  The transition from liquid metal to silicate rock in the cores of the
terrestrial planets is likely to be accompanied by a gradient in the
composition of the outer core liquid. The electrical conductivity of a volatile
enriched liquid alloy can be substantially lower than a light-element-depleted
fluid found close to the inner core boundary. In this paper, we investigate the
effect of radially variable electrical conductivity on planetary dynamo action
using an electrical conductivity that decreases exponentially as a function of
radius. We find that numerical solutions with continuous, radially outward
decreasing electrical conductivity profiles result in strongly modified flow
and magnetic field dynamics, compared to solutions with homogeneous electrical
conductivity. The force balances at the top of the simulated fluid determine
the overall character of the flow. The relationship between Coriolis and
Lorentz forces near the outer boundary controls the flow and magnetic field
intensity and morphology of the system. Our results imply that a low
conductivity layer near the top of Mercury's liquid outer core is consistent
with its weak magnetic field.
