We present results from an ensemble of 50 runs of two-dimensional hydrodynamic turbulence with spatial resolution of 2048^2 grid points, and from an ensemble of 10 runs with 4096^2 grid points. All runs in each ensemble have random initial conditions with same initial integral scale, energy, enstrophy, and Reynolds number. When both ensemble- and time-averaged, inverse energy cascade behavior is observed, even in the absence of external mechanical forcing: the energy spectrum at scales larger than the characteristic scale of the flow follows a k^(-5/3) law, with negative flux, together with a k^(-3) law at smaller scales, and a positive flux of enstrophy. The source of energy for this behavior comes from the modal energy around the energy containing scale at t=0. The results shed some light into connections between decaying and forced turbulence, and into recent controversies in experimental studies of two-dimensional and magnetohydrodynamic turbulent flows.
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