We present results of well-resolved direct numerical simulations (DNS) of the turbulent flow evolving from Richtmyer-Meshkov instability (RMI) in a shock-tube with square cross section. The RMI occurs at the interface between a mixture of O2 and N2 (light gas) and SF6 and acetone (heavy gas). The interface between the light and heavy gas is accelerated by a Ma = 1.5 planar shock wave. RMI is triggered by a well-defined multimodal initial disturbance at the interface. The DNS exhibit grid-resolution independent statistical quantities and support the existence of a Kolmogorov-like inertial range with a k-5/3 scaling unlike previous simulations found in the literature. The results are in excellent agreement with the experimental data of Weber et al. ["Turbulent mixing measurements in the Richtmyer-Meshkov instability," Phys. Fluids24, 074105 (2012)]10.1063/1.4733447.