  We have investigated the effects of a smooth transition layer at the contact
discontinuity on the growth of the Richtmyer-Meshkov instability (RMI) by
hydrodynamic numerical simulations and derived an empirical condition for the
suppression of the instability. The transition layer has little influence on
the RMI when the thickness $L$ is narrower than the wavelength of an interface
modulation $\lambda$. However, if the transition layer becomes broader than
$\lambda$, the perturbed velocity associated with the RMI is reduced
considerably. The suppression condition is interpreted as the cases that the
shock transit time through the transition layer is longer than the sound
crossing time of the modulation wavelength. The fluctuation kinetic energy
decreases as $L^{-p}$ with $p = 2.5$, which indicates that the growth velocity
of the RMI decreases in proportion to $L^{-p/2}$ by the presence of the
transition layer. This feature is found to be quite universal and appeared in a
wide range of shock-interface interactions.
