  The numerical simulation of two-dimensional decaying turbulence in a large
but finite box presented in this paper uncovered two physically different
regimes of enstrophy decay. During the initial stage, the enstrophy, generated
by a random Gaussian initial condition, decays as t^{-gamma} with gamma
approximately 0.7-0.8. After that, the flow undergoes a transition to a gas or
fluid composed of distinct vortices. Simultaneously, the magnitude of the decay
exponent crosses over to gamma approximately 0.4. An exact relation for the
total number of vortices, N(t), in terms of the mean circulation of an
individual vortex is derived. A theory predicting that N(t) is proportional to
t^{-xi} and the magnitudes of exponents gamma=2/5 and xi=4/5 is presented and
the possibility of an additional very late-time cross-over to gamma=1/3 and
xi=2/3 is also discussed.
