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

TL;DR

This paper demonstrates that the Ornstein-Uhlenbeck process exhibits large-scale lognormality similar to turbulence, providing a simple stochastic model to understand this phenomenon both numerically and analytically.

Contribution

It introduces the OU process as a minimal model to explain large-scale lognormality observed in turbulence data.

Findings

OU process shows large-scale lognormality similar to turbulence.

Analytical and numerical evidence supports the model's relevance.

Provides a simple stochastic framework for turbulence analysis.

Abstract

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.