  In the present paper, an efficient method to generate "pure" cylindrically
converging shock wave without a following contact surface is proposed firstly.
Then, the Richtmyer-Meshkov instabilities of two interfaces driven by the
generated cylindrically converging shock wave and the associated fluids' mixing
behaviors are numerically studied. The results show that the instability of the
interface is characterized by the growth of perturbation amplitude before
re-shock. However, the mixing of fluids is enhanced dramatically after
re-shock, which is manifested not only by the evolutions of flow structures but
also by the temporal behaviors of mixing parameters. Further investigation
shows that, although these two cases are of different initial perturbations,
their evolutions of mixing width and other mixing parameters such as molecular
mixing fraction, local anisotropy and density-specific volume correlation could
achieve the same laws of temporal behavior, especially during the later stage
after re-shock. These results to some extent demonstrate that there also exist
scaling law and temporal asymptotic behaviors in the mixing zone for
cylindrically converging shock wave driven interface. Moreover, the analyses of
turbulent kinetic energy spectrums in the azimuthal direction at late stage
also witness the $k^{-5/3}$ decaying law of turbulent kinetic energy for the
present inhomogeneity flows driven by cylindrically converging shock wave,
which further manifests that the fluids' mixing is indeed enhanced at later
time after re-shock.
