 443 has a density of $\sim
100\,$cm$^{-3}$. We also predict that the ambient MC of W44 is more turbulent
than that of W28 and IC 443. The ambient medium of W44 and W28 has
significantly lower average density than that of the host giant MC. This result
may be related to the stellar feedback from the SNRs' progenitors.
Alternatively, SNe may occur close to the interface between molecular gas and
lower density atomic gas. The region of shocked MC is then relatively small and
the breakout into the low density atomic gas comprises most of the SNR volume.
