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 ν as ν→0. 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.