Non-equilibrium Monte Carlo simulation of decaying Navier-Stokes turbulence

Recently a master equation for the three-dimensional Navier-Stokes equation in k-space has been proposed. It has been shown, that the Hopf-equation can be derived from the time evolution of the stochastic process given by the master equation. Therefore it reproduces exactly the correct turbulence moment hierarchy. Here we present the results of a Monte Carlo simulation of turbulence in three space dimensions using the proposed master equation. We simulate the underlying stochastic process defined by the master equation by producing realizations and calculating averages. The results of the simulation at a Taylor-Reynolds number Rλ of about 112 show a -5/3 scaling range for the energy spectrum and the Kolmogorov-constant is about 1.6. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)