Mathematics – Logic
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufm.p23e0097c&link_type=abstract
American Geophysical Union, Fall Meeting 2006, abstract #P23E-0097
Mathematics
Logic
5422 Ices, 5430 Interiors (8147), 5475 Tectonics (8149), 6218 Jovian Satellites, 6221 Europa
Scientific paper
A significant fraction of icy satellites appear to have an ice shell decoupled from the moon's solid interior by a global ocean. Such satellites when in an eccentric orbit will experience diurnal tidal deformation and stresses within the shell. Further, non-synchronous rotation (NSR) of decoupled ice shells has been suggested as a potential source of large surface stresses. These stresses may be stored elastically, released through brittle failure, or relaxed away viscously. Prior work has focused on elastic behavior, since the surface temperatures in the outer solar system are so low. However, much of a convecting ice shell may be warm enough to behave viscously on NSR timescales. Near the melting point it may even be possible for some diurnal stress to relax away. We model an ice shell as two Maxwell viscoelastic layers with independent viscosities. Frequency dependent degree-two Love numbers are calculated assuming a silicate core, global ocean, and the two layer ice shell for both NSR and diurnal forcing frequencies. When orbital eccentricity is set to zero, we find that surface stresses due to NSR depend on the ratio of the NSR forcing period to the shell's relaxation time: γ = \frac{PNSR}{τMaxwell} When γ >> 1 the shell behaves viscously, and when γ << 1 the shell behaves elastically. Since the upper and lower shells have different relaxation times, assuming the surface is colder than the interior there are three possible regimes: when both layers behave elastically, the resulting stresses are similar to previously published results. When both layers behave viscously, surface stresses are greatly reduced. When the upper layer behaves elastically, and the lower layer behaves viscously NSR stresses are effectively concentrated in the upper layer, and are somewhat larger than if the entire shell is elastic. As the elastic proportion of the shell is reduced, the magnitude of the surface stresses increases. When the lower shell behaves viscously and the upper shell behaves elastically, the surface stresses are very similar to those resulting from a thin elastic shell floating directly on a liquid ocean. If orbital eccentricity is non-zero and γ >> 1 for the upper layer, then the shorter period results in the diurnal stresses dominating. The existence of surface features on Europa that apparently stem from diurnal stresses suggests that at some point in the recent geologic past the upper shell has behaved viscously on the timescale of NSR. We would like to thank PG&G and OPR for their support of this research.
Barr Amy Courtright
Collins Geoffrey
Crawford Zane A.
Mullen M.
Pappalardo Robert T.
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