Kolmogorov’s refined similarity hypothesis for hyperviscous turbulence

Kolmogorov’s refined similarity hypothesis (RSH) is tested in high resolution numerical simulations of forced three-dimensional homogeneous turbulence. High Reynolds numbers are achieved by using hyperviscous dissipation (-1${)}^{\mathit{h}+1\mathrm{}}$ ${\mathrm{\Delta }}^{\mathit{h}}$ (h=8) instead of Newtonian (h=1) dissipation. It is found that, in the inertial range, the RSH is reasonably well satisfied for low order moments with noticeable systematic corrections for higher order moments. Within the constraints imposed by the use of hyperviscosity our data nearly eliminate trivial kinematic dependencies between longitudinal velocity differences and the energy dissipation rate thus helping to reveal the true dynamical nature of the RSH. © 1996 The American Physical Society.