The effect of Prandtl number on turbulent sheared thermal convection

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-Bénard convection, at fixed Rayleigh number $Ra=10^6$, varying the wall Reynolds number in the range $0\le R{e}_w\le 4000$ and Prandtl number $0.22\le Pr\le 4.6$, 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 $0.014\le Ri\le 100$ and show that the Prandtl number strongly influences the morphology and dynamics of the flow structures. In particular, at fixed $Ra$ and $R{e}_w$, 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 $R{e}_w$ 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-Bénard convection to the sheared case, universally describing $Nu(Ra,Pr,R{e}_w)$.

References in corpus (4)

• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• Comparison between two and three dimensional Rayleigh-Bénard convection
• What rotation rate maximizes heat transport in rotating Rayleigh-Bénard convection with Prandtl number larger than one?
• From zonal flow to convection rolls in Rayleigh-Bénard convection with free-slip plates

Cited by in corpus (11)

• Wall-sheared thermal convection: heat transfer enhancement and turbulence relaminarization
• Heat transfer in turbulent Rayleigh-Bénard convection within two immiscible fluid layers
• Particle transport and deposition in wall-sheared thermal turbulence
• Temporal modulation on mixed convection in turbulent channels
• Turbulent mixed convection in vertical and horizontal channels
• Effect of radius ratio on the sheared annular centrifugal turbulent convection
• Modeling coexisting GSF and shear instabilities in rotating stars
• Plane-layer Rayleigh-Bénard convection up to $Ra=10^{11}$: Near-wall fluctuations and role of initial conditions
• Boundary layers in turbulent vertical convection at high Prandtl number
• Geophysical flows over topography, a playground for laboratory experiments
• Analysis and reformulation of the $k$--$\omega$ turbulence model for buoyancy-driven thermal convection