Direct numerical simulation of a self-similar thermally coupled adverse pressure gradient turbulent boundary layer on the verge of separation

We conduct direct numerical simulation (DNS) of a thermally coupled turbulent boundary layer (TTBL) subjected to a strong adverse pressure gradient (APG) and approaching incipient separation at a displacement-thickness Reynolds number Reδ1 ≈2.9 ×104. Heat transfer is modelled by a temperature scalar with an isothermal wall and Pr = 0.71 (air), where the fluid is subjected to buoyancy forces via the Boussinesq approximation. A dual-domain strategy is used in which the main TTBL receives time-dependent inflow from a purely hydrodynamic turbulent boundary layer (TBL) via recycling. These DNS represent to our knowledge, the highest-resolution heated APG boundary-layer simulations with coupled thermal transport at this Reynolds number. Mean velocity and temperature profiles, Reynolds stresses, and velocity–temperature correlations exhibit near self-similarity under outer scaling with Ue and δ1, extending hydrodynamic self-similarity arguments to buoyancy-affected TTBLs. The Reynolds stresses present a secondary inner peak in the spanwise intensity, indicating enhanced near-wall activity. The turbulent kinetic energy (TKE) budget shows that buoyancy suppresses the turbulent transport term, rendering it locally a sink of TKE, in contrast to the hydrodynamic APG case where it acts as a source.