The time evolution of the Loitsianski integral at high‐Reynolds numbers is determined by computing an ensemble average of a large number of independent large‐eddy simulations of decaying isotropic turbulence. It is found that the Loitsianski integral becomes proportional tot&ggr;at large times and that &ggr; ≊0.25. The present simulations illustrate the efficient use of massively parallel computers for simulating large ensembles of turbulent flows.