  Turbulence exhibits significant velocity fluctuations even if the scale is
much larger than the scale of the energy supply. Since any spatial correlation
is negligible, these large-scale fluctuations have many degrees of freedom and
are thereby analogous to thermal fluctuations studied in the statistical
mechanics. By using this analogy, we describe the large-scale fluctuations of
turbulence in a formalism that has the same mathematical structure as used for
canonical ensembles in the statistical mechanics. The formalism yields a
universal law for the energy distribution of the fluctuations, which is
confirmed with experiments of a variety of turbulent flows. Thus, through the
large-scale fluctuations, turbulence is related to the statistical mechanics.
