NUMERICAL-SIMULATION OF RANDOMLY FORCED TURBULENT FLOWS

Several authors have proposed studying randomly forced turbulent hows (e.g., E. A. Novikov, Soviet Physics JETP, 20(5), 1290 1965). More rec ently, theoretical investigations (e.g., renormalization group) have f ocused on whim-noise forced Navier-Stokes equations (V. Yakhot and S. A. Orszag, J.Sci.Comput. 1(1), 3 1986), The present article aims to pr ovide an appropriate numerical method for the simulation of randomly f orced turbulent systems. The spatial discretization is based on the cl assical Fourier spectral method. The time integration is performed by a second-order Runge-Kutta scheme. The consistency of an extension of this scheme to treat additive noise stochastic differential equations is proved. The random number generator is based on lagged Fibonacci se ries. Results are presented for two randomly forced problems: the Burg ers and the incompressible Navier-Stokes equations with a white-noise in time forcing term characterized by a power-law correlation function in spectral space. A variety of statistics are computed for both prob lems, including the structure functions, The third-order structure fun ctions are compared with their exact expressions in the inertial subra nge. The influence of the dissipation mechanism (viscous or hypervisco us) on the inertial subrange is discussed. In particular, probability density functions of velocity increments are computed for the Navier-S tokes simulation, Finally, for both Burgers and Navier-Stokes problems , our results support the view that random sweeping is the dominant ef fect of the large-scale motion on the small-scales. (C) 1998 Academic Press.