Mathematics – Logic
Scientific paper
Dec 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002agufm.p12c..10s&link_type=abstract
American Geophysical Union, Fall Meeting 2002, abstract #P12C-10
Mathematics
Logic
5430 Interiors (8147), 5770 Tidal Forces, 6218 Jovian Satellites, 6280 Saturnian Satellites
Scientific paper
Most models of planets and satellites assume homogeneous or layered media in which each layer is one phase. However, real planets and satellites may have two phase media (e.g., solid plus liquid) throughout a significant portion of their interior. I concentrate here on percolation media (a deformable solid matrix with an interconnected fluid-filled pore space that allows fluid redistribution under the action of stress). In such a medium, the phases are individually incompressible but Darcy flow from one region to another could lead to an overall effective compressibility, pumping of liquid in spite of the overall tendency towards gravitational separation, and possibly an additional heat transfer mechanism. In particular, I answer here the following questions, which appear to be unrelated but are in fact closely related: (1) Could a partially molten asthenosphere of Io behave like a compressible medium and allow decoupling of the lithosphere from the deeper interior? (2) Could tidally -driven flow of water in the ice of Europa's crust lead to net upward transfer of liquid water? (3) Can tidal response of an ethane/methane-bearing outer layer of water ice on Titan (i.e., a hidden ocean) satisfy the requirement that the large orbital eccentricity persist over geologic time? The answers are (1) No. (2) Maybe. (3) Yes. The common factors in treating these problems are: (a)The comparison of tidal stress to the stress associated with the hydrostatic head arising from a density difference of solid and liquid over an interesting distance (e.g., 10km). Typically, these two stresses are comparable. (b)The compaction length which is the scale below which viscous stresses of a deforming solid matrix are more important in determining flow than the simple Darcy flow formula. This is typically small (e.g., 10km or less) except in outermost regions (e.g. Titan). (c) The tidally driven Darcy flux (expressed as a velocity) in comparison to the velocity of time-varying equipotentials (which is about the velocity of the surface of a body if it responds to tides like a fluid). In Io, tidal velocities cannot be matched by plausible flow velocities except for a permeability so high that the matrix would disassemble. Thus a decoupled lithosphere requires a magma ocean. In Europa. only tiny amounts of water can be pumped by tides but it can still correspond to potentially kilometers of ice thickness growth on million year time scales. On Titan, the porous region is near surface and reasonable pore sizes prevent significant relative motion during the tidal cycle, thus avoiding the dissipation that results form a true shallow sea. Thus, Titan's eccentricity can be preserved.
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