Velocity dip in turbulent mixed convection of an open Poiseuille-Rayleigh-B\'enard channel

Abstract

We study the emergence of a velocity-dip phenomenon in turbulent mixed convection in open Poiseuille-Rayleigh-B\'enard (PRB) channels with a free-slip upper boundary. Three-dimensional direct numerical simulations (DNS) are performed for Rayleigh numbers in the range $10^5 \leq Ra \leq 10^8$, at a fixed Prandtl number $Pr = 0.71$ and a bulk Reynolds number $Re_b = 2850$. In the shear-dominated regime, the flow is characterised by small-scale structures such as near-wall streaks. As buoyancy becomes comparable to shear, streamwise-oriented large-scale rolls emerge and span the full channel height. At higher Rayleigh numbers, buoyancy dominates and the rolls fragment, giving rise to a convection-cell-dominated regime. Short-time-averaged flow fields show that streamwise rolls transport low-speed fluid from the bottom wall towards the upper boundary, forming laterally extended low-speed regions, while roll fragmentation induces upstream low-speed regions near the upper boundary. Both mechanisms locally reduce the near-surface mean velocity, leading to a velocity dip in which the maximum mean streamwise velocity is located below the upper boundary. Consistent with the mean momentum budget, the near-surface region exhibits a large-scale Reynolds shear stress that exceeds the local total shear stress, implying a negative viscous contribution and a reversal of the mean velocity gradient. To model this behaviour, we propose a model based on a balance between buoyancy and shear production with dissipation, incorporating a linear wall-normal profile for the Reynolds shear stress, a wall-normal-independent buoyancy-production term, and a decomposition of the dissipation into shear-induced and buoyancy-induced contributions. Our model accurately reproduces the DNS mean velocity profiles across the explored $Ra$ range.