Effect of Schmidt Number on Forced Isotropic Turbulence with Passive Scalars

Abstract

Traditionally, Fourier spectra have been employed to gain a deeper understanding of turbulence flow structures. The investigation of isotropic forced turbulence with passive scalars offers a straightforward means to examine the disparities between velocity and passive scalar spectra. This flow configuration has been extensively studied in the past, encompassing a range of Reynolds and Schmidt numbers. In this present study, direct numerical simulations (DNS) of this flow are conducted at sufficiently high Reynolds numbers, enabling the formation of a wide inertial range. The primary focus of this investigation is to quantitatively assess the variations in scalar spectra with the Schmidt number (Sc). The spectra exhibit a transition from a k−5/3 scaling for low Sc to a k−4/3 scaling for high Sc. The emergence of the latter power law becomes evident at Sc = 2, with its width expanding as Sc increases. To gain further insights into the underlying flow structures, a statistical analysis is performed by evaluating quantities aligned with the principal axes of the strain field. The study reveals that enstrophy is primarily influenced by the vorticity aligned with the intermediate principal strain axis, while the scalar gradient variance is predominantly controlled by the compressive strain. To provide a clearer understanding of the differences between enstrophy and scalar gradient variance, joint probability density functions (PDFs) and visualizations of the budget terms for both quantities are presented. These visualizations serve to elucidate the distinctions between the two and offer insights into their respective behaviors.