Scale-dependent convection velocities of passive scalar structures in wall-bounded turbulence

The convection velocity of turbulent structures is central to Taylor's hypothesis and to the interpretation of time-resolved measurements in wall-bounded turbulence. While the convection behaviour of velocity fluctuations has been studied extensively, much less is known about passive scalar fluctuations, despite their relevance to temperature-based wall-shear-stress estimation and heat-transfer modelling. In the present work, the scale-dependent convection velocity of passive scalar structures is analysed in turbulent plane channel flow by extending the residual-minimisation approach of del \\'Alamo \\& Jim\\'enez (2009) to the passive scalar transport equation. Direct numerical simulations of doubly periodic channel flows are performed at friction Reynolds numbers $Re_\\tau=180,\\ 500,\\ 1000$, while passive scalars with Prandtl numbers $Pr=0.025,\\ 0.4,\\ 1$ are considered. The results show that the global convection velocity of passive scalar fluctuations approaches the local mean streamwise velocity away from the wall, but tends to a finite near-wall value that increases as $Pr$ decreases. This behaviour is linked to the stronger contribution of large, fast-convecting structures in low-$Pr$ flows. A scale-resolved analysis further shows that larger scalar structures convect at velocities closer to the bulk velocity, whereas smaller scales are more strongly influenced by the local mean flow. In addition, the near-wall convection behaviour is found to deviate from previously proposed empirical scaling laws for $Pr<1$ and to exhibit a measurable Reynolds-number dependence. These findings improve the physical understanding and modelling of passive-scalar convection in wall turbulence and support the development of thermographic methods for indirect wall-friction estimation.