Abstract
Numerical simulations of the Navier-Stokes equations with hyperviscosity (-1${)}^{\mathit{h}+1}$${\mathrm{\ensuremath{\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.
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