The geometric properties of high-Schmidt-number passive scalar iso-surfaces in turbulent boundary layers

Abstract

The geometric properties are quantified for concentration iso-surfaces of a high-Schmidt-number passive scalar field produced by an iso-kinetic source with an initial finite characteristic length scale released into the inertial layer of fully developed open-channel-flow turbulent boundary layers. The coverage dimension and other measures of two-dimensional transects of the passive scalar iso-surfaces are found to be scale dependent. The coverage dimension is around 1.0 at the order of the Batchelor length scale and based on our data increases in a universal manner to reach a local maximum at a length scale around the Kolmogorov scale. We introduce a new parameter called the coverage length underestimate, which demonstrates universal behaviour in the viscous–convective regime for these data and hence is a potentially useful practical tool for many mixing applications. At larger scales (in the inertial–convective regime), the fractal geometry measures are dependent on the Reynolds number, injection length scale, and concentration threshold of the iso-surfaces. Finally, the lacunarity of the iso-surface structure shows that the instantaneous scalar field is most inhomogenous around the length scale corresponding to the Kolmogorov scale.