FORCED 3-DIMENSIONAL HOMOGENEOUS TURBULENCE WITH HYPERVISCOSITY

High-resolution numerical simulations (up to 256(3) modes) are performed for the Navier-Stokes equations with hyperviscosity (-1)h+1Delta(h) (h=8). With random white-in-time forcing, the inertial-range energy spectrum has the scaling law 1/k(alpha) with alpha almost-equal-to 1.85 +/- 0.05 at small wave numbers k with a flatter region near the ultraviolet cut-off. The transitional region is characterized by a sharp change of the energy transfer mechanism. Spectra of fluctuations of higher-order correlation functions are measured. At inertial-range scales the system seems insensitive to the power h of the hyperviscosity.