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linear stability analysis.on the Influences of the Spatial Variations in Thermal Conductivity and Expansivity on the Flow Patterns of Thermal Convection with Strongly Temperature-Dependent Viscosity

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Journal of Earth Science 2014年第1期25卷 126-139页

作者： Arata Miyauchi Masanori Kameyama Hiroki Ichikawa Geodynamics Research Center Ehime University

A series of linear stability analysis.is carried out on the onset of thermal convection in the presence of spatial variations of viscosity, thermal conductivity and expansivity. We consider the temporal evolution of an infinitesimal perturbation superimposed to a static （motionless） and con- ductive state in a basally-heated planar layer. From the changes in flow patterns with increasing the amplitudes of temperature dependence of viscosity, we identified the transition into the ＂stagnant-lid＂（ST） regime, where the convection occurs only beneath a thick and stagnant-lid of cold fluid at the top surface. Detailed analysis.showed a significant increase of the aspect ratio of convection cells in ST regime induced by the spatial variations in thermal conductivity and/or expansivity： the horizon- tal length scale of ST convection can be enlarged by up to 50% with 10 times increase of thermal conductivity with depth. We further developed an analytical model of ST convection which success- fully reproduced the mechanism of increasing horizontal length scale of ST regime convection cells for given spatial variations in physical properties. Our findings may highlight the essential roles of the spatial variation of thermal conductivity on the convection patterns in the mantle.

关键词： mantle convection stagnant-lid temperature-dependent viscosity pressure- dependent thermal conductivity pressure-dependent thermal expansivity linear stability analysis.

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

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Journal of Earth Science 2013年第5期24卷 669-682页

作者： Renaud Deguen Institut de Mécanique des Fluides de Toulouse Université de Toulouse (INPT UPS) and CNRS

In a number of geophysical or planetological settings, including Earth＇s inner core, a sili- cate mantle crystallizing from a magma ocean, or an ice shell surrounding a deep water ocean--a situa- tion 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 perme- able 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 importa

关键词： planetary mantle thermal convection phase change linear stability analysis.

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