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

Numerical simulations of the Navier-Stokes equations with hyperviscosity (-1)ʰ⁺¹{{{Δ}}}ʰ$ (h=8) show that periodic-box turbulence exhibits self-similar decay. The inertial-range energy spectrum has the scaling law E(t${)}2/3$/${k}5/3$, where E(t) is the energy dissipation rate at time t. The total energy of the system decreases at 1/${t}²$. 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.