Kolmogorov and scalar spectral regimes in numerical turbulence

Abstract

Velocity and passive-scalar spectra for turbulent fields generated by a forced three-dimensional simulation and Taylormicroscale Reynolds numbers up to 83 are shown to have distinct spectral regimes, including a Kolmogorov inertial subrange. Both one- and three-dimensional spectra are shown for comparison with experiment and theory, respectively. When normalized by the Kolmogorov dissipation scales velocity spectra collapse to a single curve and a high-wavenumber bulge is seen. The bulge leads to an artificially high Kolmogorov constant, but is consistent with recent measurements of the velocity spectrum in the dissipation regime and the velocity-derivative skewness. Scalar spectra, when normalized by the Oboukov-Corrsin scales, collapse to curves which depend only on Prandtl number and show a universal inertial-convective subrange, independent of Prandtl number. When normalized by the Batchelor scales, the scalar spectra show a universal dissipation regime which is independent of Prandtl numbers from 0.1 to 1.0. The time development of velocity spectra is illustrated by energy-transfer spectra in which distinct pulses propagate to high wavenumbers