Classical and symmetrical horizontal convection is studied by means of direct numerical simulations for Rayleigh numbers $Ra$ up to 3 × 1012 and Prandtl numbers $Pr=0.1$ , 1 and 10. For both set-ups, a very good agreement in global quantities with respect to heat and momentum transport is attained. Similar to Shishkina & Wagner (Phys. Rev. Lett., vol. 116, 2016, 024302), we find Nusselt number $Nu$ versus $Ra$ scaling transitions in a region $10^{8}\leqslant Ra\leqslant 10^{11}$ . Above a critical $Ra$ , the flow undergoes either a steady–oscillatory transition (small $Pr$ ) or a transition from steady state to a transient state with detaching plumes (large $Pr$ ). The onset of the oscillations takes place at $Ra\,Pr^{-1}\approx 5\times 10^{9}$ and the onset of detaching plumes at $Ra\,Pr^{5/4}\approx 9\times 10^{10}$ . These onsets coincide with the onsets of scaling transitions.

中文翻译：

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经典对称水平对流：分离羽流和振荡

通过对高达 3 × 1012 的瑞利数 $Ra$ 和普朗特数 $Pr=0.1$、1 和 10 的直接数值模拟，研究了经典和对称水平对流。对于这两种设置，在全球数量上非常一致实现了热量和动量传输。与 Shishkina & Wagner (Phys. Rev. Lett., vol. 116, 2016, 024302) 类似，我们发现在 $10^{8}\leqslant Ra\leqslant 10^ 区域内的 Nusselt 数 $Nu$ 与 $Ra$ 缩放转换{11}$。在临界 $Ra$ 之上，流动经历稳定振荡转变（小 $Pr$）或从稳定状态过渡到具有分离羽流的瞬态（大 $Pr$）。振荡开始发生在 $Ra\,Pr^{-1}\approx 5\times 10^{9}$ 和分离羽流发生在 $Ra\,Pr^{5/4}\approx 9 \times 10^{10}$ 。