The fractional Ornstein-Uhlenbeck process as a representation of homogeneous Eulerian velocity turbulence

Abstract

Abstract A fractional Langevin equation is an analogy to the Langevin equation but with fractional Gaussian noise as the source of randomness. The fractional Ornstein-Uhlenbeck process determined by the fractional Langevin equation is a stationary Gaussian process with a structure function which may differ from being proportional to time increment depending on a characteristic model parameter H. Such a model can be applied to simulate a range of random processes in turbulent flows by varying H, including homogeneous Eulerian and Lagrangian turbulence ( H = 1 3 and 1 2 , respectively). Theoretical analysis, numerical tests and comparisons between simulation and observation show that with H = 1 3 , the fractional Ornstein-Uhlenbeck process reproduces the basic statistical features of homogeneous Eulerian turbulence. The model provides a promising technique for describing the diffusion of nonpassive particles in turbulent flows.