Numerical data from mean-field simulations of a trapped atomic superfluid in a Vinen turbulent regime CidrimA WhiteA AllenAJ BagnatoV BarenghiC 2017 Data set associated with the numerical simulations of the Gross-Pitaevskii equation, describing the dynamics of multicharged vortices in a trapped Bose-Einstein condensate. A protocol to generate turbulence is presented, which takes advantage of the decay of the multicharged vortices to reduce surface oscillations. The data contain the velocity statistics, the energy spectrum, the correlation functions, and the temporal decay of the proposed scenario, which were used to generate the figures in the corresponding article. These results support the claim that the disordered vortex state produced can be identified with the Vinen regime of turbulence, first observed in superfluid helium experiments. A detailed description on the data generation is provided in associated publication.