In this study we consider the effect of a horizontal magnetic field on the Rayleigh-Bénard convection in a finite liquid metal layer contained in a cuboid vessel $(200\times 200\times 40\mathrm{m}{\mathrm{m}}^3)$ of aspect ratio $\mathrm{\Gamma }=5$ . Laboratory experiments are performed for measuring temperature and flow field in the low melting point alloy GaInSn at Prandtl number $Pr\approx 0.03$ and in a Rayleigh number range $2.3\times {10}^4\le Ra\le 2.6\times {10}^5$. The field direction is aligned parallel to one pair of the two side walls. The field strength is varied up to a maximum value of 320 mT ($Ha=2470$, $Q=6.11\times {10}^6$, definitions of all nondimensional numbers are given in the text). The magnetic field forces the flow to form two-dimensional (2D) rolls whose axes are parallel to the direction of the field lines. The experiments confirm the predictions made by Busse and Clever [Busse and Clever, Stability of convection rolls in the presence of a horizontal magnetic field, J. de Méc. Théor. et Appl. 2, 495 (1983)] who showed that the application of the horizontal magnetic field extends the range in which steady 2D roll structures exist (Busse balloon) towards higher Ra numbers. A transition from the steady to a time-dependent oscillatory flow occurs when Ra exceeds a critical value for a given Chandrasekhar number Q, which is also equivalent to a reduction of the ratio $Q/Ra$. Our measurements reveal that the first developing oscillations are clearly of 2D nature, in particular a mutual increase and decrease in the size of adjacent convection rolls is observed without the formation of any detectable gradients in the velocity field along the magnetic field direction. At a ratio of $Q/Ra\approx 1$, the first 3D structures appear, which initially manifest themselves in a slight inclination of the rolls with respect to the magnetic field direction. Immediately in the course of this, there arise also disturbances in the spaces between adjacent convection rolls, which are advected along the rolls due to the secondary flow driven by Ekman pumping. The transition to fully developed 3D structures and then to a turbulent regime takes place with further lowering $Q/Ra$.

中文翻译：

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在水平磁场作用下，Rayleigh-Bénard对流从稳态对流辊过渡到振荡对流辊

在这项研究中，我们考虑了水平磁场对长方体容器中有限的液态金属层中的瑞利-贝纳德对流的影响 $（200\times 200\times 40\mathrm{米}{\mathrm{米}}^3）$ 长宽比 $\mathrm{\Gamma }=5$。进行实验室实验以测量Prandtl值低熔点合金GaInSn中的温度和流场$P\mathrm{[R}\approx 0.03$ 并且在瑞利数范围内 $2.3\times {10}^4\le \mathrm{[R}\mathrm{一种}\le 2.6\times {10}^5$。场方向平行于两个侧壁中的一对。场强变化最大为320 mT（$H\mathrm{一种}=2470$， $问=6.11\times {10}^6$，文字中给出了所有无量纲数字的定义）。磁场迫使流体形成二维（2D）辊，其轴线平行于磁力线的方向。实验证实了Busse和Clever所做的预测[Busse and Clever，在水平磁场存在下，对流辊的稳定性，J。deMéc。é 等应用 [2，495（1983）]指出，水平磁场的施加将稳定的2D滚动结构（Busse气球）存在的范围扩展到了更高的Ra数。当Ra超过给定Chandrasekhar数Q的临界值时，就会发生从稳态到与时间有关的振荡流的过渡，这也等于比率的减小$问/\mathrm{[R}\mathrm{一种}$。我们的测量结果表明，最初形成的振荡显然具有二维性质，尤其是观察到相邻对流辊尺寸的相互增加和减小，而沿磁场方向在速度场中未形成任何可检测到的梯度。比例为$问/\mathrm{[R}\mathrm{一种}\approx \mathrm{1个}$，出现了第一个3D结构，这些结构最初以辊子相对于磁场方向的轻微倾斜体现出来。紧接着在此过程中，在相邻对流辊之间的空间中也产生了扰动，这些扰动由于由埃克曼泵浦驱动的二次流而沿辊对流。过渡到完全发展的3D结构，然后过渡到湍流状态，进一步降低$问/\mathrm{[R}\mathrm{一种}$。