SUMMARY

The presence of a magma ocean may have characterized the beginning of terrestrial planets and, depending on how the solidification has proceeded, the solid mantle may have been in contact with a magma ocean at its upper boundary, its lower boundary, or both, for some period of time. At the interface where the solid is in contact with the liquid the matter can flow through by changing phase, and this affects convection in the solid during magma ocean crystallization. Linear and weakly non-linear analyses have shown that Rayleigh–Bénard flow subject to two liquid–solid phase change boundary conditions is characterized by a non-deforming translation or weakly deforming long wavelength mode at relatively low Rayleigh number. Both modes are expected to transfer heat very efficiently, at least in the range of applicability of weakly non-linear results for the deforming mode. When only one boundary is a phase change, the critical Rayleigh number is also reduced, by a factor of about 4, and the heat transfer is also greatly increased. In this study we use direct numerical simulations in 2-D Cartesian geometry to explore how the solid convection may be affected by these boundary conditions for values of the Rayleigh number extending beyond the range of validity of the weakly non-linear results, up to 10³ times the critical value. Our results suggest that solid-state convection during magma ocean crystallization may have been characterized by a very efficient mass and heat transfer, with a heat flow and velocity at the least twice the value previously thought when only one magma ocean is present, above or below. In the situation with a magma ocean above and below, we show that the convective heat flow through the solid layer could reach values of the same order as that of the black-body radiation at the surface of the magma ocean.

中文翻译：

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地幔对流与岩浆海洋相互作用

概要

岩浆海洋的存在可能是地球行星的开始的特征，并且根据凝固的进行方式，固体地幔可能已经与岩浆海洋在其上边界，下边界或两者接触，对于某些情况而言一段的时间。在固体与液体接触的界面处，物质可以通过改变相而流过，这会影响岩浆海洋结晶过程中固体的对流。线性和弱非线性分析表明，在两个液相-固相​​变化边界条件下的瑞利-贝纳德流特征是在相对较低的瑞利数下无变形平移或弱变形的长波长模式。两种模式都有望非常有效地传热，至少在变形模型的弱非线性结果的适用范围内。当只有一个边界是相变时，临界瑞利数也减少了约4倍，并且热传递也大大增加了。在这项研究中，我们使用二维笛卡尔几何中的直接数值模拟来研究固体对流如何受到这些边界条件的影响，因为瑞利数的值超出了弱非线性结果的有效范围，最高可达10临界值的³倍。我们的研究结果表明，岩浆海洋结晶过程中的固态对流可能具有非常有效的质量和热传递特征，其热流和速度至少是先前仅存在一个岩浆海洋时所认为的两倍或以上。 。在上下具有岩浆海洋的情况下，我们表明流经固体层的对流热能达到与岩浆海洋表面黑体辐射相同的数量级。