The effect of Schmidt number on space–time correlation of scalar fluctuations in wall-bounded shear flow

Scalar turbulence, involving the chaotic transport of passive scalars such as temperature, pollution and chemical concentration, plays a critical role in scientific and engineering applications. Transport of scalars is largely affected by its inherent characteristic molecular diffusivity through the Schmidt number ( italic Sc Sc $\\textit{Sc}$ , the ratio of fluid viscosity and diffusivity). This study explores the scalar convection speed and Taylor microscale in fully developed pipe flow with a localised scalar plume at Reynolds number italic Re equals 10 000 Re = 10 000 $\\textit{Re} = 10\\,000$ for 10 Superscript negative 3 Baseline less than or slanted equals italic Sc less than or slanted equals 10 10 − 3 ⩽ Sc ⩽ 10 $10^{-3} \\leqslant \\textit{Sc} \\leqslant 10$ . We employ a hybrid approach combining direct numerical simulations for the velocity field with Lagrangian scalar tracking to capture the scalar field’s evolution under turbulent convection and molecular diffusion. The scalar concentration data are obtained in the Eulerian cylindrical coordinates. In a fixed range of streamwise positions, the scalar convection speed aligns with the convection speed of velocity fluctuations at italic Sc equals 1 Sc = 1 $\\textit{Sc} = 1$ , but it is smaller and larger than the velocity convection speed for italic Sc less than 1 Sc < 1 $\\textit{Sc} \\lt 1$ and italic Sc greater than 1 Sc > 1 $\\textit{Sc} \\gt 1$ , respectively, and also for the radial positions close to the pipe wall. The Taylor microscale scales approximately as italic Sc Superscript negative 1 divided by 2