STOCHASTIC SIMULATIONS OF HIGH-REYNOLDS-NUMBER TURBULENCE IN 2 DIMENSIONS

The dynamics of two-dimensional (2D) turbulence is studied by a stocha stic simulation method. The latter is based on a representation of the random vorticity field and stream function by a multivariate stochast ic process defined by a discrete master equation. It is demonstrated t hat in the continuum Limit the complete hierarchy of coupled moment eq uations for the statistical formulation of the 2D Navier-Stokes equati on is obtained. The probabilistic time evolution leads to random stres ses, which can be traced to thermal fluctuations and allow one to dise ntangle hydrodynamic and thermodynamic degrees of freedom by some kind of renormalization procedure. The stochastic simulations at a large-s cale Reynolds number of 2.5 x 10(5) clearly show the existence of a k( -3) power law, where k is the wave number, in the inertial range of th e energy spectrum, as is predicted by the Kraichnan-Batchelor theory.