Effects of Wavenumber Truncation on High-Resolution Direct Numerical Simulation of Turbulence

The effects of wavenumber truncation on the direct numerical simulation (DNS) of incompressible turbulence at high Reynolds numbers using the Fourier spectral method were studied by comparing DNS fields with different truncation wavenumbers, K_max. The comparison suggests that the error due to truncation increases faster at higher wavenumbers, k, and the increase obeys a simple scaling law in the inertial subrange k ≪ K_max. Some statistics, such as the energy and dissipation spectra, may remain insensitive to the error, even in the later period, provided that K_max η ∼ 1 (η is the Kolmogorov length scale), although DNS fields with different K_max are then essentially uncorrelated to each other.