Synthetic turbulence

A family of schemes is outlined for constructing stochastic fields that are close to turbulence. The fields generated from the more sophisticated versions of these schemes differ little in terms of one-point and two-point statistics from velocity fluctuations in high-Reynolds-number turbulence; we shall designate such fields as synthetic turbulence. All schemes, implemented here in one dimension, consist of the following three ingredients, but differ in various details. First, a simple multiplicative procedure is utilized for generating an intermittent signal which has the same properties as those of the turbulent energy dissipation rate ε. Second, the properties of the intermittent signal averaged over an interval of size r are related to those of longitudinal velocity increments Δu(r), evaluated over the same distance r, through a stochastic variable V introduced in the spirit of Kolmogorov's refined similarity hypothesis. The third and final step, which partially resembles a well-known procedure for constructing fractional Brownian motion, consists of suitably combining velocity increments to construct an artificial velocity signal. Various properties of the synthetic turbulence are obtained both analytically and numerically, and found to be in good agreement with measurements made in the atmospheric surface layer. A brief review of some previous models is provided.