Other
Scientific paper
Dec 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agufm.p53b1244c&link_type=abstract
American Geophysical Union, Fall Meeting 2007, abstract #P53B-1244
Other
5422 Ices, 6221 Europa, 8121 Dynamics: Convection Currents, And Mantle Plumes, 8149 Planetary Tectonics (5475)
Scientific paper
We calculate tidally induced stress at the surface of an icy satellite based on the gravitational potential. The ice shell is treated as a viscoelastic Maxwell solid, and assumed to float atop a global ocean. The shell is thus capable of differential rotation relative to the silicate core, which is presumed to rotate synchronously. If the shell experiences non-synchronous rotation (NSR), stresses result from the time-varying potential. In a Maxwell solid both the magnitude and time-variability of stress induced by a forcing depend on the frequency of the forcing. Viscous relaxation allows stress to dissipate, and the non-instantaneous response of the material creates a phase lag between the forcing function and the stresses resulting from it. The importance of viscous effects in an ice shell undergoing NSR will be determined by its viscosity (η), shear modulus (μ), and the rotation period (T), and can be parameterized by the quantity: Δ \equiv \frac{T}{2π~τM} = \frac{μ}{η ω}} Where ω is the forcing frequency, and τM is the Maxwell time. If Δ \gg 1 the response is fluid; no shear stress is supported. If Δ \ll 1 the response is elastic; shear stresses may be large, and will be in phase with the forcing function. For Δ ≍ 1 the response is viscous; shear stresses may be large or small, have a phase lag relative to the forcing function, and are very sensitive to Δ. Choosing values appropriate to Europa and its ice shell (η ~ 1022 Pa sec, T ~ 107 yr, μ ~ 109 Pa) yields Δ ≍ 1. Between Δ=10-1 and Δ=101 the stresses due to NSR shift ~ 40° in longitude and relax from 3.5 MPa to 0.5 MPa. Because of this sensitivity, and because our knowledge of the shell's viscosity and rotation rate is limited, it is impossible to make confident predictions of stress magnitude or longitudinal dependence. We demonstrate this uncertainty through a study of the global arcuate lineaments on Europa that have previously been interpreted as tensile fractures due to NSR stresses. If a variable rotation rate is considered, it becomes difficult to use a lineament's apparent longitude of formation as a proxy for time of formation relative to other lineaments, since the stress field will sweep across the surface as ω changes. We demonstrate that a small reorientation of an otherwise synchronously rotating shell can produce lineaments spread across up to 45° in longitude.
Crawford Zane A.
Pappalardo Robert T.
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