Energetic aspects of the Reynolds analogy in rough-wall turbulent forced convection

This work investigates the Reynolds analogy in turbulent forced convection over rough walls using an energetic framework. Extending the analysis of Secchi et al. [1], we relate momentum and scalar transfer to the integral dissipation rates of mechanical energy and the squared scalar field, examining how these quantities depend on the method used to drive the flow. Direct numerical simulations of rough-wall channel flows at friction Reynolds numbers up to Re$_τ$ = 540 are rescaled to compare three driving strategies: constant pressure gradient (CPG), constant flow rate (CFR), and constant power input (CPI). For each flow driving strategy appropriate indexes for measuring the net momentum and scalar transfer are identified and their relationships to the integral dissipation rates of mechanical and squared scalar field are investigated.