Abstract. This paper presents the results of modeling the interaction between internal waves (IWs) and turbulence using direct numerical simulation (DNS). Turbulence is excited and supported by a random forcing localized in a vertical layer separated from the pycnocline. The main attention is paid to the internal wave damping due to turbulence and comparison of the results with those obtained theoretically by using the semi-empirical approach. It is shown that the IW damping rate predicted by the theory agrees well with the DNS results when turbulence is sufficiently strong to be only weakly perturbed by the internal wave; however, the theory overestimates the damping rate of IWs for a weaker turbulence. The DNS parameters are matched to the parameters of the laboratory experiment, and an extrapolation to the oceanic scales is also provided.