球壳中的热对流在其一个或两个边界处熔化/冻结
Thermal convection in a spherical shell with melting/freezing at either or both of its boundaries
摘要：
在许多地球物理学或行星学的环境中（地球的内核，从岩浆海洋结晶的硅酸盐地幔，或围绕深水海洋的冰壳），对流结晶层与其熔体层接触。允许在固体层的一个或两个边界处熔化/冻结可能会影响层中的对流模式。在这里，我们研究的发病热对流在一个粘性球壳动态诱导熔化/冻结在其边界之一或两者。结果表明，每个界面的行为取决于维数P的值，这是一个熔融/冻结的时间尺度的粘性松弛时间尺度的比率。较小的P值对应于渗透性边界条件，而较大的P值对应于非渗透性边界条件。线性稳定性分析预测的半渗透边界的显着效果时，任何一个边界的特征数量P是足够小的：允许融化/冻结在任何一个边界的结果在出现较大规模的对流模式。当外边界是可渗透的时，效果特别剧烈，因为即使在薄球壳的情况下，1度模式仍然是最不稳定的。在具有可渗透的内边界和外边界的球壳的情况下，最不稳定的模式包括固体壳的整体平移，没有变形。在具有可渗透外边界的完整球体的极限中，这对应于最近为地球内核提出的“对流平移”模式。作为可能的应用的一个例子，我们讨论的情况下，热对流在土卫二的冰壳假设存在一个全球性的地下海洋，并发现，融化/冻结可能有一个重要的影响对流模式的冰壳。
英文摘要：
In a number of geophysical or planetological settings (Earth's inner core, a silicate mantle crystallizing from a magma ocean, or an ice shell surrounding a deep water ocean) a convecting crystalline layer is in contact with a layer of its melt. Allowing for melting/freezing at one or both of the boundaries of the solid layer is likely to affect the pattern of convection in the layer. We study here the onset of thermal convection in a viscous spherical shell with dynamically induced melting/freezing at either or both of its boundaries. It is shown that the behavior of each interface depends on the value of a dimensional number P, which is the ratio of a melting/freezing timescale over a viscous relaxation timescale. A small value of P corresponds to permeable boundary conditions, while a large value of P corresponds to impermeable boundary conditions. The linear stability analysis predicts a significant effect of semi-permeable boundaries when the number P characterizing either of the boundary is small enough: allowing for melting/freezing at either of the boundary results in the emergence of larger scale convective modes. The effect is particularly drastic when the outer boundary is permeable, since the degree 1 mode remains the most unstable even in the case of thin spherical shells. In the case of a spherical shell with permeable inner and outer boundaries, the most unstable mode consists in a global translation of the solid shell, with no deformation. In the limit of a full sphere with permeable outer boundary, this corresponds to the "convective translation" mode recently proposed for Earth's inner core. As an example of possible application, we discuss the case of thermal convection in Enceladus' ice shell assuming the presence of a global subsurface ocean, and found that melting/freezing could have an important effect on the pattern of convection in the ice shell.
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