Convective Instabilities in Europa's Floating Ice Shell
W.B. McKinnon (Dept EPSc, Wash Univ)
Models of the tidally heated ice shell proposed by Ojakangas and
Stevenson for Europa generally find shell thicknesses less than 30 km.
Past parameterized convection models indicate that these shell
thicknesses are stable to convective overturn and should not lead to
freezing of the ocean underneath. Here I apply the temperature-
dependent viscosity convection scaling developed by Solomatov to the
Europan ice shell. This scaling applies to basally heated square boxes
with free-slip boundaries, which should be a good match to the Europan
situation. The temperature-dependent properties of ice are linearized
about 250 K, as any convective interior should be close to this
temperature, with the colder ice forming an ostensibly passive, stagnant
lid.
Ice shells greater than 20 km (at the equator) are found to be
unstable to convection at their base, for melting point viscosities of
10 Pa-s. The critical shell thickness for convective onset is
greater at the poles; it also depends on viscosity near the melting
point, and so by the latest rheological laws, on grain size.
Convection at the base of the ice shell does not freeze the ocean,
however. Because of tidal heating, a "stagnant lid regime" ice shell
is much more dissipative than a conductive shell of the same thickness.
This causes a shell in which convection
occurs to be thinner than a conductive shell undergoing the same tidal
strain. The overall effect is to moderate the second-degree shell
thickness variations found by Ojakangas and Stevenson (unless the shell
is sufficiently thin to begin with), and impose an effective upper limit
on the shell thickness. Tidal heating in the convecting base of the
shell is
non-uniform, which may lead to thermal instabilities, and the maximum
stresses in the viscously creeping lid may be several 0.1 MPa, which
could resolve as drag on the cold, elastic lithosphere. This research
supported by NASA Planetary Geology and Geophysics grant NAG5-
3657.