HR: 0830h
AN: G21C-0278    [PDF]
TI: Characterization of Instabilities in the Tidal Deformation of a Planetary Body
AU: * Frey, S E
EM: sfrey@math.arizona.edu
AF: Program in Applied Mathematics University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721 United States
AU: Hurford, T A
EM: hurfordt@lpl.arizona.edu
AF: Lunar and Planetary Laboratory University of Arizona, 1629 E. Univeristy Blvd., Tucson, AZ 85721 United States
AU: Greenberg, R J
EM: greenber@lpl.arizona.edu
AF: Lunar and Planetary Laboratory University of Arizona, 1629 E. Univeristy Blvd., Tucson, AZ 85721 United States
AB: In 1911, A.E.H. Love published a linear elastic model for the tidal amplitude of a uniform, compressible, self-gravitating body. Recent numerical evaluations of the solution to his governing equations reveal portions of parameter space for which infinitesimal tide raisers can raise tides of arbitrary height. In addition, using a solution technique somewhat different from Love's, investigations have been made into the effect of allowing non-uniform, radially varying material parameters in Love's formulation. The solution depends only on the effective gravitational rigidity, $ \rho g R / \mu $, and the ratio of rigidity to Lam\'{e} constant, $ \mu / \lambda $. It has been found that the tidal instabilities persist when the body has a radially dependent density profile. However, as the magnitude of the density variation is increased, the singularity can be stabilized for certain fixed nonzero values of the rigidity and compressibility. In the two dimensional projection of the phase space (defined by the two ratios mentioned previously), it can be seen that increasing the magnitude of the density variation tends to move the location of the singularities out of the region of "physically significant" material parameters.
DE: 1227 Planetary geodesy and gravity (5420, 5714, 6019)
DE: 1249 Tides--Earth
DE: 1255 Tides--ocean (4560)
SC: Geodesy [G]
MN: 2003 Fall Meeting