Summary: We focus on the late time turbulence of an accelerated inhomogeneous flow environment, which is a generalization of the Richtmyer--Meshkov environment. The numerical investigation is based on two-dimensional (2D) compressible Euler simulation, which is initiated by a shock wave hitting a gas layer (curtain). Although our unforced study is based on the intrinsic numerical dissipation, we observe excellent agreement with the previous decay analysis on 2D viscous isotropic homogeneous turbulence at inertial range [J. R. Chasnov, Phys. Fluids 9, 171--180 (1997)]. The baroclinic circulation in our environment plays a major role in the mass transport and mixing. The mass-transport induced density gradient intensification, in turn, enhances the circulation baroclinically and provides an intrinsic forcing at intermediate to high wave number range. With the assistance of a computer graphics based feature extraction and tracking algorithm, we address quantitatively the spatial and temporal diffusivity of the mixing zone. We study and compare both the slow/fast/slow and fast/slow/fast cases to illustrate heuristically the correlation of mass and momentum diffusivity.