Evolution of passive scalar statistics in a spatially developing turbulence

Abstract

We investigate the evolution of passive scalar statistics in a spatially developing turbulence using Direct Numerical Simulation. Turbulence is generated by a square grid-element, which is heated continuously, and the passive scalar is temperature. The square element is the fundamental building block for both regular and fractal grids. We trace the dominant mechanisms responsible for the dynamical evolution of scalar variance and scalar dissipation along the bar and grid-element centrelines. The scalar-variance is generated predominantly by the action of mean scalar gradient behind the bar and is transported laterally by turbulent fluctuations to the grid-element centreline. The scalar dissipation (proportional to the scalar gradient variance) is produced primarily by the compression of the fluctuating scalar gradient vector by the turbulent strain-rate, while the contribution of mean velocity and scalar fields is negligible. Close to the grid element the scalar spectrum exhibits a well-defined -5/3 power law, even though the basic premises of the Kolmogorov-Obukhov-Corrsin theory are not satisfied (the fluctuating scalar field is highly intermittent, inhomogeneous and anisotropic, and the local Corrsin-microscale-Peclet number is small). At this location, the PDF of scalar gradient production is only slightly skewed towards positive and the fluctuating scalar gradient vector aligns only with the compressive strain-rate eigenvector. The scalar gradient vector is stretched/compressed stronger than the vorticity vector by turbulent strain-rate throughout the grid-element centreline. However, the alignment of the former changes much earlier in space than that of the latter, resulting in scalar dissipation to decay earlier along the grid-element centreline compared to the turbulent kinetic energy dissipation. The universal alignment behaviour of the scalar gradient vector is found far-downstream although the local Reynolds and Peclet numbers (based on the Taylor and Corrsin length scales respectively) are low.