Large-scale lognormality in turbulence modeled by the Ornstein-Uhlenbeck process.

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.