Abstract
A stochastic representation of the turbulent dynamics of the two-dimensional Navier-Stokes equation is developed. This stochastic formulation interprets the fluctuating velocity field as a discrete, multivariate stochastic process which is governed by a master equation. By deriving the Hopf functional equation of statistical fluid mechanics it is shown that this approach yields a complete description of the stochastic properties of the turbulent velocity field. On the basis of the multivariate master equation a stochastic simulation method for the two-dimensional Navier-Stokes equation is constructed. This method is applied to the stochastic simulation of high-Reynolds-number turbulent flows.
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