Direct numerical simulation of homogeneous turbulence with hyperviscosity

We perform direct numerical simulations (DNS) of the hyperviscous Navier-Stokes equations in a periodic box. We consider values of the hyperviscosity index h=1, 2, 8, and vary the hyperviscosity to obtain the largest range of lengthscale ratios possible for well-resolved pseudo-spectral DNS. It is found that the spectral bump, or bottleneck, in the energy spectrum observed at the start of the dissipation range becomes more pronounced as the hyperviscosity index is increased. The calculated energy spectra are used to develop an empirical model for the dissipation range which accurately represents the bottleneck. This model is used to predict the approach of the turbulent kinetic energy k to its asymptotic value, k(infinity), as the hyperviscosity tends to zero. (C) 2005 American Institute of Physics.