Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box

High-resolution direct numerical simulations (DNSs) of incompressible homogeneous turbulence in a periodic box with up to 4096³ grid points were performed on the Earth Simulator computing system. DNS databases, including the present results, suggest that the normalized mean energy dissipation rate per unit mass tends to a constant, independent of the fluid kinematic viscosity v as v→. The DNS results also suggest that the energy spectrum in the inertial subrange almost follows the Kolmogorov k^-5/3 scaling law, where k is the wavenumber, but the exponent is steeper than -5/3 by about 0.1.