Competition between Rayleigh–Bénard and horizontal convection

We investigate the dynamics of a fluid layer subject to bottom heat flux and top monotonically increasing temperature profile driving horizontal convection (HC). use direct numerical simulations consider large range flux-based Rayleigh numbers $10^6 \leq Ra_F 10^9$ imposed vertical ratios $0 \varLambda 1$ . The domain is closed two-dimensional box with aspect ratio $4\leq \varGamma 16$ we no-slip boundaries adiabatic side walls. demonstrate regime transition from Rayleigh–Bénard (RB) HC at $\varLambda \approx 10^{-2}$ , which independent $Ra_F$ $\varGamma$ At small $\varLambda$ flow organised in multiple overturning cells approximately unit ratio, whereas single cell obtained. RB-relevant Nusselt number scaling HC-relevant $Ra_L=Ra_F\varLambda ^4$ are good agreement previous results classical RB studies limit \ll \gg respectively. that system multi-stable near i.e. exact not only depends on but also system's history. Our suggest subglacial lakes, motivated this study, likely be dominated by convection, unless slope ice–water interface, controls gradient via pressure-dependence freezing point, greater than unity.