Direct numerical simulations of compressible turbulent channel flow including passive scalar transport have been performed at five Mach numbers, M, ranging from 0.3 to 3.5 and Reynolds numbers, Re τ , ranging from 181 to 1030. The Prandtl and Schmidt numbers are 0.7 and 1.0, respectively, in all cases. The passive scalar is added to the flow through one channel wall and removed through the other, leading to an S-shaped mean scalar profile with non-zero gradient in the channel centre. The paper

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... escribes the set of compressible flow equations, which is integrated using high-order numerical schemes in space and time. Statistical equations are presented for fully developed flow, including budgets for the Reynolds stresses, the turbulent scalar fluxes and the scalar variance. Results are presented for second order moments and the terms in the mentioned balance equations. Outer scalings are found suitable to collapse incompressible and compressible data. The reduction in the near-wall pressure-strain and pressure-scalar gradient correlations due to compressibility is explained using a Green-function-based analysis of the fluctuating pressure field.