Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers $Pr$. This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $Ra$ and Prandtl number $Pr$. For the considered parameter range $1leq Pr leq 100$, $10^6 leq Ra leq 10^9$, we find the flow to be consistent with a buoyancy-controlled regime where the heat flux is independent of the wall separation. For given $Pr$, the heat flux is found to scale linearly with the friction velocity $V_ast$. Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice-ocean interfaces.
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