NUMERICAL STUDY OF 3-DIMENSIONAL KOLMOGOROV FLOW AT HIGH REYNOLDS-NUMBERS

High-resolution numerical simulations (with up to 256(3) modes) are pe rformed for three-dimensional flow driven by the large-scale constant force f(y) = F cos(x) in a periodic box of size L = 2 pi (Kolmogorov f low). High Reynolds number is attained by solving the Navier-Stokes eq uations with hyperviscosity (-1)(h+1)Delta(h) (h = 8). It is shown tha t the mean velocity profile of Kolmogorov flow is nearly independent o f Reynolds number and has the 'laminar' form upsilon(y) = V cos(x) wit h a nearly constant eddy viscosity. Nevertheless, the flow is highly t urbulent and intermittent even at large scales. The turbulent intensit ies, energy dissipation rate and various terms in the energy balance e quation have the simple coordinate dependence af b cos(2x) (with a,b c onstants). This makes Kolmogorov flow a good model to explore the appl icability of turbulence transport approximations in open time-dependen t flows. It turns out that the standard expression for effective (eddy ) viscosity used in K-E transport models overpredicts the effective vi scosity in regions of high shear rate and should be modified to accoun t for the non-equilibrium character of the flow. Also at large scales the flow is anisotropic but for large Reynolds number the flow is isot ropic at small scales. The important problem of local isotropy is syst ematically studied by measuring longitudinal and transverse components of the energy spectra and crosscorrelation spectra of velocities and velocity-pressure-gradient spectra. Cross-spectra which should vanish in the case of isotropic turbulence decay only algebraically but somew hat faster than corresponding isotropic correlations. It is verified t hat the pressure plays a crucial role in making the flow locally isotr opic. It is demonstrated that anisotropic large-scale flow may be cons idered locally isotropic at scales which are approximately ten times s maller than the scale of the flow.