Mix is a critical input to hydro simulations used in modeling chemical or nuclear reaction processes in fluids. It has been identified as a possible cause of performance degradation in inertial confinement fusion (ICF) targets. Mix contributes to numerical solution uncertainty through its dependence on turbulent transport coefficients, themselves uncertain and even controversial quantities. These coefficients are a central object of study in this paper, carried out in an Richtmyer–Meshkov unstable circular two-dimensional (2D) geometry suggested by an ICF design. We study a pre-turbulent regime and a fully developed regime. The former, at times between the first shock passage and reshock, is characterized by mixing in the form of interpenetrating but coherent fingers and the latter, at times after reshock, has fully developed turbulent structures. This paper focuses on the scaling of spatial averages of turbulence coefficients under mesh refinement and under variation of molecular viscosity [i.e., Reynolds number (Re)]. We find that the coefficients scale under mesh refinement with a power of spatial grid spacing derived from the Kolmogorov 2/3 law, especially after reshock. We document the dominance of turbulent over molecular transport and convergence of the turbulent transport coefficients in the infinite Re limit. The transport coefficients do not coincide for the pre- and post-reshock flow regimes, with significantly stronger transport coefficients after reshock.