Boundary layers in turbulent vertical convection at high Prandtl number

TL;DR

This study uses advanced simulations to analyze turbulent boundary layers in high Prandtl number vertical convection, revealing how heat flux and boundary layer widths depend on Rayleigh and Prandtl numbers, with implications for environmental flows.

Contribution

It introduces a multiple-resolution simulation approach to explore turbulent boundary layers across a wide range of Prandtl numbers, providing new insights into their parameter dependence.

Findings

Flow is buoyancy-controlled with heat flux independent of wall separation.

Heat flux scales linearly with friction velocity for given Prandtl number.

Results inform parameterization of heat and salt fluxes at ice-ocean interfaces.

Abstract

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 $1\leq Pr \leq 100$, $10^6 \leq Ra \leq 10^9$, 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.