Buoyancy-induced velocity dip in turbulent open Poiseuille--Rayleigh--B\'enard convection

Abstract

We investigate buoyancy-induced transitions in flow structure and the associated velocity dip in turbulent mixed convection. Numerical simulations are performed for an open Poiseuille--Rayleigh--B\'enard system with a heated no-slip lower wall and a cooled free-slip upper boundary over $10^5 \leq Ra \leq 10^8$, $90 \leq Re_b \leq 5700$, $Pr=0.71$, and $0.013 \leq Ri_b \leq 17$. The flow organisation is governed primarily by the bulk Richardson number $Ri_b$. As buoyancy increases, the flow changes from a shear-dominated state to streamwise-oriented large-scale rolls and then to fragmented rolls. Roll formation coincides with a reorganisation of the velocity statistics about the channel midplane and a displacement of the maximum mean streamwise velocity from the upper boundary into the channel interior, producing a velocity dip. The mean momentum balance shows that spatially uniform streamwise forcing imposes a linear total-stress profile. Wherever the Reynolds shear stress exceeds the local total stress, the viscous stress and mean velocity gradient must be negative. A triple decomposition attributes most of the Reynolds-stress excess in the roll states to slowly varying, roll-associated motions. The roll-associated stress and dip strength vary non-monotonically with $Ri_b$. Quadrant analysis shows that ejections and sweeps sustain the net roll-associated stress, whereas roll fragmentation strengthens the cancellation between positive and negative contributions and weakens the dip. The turbulent kinetic energy (TKE) budget shows a corresponding shift from near-wall shear production to bulk buoyancy production, with shear production becoming negative above the velocity maximum. Finally, a case-specific \textit{a posteriori} simplification of the core-region TKE budget yields an approximate velocity profile that captures the gradient reversal.