THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS AS A REPRESENTATION OF HOMOGENEOUS EULERIAN VELOCITY TURBULENCE

A fractional Langevin equation is an analogy to the Langevin equation but with fractional Gaussian noise as the source of randomness. The fr actional Ornstein-Uhlenbeck process determined by the fractional Lange vin equation is a stationary Gaussian process with a structure functio n which may differ from being proportional to time increment depending on a characteristic model parameter H. Such a model dan 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 compari sons between simulation and observation show that with H = 1/3, the fr actional Ornstein-Uhlenbeck process reproduces the basic statistical f eatures of homogeneous Eulerian turbulence. The model provides a promi sing technique for describing the diffusion of nonpassive particles in turbulent flows.