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Thermal Convection in a Spherical Shell with Melting/Freezing at either or both of Its Boundaries

查看全文 作　　者：Renaud [1]Deguen 高影响力作者 机构地区：[1]Institut de Mécanique des Fluides de Toulouse, Université de Toulouse (INPT, UPS) and CNRS高影响力机构 出　　处：《Journal of Earth Science》索引2013年第24卷第5期,共14页高影响力期刊 基　　金：supported by the ANR(Agence Nationale de la Recherche) of France(No.ANR-12-PDOC-0015-01) 摘　　要：In a number of geophysical or planetological settings, including Earth's inner core, a silicate mantle crystallizing from a magma ocean, or an ice shell surrounding a deep water ocean—a situation possibly encountered in a number of Jupiter and Saturn's icy satellites—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—permeable or impermeable—depends on the value of a dimensionless number P(one for each boundary), 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.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 allows 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 another 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. 关 键 词：边界条件 热对流 薄球壳 凝固 线性稳定性分析 熔解 地球内核 渗透率
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