To directly check the prediction for the steepening of the enstrophy spectrum and for the statistics of small scale fluctuations of vorticity obtained in the previous section using the analogy with the passive scalar problem, we have performed numerical integration of Navier-Stokes equation for the vorticity field (Eq. (2.6))
The numerical integration is performed by a fully de-aliased
pseudo-spectral code with a second-order Runge-Kutta scheme,
on a doubly periodic square domain of size
at different resolutions:
grid points.
Simulations have been partially performed at CINECA on
IBM SP3 and SP4 parallel computers.
The vorticity fluctuations are injected by
a large-scale forcing which is Gaussian,
-correlated in time, and limited to a shell of wave-numbers around
. Forcing amplitude is chosen to provide an enstrophy
injection rate
. At variance with other choices for
commonly used (e.g. large-scale shear) this kind of forcing
ensures the statistical isotropy and homogeneity of the vorticity field.
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Different values of the friction
has been tested, and a small viscosity (see Table (2.7))
is used to remove the remnant enstrophy flux at small scales.