On the Reynolds analogy for high-speed rough-wall flows: implications for wall modelling
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arXiv
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| Format: | Preprint |
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2026
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| author | Cogo, Michele Depieri, Davide Bernardini, Matteo Picano, Francesco |
| author_facet | Cogo, Michele Depieri, Davide Bernardini, Matteo Picano, Francesco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05786 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Reynolds analogy for high-speed rough-wall flows: implications for wall modelling Cogo, Michele Depieri, Davide Bernardini, Matteo Picano, Francesco Fluid Dynamics 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. |
| title | On the Reynolds analogy for high-speed rough-wall flows: implications for wall modelling |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2601.05786 |