SCALINGS AND RELATIVE SCALINGS IN THE NAVIER-STOKES TURBULENCE

High-resolution direct numerical simulations of 3D Navier-Stokes turbu lence with normal viscosity and hyperviscosity are carried out. It is found that the inertial-range statistics, both the scalings and the pr obability density functions, are independent of the dissipation mechan ism, while the near-dissipation-range fluctuations show significant st ructural differences. Nevertheless, the relative scalings expressing t he dependence of the moments at different orders are universal, and sh ow unambiguous departure from the Kolmogorov 1941 description, includi ng the 2/3 law for the kinetic energy. Implications for numerical mode ling of turbulence are discussed.