  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.
