Transition between quasi-two-dimensional and three-dimensional Rayleigh-Bénard convection in a horizontal magnetic field

2018 ◽  
Vol 3 (1) ◽  
Author(s):  
Tobias Vogt ◽  
Wataru Ishimi ◽  
Takatoshi Yanagisawa ◽  
Yuji Tasaka ◽  
Ataru Sakuraba ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Regular flow reversals in Rayleigh-Bénard convection in a horizontal magnetic field

2016 ◽  
Vol 93 (4) ◽  
Author(s):  
Yuji Tasaka ◽  
Kazuto Igaki ◽  
Takatoshi Yanagisawa ◽  
Tobias Vogt ◽  
Till Zuerner ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Horizontal Magnetic Field ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Flow Reversals ◽  
Rayleigh Benard ◽  
Regular Flow

A model for the emergence of thermal plumes in Rayleigh–Bénard convection at infinite Prandtl number

2000 ◽  
Vol 414 ◽  
pp. 225-250 ◽  
Author(s):  
C. LEMERY ◽  
Y. RICARD ◽  
J. SOMMERIA
Keyword(s):  
Prandtl Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Thermal Plumes ◽  
Bénard Convection ◽  
Benard Convection ◽  
Two Dimensional Model ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

We propose a two-dimensional model of three-dimensional Rayleigh–Bénard convection in the limit of very high Prandtl number and Rayleigh number, as in the Earth's mantle. The model equation describes the evolution of the first moment of the temperature anomaly in the thermal boundary layer, which is assumed thin with respect to the scale of motion. This two-dimensional field is transported by the velocity that it induces and is amplified by surface divergence. This model explains the emergence of thermal plumes, which arise as finite-time singularities. We determine critical exponents for these singularities. Using a smoothing method we go beyond the singularity and reach a stage of developed convection. We describe a process of plume merging, leaving room for the birth of new instabilities. The heat flow at the surface predicted by our two-dimensional model is found to be in good agreement with available data.

On non-Oberbeck–Boussinesq effects in three-dimensional Rayleigh–Bénard convection in glycerol

2013 ◽  
Vol 724 ◽  
pp. 175-202 ◽  
Author(s):  
Susanne Horn ◽  
Olga Shishkina ◽  
Claus Wagner
Keyword(s):  
Boundary Layer ◽  
Material Properties ◽  
Three Dimensional ◽  
Bottom Plate ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Viscous Boundary ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

AbstractRayleigh–Bénard convection in glycerol (Prandtl number $\mathit{Pr}= 2547. 9$) in a cylindrical cell with an aspect ratio of $\Gamma = 1$ was studied by means of three-dimensional direct numerical simulations (DNS). For that purpose, we implemented temperature-dependent material properties into our DNS code, by prescribing polynomial functions up to seventh order for the viscosity, the heat conductivity and the density. We performed simulations with the common Oberbeck–Boussinesq (OB) approximation and with non-Oberbeck–Boussinesq (NOB) effects within a range of Rayleigh numbers of $1{0}^{5} \leq \mathit{Ra}\leq 1{0}^{9} $. For the highest temperature differences, $\Delta = 80~\mathrm{K} $, the viscosity at the top is ${\sim }360\hspace{0.167em} \% $ times higher than at the bottom, while the differences of the other material properties are less than $15\hspace{0.167em} \% $. We analysed the temperature and velocity profiles and the thermal and viscous boundary-layer thicknesses. NOB effects generally lead to a breakdown of the top–bottom symmetry, typical for OB Rayleigh–Bénard convection. Under NOB conditions, the temperature in the centre of the cell ${T}_{c} $ increases with increasing $\Delta $ and can be up to $15~\mathrm{K} $ higher than under OB conditions. The comparison of our findings with several theoretical and empirical models showed that two-dimensional boundary-layer models overestimate the actual ${T}_{c} $, while models based on the temperature or velocity scales predict ${T}_{c} $ very well with a standard deviation of $0. 4~\mathrm{K} $. Furthermore, the obtained temperature profiles bend closer towards the cold top plate and further away from the hot bottom plate. The situation for the velocity profiles is reversed: they bend farther away from the top plate and closer towards to the bottom plate. The top boundary layers are always thicker than the bottom ones. Their ratio is up to 2.5 for the thermal and up to 4.5 for the viscous boundary layers. In addition, the Reynolds number $\mathit{Re}$ and the Nusselt number $\mathit{Nu}$ were investigated: $\mathit{Re}$ is higher and $\mathit{Nu}$ is lower under NOB conditions. The Nusselt number $\mathit{Nu}$ is influenced in a nonlinear way by NOB effects, stronger than was suggested by the two-dimensional simulations. The actual scaling of $\mathit{Nu}$ with $\mathit{Ra}$ in the NOB case is $\mathit{Nu}\propto {\mathit{Ra}}^{0. 298} $ and is in excellent agreement with the experimental data.

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

2021 ◽  
Vol 911 ◽  
Author(s):  
Jian-Lin Yang ◽  
Yi-Zhao Zhang ◽  
Tian-cheng Jin ◽  
Yu-Hong Dong ◽  
Bo-Fu Wang ◽  
...  
Keyword(s):  
Roughness Height ◽  
Two Dimensional ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

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