Thermal boundary-layer structure in laminar horizontal convection

We present experimentally obtained time-averaged vertical temperature profiles $\theta (z)$ in horizontal convection (HC) in water (Prandtl number $Pr \simeq 6$), which were measured near the heating and cooling plates that are embedded in the bottom of HC samples. Three HC rectangular samples of di...

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Bibliographic Details
Published in:Journal of fluid mechanics 2021-03, Vol.915, Article R5
Main Authors: Yan, Bo, Shishkina, Olga, He, Xiaozhou
Format: Article
Language:English
Subjects:
Approximation
Aspect ratio
Boundary conditions
Boundary layers
Convection
Cooling
Experiments
Heat
Heating
JFM Rapids
Kinematics
Ocean circulation
Prandtl number
Rayleigh number
Reynolds number
Scaling
Temperature
Temperature distribution
Temperature fields
Temperature profile
Temperature profiles
Thermal boundary layer
Thickness
Viscosity
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Summary:We present experimentally obtained time-averaged vertical temperature profiles $\theta (z)$ in horizontal convection (HC) in water (Prandtl number $Pr \simeq 6$), which were measured near the heating and cooling plates that are embedded in the bottom of HC samples. Three HC rectangular samples of different sizes but the same aspect ratio $\varGamma \equiv L:W:H = 10:1:1$ ($L$, $W$ and $H$ are the length, width and height of the sample, respectively) were used in the experiments, which allowed us to study HC in a Rayleigh-number range $2 \times 10^{10} \lesssim {Ra} \lesssim 9 \times 10^{12}$. The measurements revealed that above the cooling plate, the mean temperature profiles have a universal scaling form $\theta (z/\lambda _c)$ with $\lambda _c$ being a $Ra$-dependent thickness of the cold thermal boundary layer (BL). The $\theta (z/\lambda _c)$-profiles agree well with solutions to a laminar BL equation in HC, which is derived under assumption that the large-scale horizontal velocity achieves its maximum near the plate and vanishes in the bulk. Above the heating plate, the mean temperature field has a double-layer structure: in the lower layer, the $\theta$ profiles scale with the hot thermal BL thickness $\lambda _h$, while in the upper layer, they again scale with $\lambda _c$. Both scaling forms are in good agreement with the solutions to the BL equation with a proper parameter choice.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2021.226