Simulation of three‐dimensional turbulence with given second‐order statistical structure

Abstract

AbstractA method is presented for generating a turbulent, three‐dimensional flow field with correct mean flows, Reynolds' stresses, and energies, along with boundary layer structure. The details of the simulation of turbulent plane Poiseuille flow are given as an example. Plane Poiseuille flow was chosen because it is a useful model for many applications, and has available reliable and extensive measurements. All nine of the components of the spectral matrix are included, from actual measurements, along with incompressibility, a sheared mean flow, and measured boundary‐layer structure of the turbulence. The results appear to be realistic, and the statistical structure imposed is adequate for a variety of turbulence studies of three‐dimensional flows, in particular turbulent dispersion. Compared with finite‐difference methods for solving the dynamic flow equations, with comparable resolution, the method presented here requires some two orders of magnitude less storage, and some four orders of magnitude less computer time.