  Lognormality was found experimentally for coarse-grained squared turbulence
velocity and velocity increment when the coarsening scale is comparable to the
correlation scale of the velocity (Mouri et al. Phys. Fluids 21, 065107, 2009).
We investigate this large-scale lognormality by using a simple stochastic
process with correlation, the Ornstein-Uhlenbeck (OU) process. It is shown that
the OU process has a similar large-scale lognormality, which is studied
numerically and analytically.
