The -dependence of the critical roughness height in two-dimensional turbulent Rayleigh–Bénard convection

Yang, Jing; Zhang, Yi-Zhao; Jin, Tian-Cheng; Dong, Yuhong; Wang, Bo-Fu; Zhou, Quan

doi:10.1017/jfm.2020.1091

Cited by 32 publications

(10 citation statements)

References 70 publications

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“…Then these hot plumes move upwards along the sidewall, and they encounter and interact with the confronting cold plumes carried by the main LSC. This flow pattern is the same as observed in previous studies (Sugiyama et al 2010;Huang & Zhou 2013;Zhang et al 2017Zhang et al , 2018Yang et al 2021a). However, for small k (e.g.…”

Section: Cause Of Corner-roll Suppressionsupporting

confidence: 90%

Suppression of flow reversals via manipulating corner rolls in plane Rayleigh–Bénard convection

Zhao

Wang

et al. 2022

J. Fluid Mech.

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In this paper, we report that reversals of the large-scale circulation in two-dimensional Rayleigh–Bénard (RB) convection can be suppressed by imposing sinusoidally distributed heating to the bottom plate. We examine how the frequency of flow reversals depends on the dimensionless wavenumber $k$ of the spatial temperature modulation with various modulation amplitude $A$ . For sufficiently large $k$ , the flow reversal frequency is close to that in the standard RB convection under uniform heating. However, when $k$ decreases, the frequency of flow reversal gradually becomes lower and can even be largely reduced. Furthermore, we examine the growth of the corner roll and the global flow structure based on Fourier mode decomposition, and reveal that the size of the corner roll diminishes as the wavenumber decreases. The reason is that the regions occupied by the cold phase can absorb heat from the hot plumes and thus lower their temperature, which reduces the corner roll's kinetic energy input provided by the buoyancy force, and weakens the feeding process of the corner rolls. This results in the locking of the corner roll into a smaller region near the corner, making it harder for a reversal to occur. Using the concept of horizontal convection caused by non-uniform heating, we find a relevant parameter $k/A$ to describe briefly how the reversal frequency depends on wavenumber and modulation amplitude. The present work provides a new way to control the flow reversals in RB convection through modifying temperature boundary conditions.

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Section: Cause Of Corner-roll Suppressionsupporting

confidence: 90%

Suppression of flow reversals via manipulating corner rolls in plane Rayleigh–Bénard convection

Zhao

Wang

et al. 2022

J. Fluid Mech.

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“…We also find that Re decreases as P r −0.81±0.01 . The P r-dependence of Re in the NOB flows is qualitatively similar to that in OB convection [57,60,61].…”

Section: Turbulent Prandtl Number In Non-oberbeck-boussinesq Convecti...supporting

confidence: 59%

Non-Boussinesq convection at low Prandtl numbers relevant to the Sun

Pandey,

Schumacher,

Sreenivasan

2021

Preprint

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Convection in the Sun occurs at Rayleigh numbers, Ra, as high as 10 22 , molecular Prandtl number, P r, as low as 10 −6 , and occurs under conditions that are far from satisfying the Oberbeck-Boussinesq (OB) idealization. The effects of these extreme circumstances on turbulent heat transport are unknown, and no comparable conditions exist on Earth. Our goal is to understand how these effects scale (since we cannot yet replicate the Sun's conditions faithfully). We study thermal convection by using direct numerical simulations, and determine the variation with respect to P r, up to P r as low as 10 −4 , of the turbulent Prandtl number, P rt, which is the ratio of turbulent viscosity to thermal diffusivity. The simulations are primarily two-dimensional but we draw upon some three-dimensional results as well. We focus on non-Oberbeck-Boussinesq (NOB) conditions of a certain type, but also study OB convection for comparison. The OB simulations are performed in a rectangular box of aspect ratio 2 by varying P r from O(10) to 10 −4 at fixed Grashof number Gr ≡ Ra/P r = 10 9 . The NOB simulations are done in the same box by letting only the thermal diffusivity depend on the temperature. Here, the Rayleigh number is fixed at the top boundary while the mean P r varies in the bulk from 0.07 to 5 × 10 −4 . The three-dimensional simulations are performed in a box of aspect ratio 25 at a fixed Rayleigh number of 10 5 , and 0.005 < P r < 7. The principal finding is that P rt increases with decreasing P r in both OB and NOB convection: P rt ∼ P r −0.3 for OB convection and P rt ∼ P r −1 for the NOB case. The P rt-dependence for the NOB case especially suggests that convective flows in the astrophysical settings behave effectively as in high-Prandtl-number turbulence.

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“…The single-phase Rayleigh–Bénard (RB) convection, which is a paradigmatic example used to study the buoyancy-driven fluid flow, has been extensively investigated in the recent decades (Ahlers, Grossmann & Lohse 2009; Lohse & Xia 2010; Wang, Zhou & Sun 2020; Yang et al. 2021). As for the RB convection laden with micro isothermal inertial particles, Oresta & Prosperetti (2013) found that mechanical coupling plays a greater role in the increase of the Nusselt number ( Nu ) than the thermal coupling in a cylindrical cell.…”

Section: Introductionmentioning

confidence: 99%

Dynamic coupling between carrier and dispersed phases in Rayleigh–Bénard convection laden with inertial isothermal particles

et al. 2021

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We investigate the dynamic couplings between particles and fluid in turbulent Rayleigh–Bénard (RB) convection laden with isothermal inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of Rayleigh number $1\times 10^6 \le {Ra}\le 1 \times 10^8$ at Prandtl number ${Pr}=0.678$ for three Stokes numbers ${St_f}=1 \times 10^{-3}$ , $8 \times 10^{-3}$ and $2.5 \times 10^{-2}$ . It is found that the global heat transfer and the strength of turbulent momentum transfer are altered a small amount for the small Stokes number and large Stokes number as the coupling between the two phases is weak, whereas they are enhanced a large amount for the medium Stokes number due to strong coupling of the two phases. We then derived the exact relation of kinetic energy dissipation in the particle-laden RB convection to study the budget balance of induced and dissipated kinetic energy. The strength of the dynamic coupling can be clearly revealed from the percentage of particle-induced kinetic energy over the total induced kinetic energy. We further derived the power law relation of the averaged particles settling rate versus the Rayleigh number, i.e. $S_p/(d_p/H)^2{\sim} Ra^{1/2}$ , which is in remarkable agreement with our simulation. We found that the settling and preferential concentration of particles are strongly correlated with the coupling mechanisms.

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The -dependence of the critical roughness height in two-dimensional turbulent Rayleigh–Bénard convection

Abstract: Abstract

Cited by 32 publications

References 70 publications

Suppression of flow reversals via manipulating corner rolls in plane Rayleigh–Bénard convection

Suppression of flow reversals via manipulating corner rolls in plane Rayleigh–Bénard convection

Non-Boussinesq convection at low Prandtl numbers relevant to the Sun

Dynamic coupling between carrier and dispersed phases in Rayleigh–Bénard convection laden with inertial isothermal particles

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