2013/03/19 by Renaud Deguen, Deguen, Renaud
Earth and Planetary Sciences · Environmental Science · Biochemistry, Genetics and Molecular Biology · #Geology and Paleoclimatology Research #Methane Hydrates and Related Phenomena #Geomagnetism and Paleomagnetism Studies
paper · pdf · doi:10.48550/arxiv.1303.4513
In a number of geophysical or planetological settings (Earth's inner core, a\nsilicate mantle crystallizing from a magma ocean, or an ice shell surrounding a\ndeep water ocean) a convecting crystalline layer is in contact with a layer of\nits melt. Allowing for melting/freezing at one or both of the boundaries of the\nsolid layer is likely to affect the pattern of convection in the layer. We\nstudy here the onset of thermal convection in a viscous spherical shell with\ndynamically induced melting/freezing at either or both of its boundaries. It is\nshown that the behavior of each interface depends on the value of a dimensional\nnumber P, which is the ratio of a melting/freezing timescale over a viscous\nrelaxation timescale. A small value of P corresponds to permeable boundary\nconditions, while a large value of P corresponds to impermeable boundary\nconditions. The linear stability analysis predicts a significant effect of\nsemi-permeable boundaries when the number P characterizing either of the\nboundary is small enough: allowing for melting/freezing at either of the\nboundary results in the emergence of larger scale convective modes. The effect\nis particularly drastic when the outer boundary is permeable, since the degree\n1 mode remains the most unstable even in the case of thin spherical shells. In\nthe case of a spherical shell with permeable inner and outer boundaries, the\nmost unstable mode consists in a global translation of the solid shell, with no\ndeformation. In the limit of a full sphere with permeable outer boundary, this\ncorresponds to the "convective translation" mode recently proposed for Earth's\ninner core. As an example of possible application, we discuss the case of\nthermal convection in Enceladus' ice shell assuming the presence of a global\nsubsurface ocean, and found that melting/freezing could have an important\neffect on the pattern of convection in the ice shell.\n