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Convective instability in ice I with non-Newtonian rheology: Application to the icy Galilean satellites
Journal of Geophysical Research-Planets, 109 (E12): E12008 (2004)
Аннотация
1 At the temperatures and stresses associated with the onset of
convection in an ice I shell of the Galilean satellites, ice behaves
as a non-Newtonian fluid with a viscosity that depends on both temperature
and strain rate. The convective stability of a non-Newtonian ice
shell can be judged by comparing the Rayleigh number of the shell
to a critical value. Previous studies suggest that the critical Rayleigh
number for a non-Newtonian fluid depends on the initial conditions
in the fluid layer, in addition to the thermal, rheological, and
physical properties of the fluid. We seek to extend the existing
definition of the critical Rayleigh number for a non-Newtonian, basally
heated fluid by quantifying the conditions required to initiate convection
in an ice I layer initially in conductive equilibrium. We find that
the critical Rayleigh number for the onset of convection in ice I
varies as a power (- 0.6 to -0.5) of the amplitude of the initial
temperature perturbation issued to the layer, when the amplitude
of perturbation is less than the rheological temperature scale. For
larger-amplitude perturbations, the critical Rayleigh number achieves
a constant value. We characterize the critical Rayleigh number as
a function of surface temperature of the satellite, melting temperature
of ice, and rheological parameters so that our results may be extrapolated
for use with other rheologies and for a generic large icy satellite.
The values of critical Rayleigh number imply that triggering convection
from a conductive equilibrium in a pure ice shell less than 100 km
thick in Europa, Ganymede, or Callisto requires a large, localized
temperature perturbation of a few kelvins to tens of kelvins to soften
the ice and therefore may require tidal dissipation in the ice shell.
