Modified scaling for turbulent heat transfer on rough surfaces

This study proposes a modified scaling for turbulent heat transfer on rough walls. The formulation introduces modified friction quantities uτ∗ and Tτ∗, exploiting a non-dimensional parameter G. Directly computed from simulations, G enters the Reynolds analogy and reflects the absence of a heat-transfer counterpart to local pressure gradients. Two numerical databases at comparable Pr∼0.7 are examined: a periodic channel DNS over sinusoidal roughness, and a turbulent thermal boundary layer LES over irregular ice roughness. Despite their differing topologies, both reveal a proportionality between G and the roughness Stanton number Stk−1. A relation was fitted that provides accurate St estimates and supports the interpretation of G as a measure of thermal resistance relative to momentum transfer, similarly to Stk−1. Furthermore, a correction to the classical ΔΘ+(ks+) scaling, based on G, yields improved collapse of temperature and velocity log-layer shifts. The results indicate that G could be potentially used to extend Reynolds analogy models based on the proposed scaling. While being limited to specific roughness datasets and flow conditions, this framework offers a first step towards an alternative numerical modeling of heat transfer in rough-wall turbulence.