The effect of Prandtl number on turbulent sheared thermal convection

Blass, Alexander; Tabak, Pier; Verzicco, Roberto; Stevens, Richard J. A. M.; Lohse, Detlef

doi:10.1017/jfm.2020.1019

Cited by 18 publications

(37 citation statements)

References 54 publications

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“…Compared with RBC, where large-scale thermal structures do not exhibit a preferred direction, the mean shear at the wall in VC introduces significant anisotropy to the wall structures. Streaky structures elongated in the vertical (y) direction are prominent in figure 2, similar to those seen in the sheared RBC set-up of Blass et al (2021). Furthermore, in that study, an increased Pr (for fixed Ra and Re) was found to enhance momentum transport from the walls, allowing the wall shear to affect the flow structures in the bulk more easily.…”

Section: Flow Visualisationsupporting

confidence: 71%

Boundary layers in turbulent vertical convection at high Prandtl number

Howland

Verzicco

et al. 2021

J. Fluid Mech.

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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 $\mbox {{Ra}}$ and Prandtl number ${Pr}$ . For the considered parameter range $1\leq {Pr} \leq 100$ , $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$ , 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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Section: Flow Visualisationsupporting

confidence: 71%

Boundary layers in turbulent vertical convection at high Prandtl number

Howland

Verzicco

et al. 2021

J. Fluid Mech.

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“…As discussed above, Nu-enhancement is observed in the buoyancy-dominant regime (see figure 6b). This finding is different from Nu being initially suppressed by the shear-induced plume-sweeping effects in previous studies of Couette-RB (Blass et al 2020(Blass et al , 2021 or Poiseuille-RB (Scagliarini et al 2014) convection over smooth plates. Then the question is how the heat-transfer efficiency is improved in rough cases.…”

Section: Heat-transport Enhancement In the Buoyancy-dominant Regimecontrasting

confidence: 99%

“…For the smooth case (h = 0), it is seen that Nu is nearly unchanged in the buoyancy-dominated regime, then slowly transits to the minimum value in the shear-dominant regime. This result shows that shear-induced modification on heat transfer for two-dimensional cases is different from that for three-dimensional cases as studied by (Blass et al 2020(Blass et al , 2021 in thermal convection over smooth surfaces, due to the lack of fluid motion in the third direction. When the roughness is applied, the mechanism of heat transfer enhancement due to the combined effects of roughness and shear begins to work, Nu tends to be enhanced, and with increasing h, the maximal Nu-enhancement rate becomes larger.…”

Section: The Influence Of Roughness Heightmentioning

confidence: 61%

“…A similar result was also found in the case of sheared stably stratified turbulence (Zonta & Soldati 2018). The effects of Pr on wall-sheared RB convection (Blass et al 2021) and on sheared stably stratified flow (Langham, Eaves & Kerswell 2020) were further studied. Moreover, Scagliarini et al (2015) studied the BL characteristics of sheared RB turbulence.…”

Section: Introductionmentioning

confidence: 99%

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Shear-induced modulation on thermal convection over rough plates

Jin

Zhang

et al. 2022

J. Fluid Mech.

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External modulation on thermal convection has been studied extensively to achieve the control of flow structures and heat-transfer efficiency. In this paper, we carry out direct numerical simulations on Rayleigh–Bénard convection accounting for both the modulation of wall shear and roughness over the Rayleigh number range $1.0 \times 10^6 \le Ra \le 1.0 \times 10^8$ , the wall shear Reynolds number range $0 \le Re_w \le 5000$ , the aspect-ratio range $2 \le \varGamma \le 4{\rm \pi}$ , and the dimensionless roughness height range $0 \le h \le 0.2$ at fixed Prandtl number $Pr = 1$ . Under the combined actions of wall shear and roughness, with increasing $Re_w$ , the heat flux is initially enhanced in the buoyancy-dominant regime, then has an abrupt transition near the critical shear Reynolds number $Re_{w,cr}$ , and finally enters the purely diffusion regime dominated by shear. Based on the crossover of the kinetic energy production between the buoyancy-dominant and shear-dominant regimes, a physical model is proposed to predict the transitional scaling behaviour between $Re_{w,cr}$ and $Ra$ , i.e. $Re_{w,cr} \sim Ra^{9/14}$ , which agrees well with our numerical results. The reason for the observed heat-transport enhancement in the buoyancy-dominant regime is further explained by the fact that the moving rough plates introduce an external shear to strengthen the large-scale circulation (LSC) in the vertical direction and serve as a conveyor belt to increase the chances of the interaction between the LSC and secondary flows within cavities, which triggers more thermal plumes, efficiently transports the trapped hot (cold) fluids outside cavities.

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“…However, this general practice is considered heretical by most fluid dynamicists, as there is a wealth of evidence showing that doing this often gives nonsensical results. For example, adding shear to convection or fingering convection can reduce mixing considerably (Garaud et al 2019;Blass et al 2021) instead of increasing it.…”

Section: Coexistence Of Shear and Gsf Instabilitiesmentioning

confidence: 99%

Modeling coexisting GSF and shear instabilities in rotating stars

Chang,

Garaud

2021

Preprint

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Zahn's widely-used model for turbulent mixing induced by rotational shear has recently been validated (with some caveats) in non-rotating shear flows. It is not clear, however, whether his model remains valid in the presence of rotation, even though this was its original purpose. Furthermore, new instabilities arise in rotating fluids, such as the Goldreich-Schubert-Fricke (GSF) instability. Which instability dominates when more than one can be excited, and how they influence each other, were open questions that this paper answers. To do so, we use direct numerical simulations of diffusive stratified shear flows in a rotating triply-periodic Cartesian domain located at the equator of a star. We find that either the GSF instability or the shear instability tends to take over the other in controlling the system, suggesting that stellar evolution models only need to have a mixing prescription for each individual instability, together with a criterion to determine which one dominates. However, we also find that it is not always easy to predict which instability "wins" for given input parameters, because the diffusive shear instability is subcritical, and only takes place if there is a finite-amplitude turbulence "primer" to seed it. Interestingly, we find that the GSF instability can in some cases play the role of this primer, thereby providing a pathway to excite the subcritical shear instability. This can also drive relaxation oscillations, that may be observable. We conclude by proposing a new model for mixing in the equatorial regions of stellar radiative zones due to differential rotation.

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The effect of Prandtl number on turbulent sheared thermal convection

Abstract: Abstract

Cited by 18 publications

References 54 publications

Boundary layers in turbulent vertical convection at high Prandtl number

Boundary layers in turbulent vertical convection at high Prandtl number

Shear-induced modulation on thermal convection over rough plates

Modeling coexisting GSF and shear instabilities in rotating stars

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