BURGERS TURBULENCE MODEL AS A STOCHASTIC DYNAMIC SYSTEM - MASTER EQUATION AND SIMULATION

By means of Burgers's equation a stochastic description of turbulent fluid flows is explained which is based on a discrete master equation. The latter governs the dynamics of a discrete multivariate stochastic process representing the random velocity field of the fluid. From the characteristic function corresponding to this stochastic process, the Hopf functional equation of turbulence is obtained. This implies that the infinite hierarchy of correlation functions can be derived from the master equation. The master-equation description naturally leads to a simple stochastic simulation algorithm which is well suited to numerical implementation. Stochastic simulations of the Burgers model of turbulence are performed and are shown to yield very accurate results.