The effect of Prandtl number on turbulent sheared thermal convection

TL;DR

This study investigates how the Prandtl number influences flow structures and heat transport in turbulent sheared thermal convection through direct numerical simulations at fixed Rayleigh number, revealing the emergence of turbulent boundary layers and extending existing theoretical models.

Contribution

It extends prior work by analyzing the impact of Prandtl number on flow regimes and heat transport in sheared Rayleigh-Bénard convection, incorporating boundary layer behavior and theoretical model extension.

Findings

Prandtl number significantly affects flow morphology and dynamics.

High Prandtl numbers enhance wall momentum transport and shear effects.

Turbulent boundary layers with Prandtl-von Karman log-layer emerge at high shear and Prandtl numbers.

Abstract

In turbulent wall sheared thermal convection, there are three different flow regimes, depending on the relative relevance of thermal forcing and wall shear. In this paper we report the results of direct numerical simulations of such sheared Rayleigh-B\'enard convection, at fixed Rayleigh number $Ra=10^6$, varying the wall Reynolds number in the range $0 \leq Re_w \leq 4000$ and Prandtl number $0.22 \leq Pr \leq 4.6$, extending our prior work by Blass et al. (2020), where $Pr$ was kept constant at unity and the thermal forcing ($Ra$) varied. We cover a wide span of bulk Richardson numbers $0.014 \leq Ri \leq 100$ and show that the Prandtl number strongly influences the morphology and dynamics of the flow structures. In particular, at fixed $Ra$ and $Re_w$, a high Prandtl number causes stronger momentum transport from the walls and therefore yields a greater impact of the wall shear on the flow structures, resulting in an increased effect of $Re_w$ on the Nusselt number. Furthermore, we analyse the thermal and kinetic boundary layer thicknesses and relate their behaviour to the resulting flow regimes. For the largest shear rates and $Pr$ numbers, we observe the emergence of a Prandtl-von Karman log-layer, signalling the onset of turbulent dynamics in the boundary layer. Finally, our results allow to extend the Grossmann-Lohse theory for heat transport in Rayleigh-B\'enard convection to the sheared case, universally describing $Nu(Ra,Pr,Re_w)$.