We have studied the transport of a passive scalar for passive scalar with Prandtl numbers near unity in a plane channel with rough walls. The study was carried out by direct numerical simulations of the Navier-Stokes equations; an immersed boundary method was used to model the roughness. The well-known departure from the Reynolds analogy, which postulates similarity between the statistics of the scalar and the velocity, is verified. Townsend's similarity, suggesting the smooth-wall and rough-wall statistics collapse away from the wall is confirmed. The role of the form-induced production was a focus of this work. Additional form-induced contributions appear in the Reynolds-stress and scalar-variance budgets due to the roughness; they were quantified and compared between passive scalar and momentum. The form-induced production is more significant for the scalar variance than for the streamwise Reynolds stress and could be the cause of the reduced damping of scalar fluctuations by the roughness. The sheltering caused by tall roughness elements decreases the mean gradients significantly but, in the case of the scalar, is countered by diffusion, so that the form-induced production is larger for the scalar variance. The implications of this finding are discussed.

• Received 5 June 2020
• Accepted 21 October 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.114607