Self-similar decay of three-dimensional homogeneous turbulence with hyperviscosity

Numerical simulations of the Navier-Stokes equations with hyperviscosity (-1${)}^{\mathit{h}+1\mathrm{}}$ ${\mathrm{\Delta }}^{\mathit{h}}$ (h=8) show that periodic-box turbulence exhibits self-similar decay. The inertial-range energy spectrum has the scaling law E(t${)}^{2/3}$/${\mathit{k}}^{5/3}$, where E(t) is the energy dissipation rate at time t. The total energy of the system decreases at 1/${\mathit{t}}^2$. The concept of constant Reynolds number decay is introduced, enabling us to perform long time averages and reliably measure higher-order correlation functions. Comparisons are made with the case of forced turbulence reported earlier.