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arXiv · 2601.05786

On the Reynolds analogy for high-speed rough-wall flows: implications for wall modelling

Michele Cogo·Davide Depieri·Matteo Bernardini·Francesco Picano
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Abstract

We study the validity of the generalized Reynolds analogy (GRA) in compressible turbulent boundary layers over prism-shaped roughness by mining direct numerical simulation data of Mach 2 and Mach 4 compressible turbulent boundary layers with adiabatic and cooled surfaces. Although the direct influence of roughness strongly disrupts the near-wall coupling between momentum and energy, we show that this breakdown is confined to the roughness sublayer. Above this layer, the enthalpy and velocity fields recover a smooth-wall-like similarity, and the GRA becomes asymptotically valid by naturally accounting for roughness-enhanced wall shear stress and heat flux. Building on these results, we propose a GRA-based wall model for predicting heat transfer over rough surfaces, which is coupled with a drag-predictive physics-based method developed for prism-shaped roughness by means of compressibility transformations.

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Michele Cogo, Davide Depieri, Matteo Bernardini, Francesco Picano. 2026-01-09. On the Reynolds analogy for high-speed rough-wall flows: implications for wall modelling. https://arxiv.org/abs/2601.05786

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