Spectra of energy dissipation, enstrophy and pressure by high-resolution direct numerical simulations of turbulence in a periodic box

The spectra of the squares of velocity quadratics including the energy dissipation rate ε per unit mass, the enstrophy ω² and the pressure p were measured using the data obtained from direct numerical simulations (DNSs) of incompressible turbulence in a periodic box with number of grid points up to 2048³. These simulations were performed using the Earth Simulator computing system. The spectra for ε, ω² and p exhibited a wave number range in which the spectra scaled with the wave number k as ∝^-a. Exponent a for p was about 1.81, which is in good agreement with the value obtained by assuming the joint probability distribution of the velocity field to be Gaussian, while a values for ε and ω² were about 2/3, and very different from the Gaussian approximation values.