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 (22)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Scaling in thermal convection: A unifying theory
• Thermal convection for large Prandtl numbers
• Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
• Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection
• The unifying theory of scaling in thermal convection: The updated prefactors
• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• Comparison between two and three dimensional Rayleigh-Bénard convection
• Transition to the ultimate regime in two-dimensional Rayleigh-Bénard convection
• Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection
• AFiD-GPU: a versatile Navier-Stokes Solver for Wall-Bounded Turbulent Flows on GPU Clusters
• Exploring the phase diagram of fully turbulent Taylor-Couette flow
• Mixed convection in turbulent channels with unstable stratification
• Extreme-scale motions in turbulent plane Couette flows
• Comparison of computational codes for direct numerical simulations of turbulent Rayleigh-Bénard convection
• Universal continuous transition to turbulence in a planar shear flow
• Flow organization and heat transfer in turbulent wall sheared thermal convection
• Heat flux scaling in turbulent Rayleigh-Bénard convection with an imposed longitudinal wind
• Law of the wall in an unstably stratified turbulent channel flow
• What rotation rate maximizes heat transport in rotating Rayleigh-Bénard convection with Prandtl number larger than one?
• The Surprising Transition in Atmospheric Boundary Layer Turbulence Structure from Neutral to Moderately Convective Stability States and Mechanisms Underlying Large-scale Rolls
• From zonal flow to convection rolls in Rayleigh-Bénard convection with free-slip plates

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