  A viscosity profile across the entire fluid outer core is found by
interpolating between measured boundary values, using a differential form of
the Arrhenius law governing pressure and temperature dependence. The discovery
that both the retrograde and prograde free core nutations are in free decay
(Palmer and Smylie, 2005) allows direct measures of viscosity at the top of the
outer core, while the reduction in the rotational splitting of the two
equatorial translational modes of the inner core allows it to be measured at
the bottom. We find 2,371 plus/minus 1,530 Pa.s at the top and 1.247 plus/minus
0.035 x 10^11 Pa.s at the bottom. Following Brazhkin (1998) and Brazhkin and
Lyapin (2000) who get 10^2 Pa.s at the top, 10^11 Pa.s at the bottom, by an
Arrhenius extrapolation of laboratory experiments, we use a differential form
of the Arrhenius law to interpolate along the melting temperature curve to find
a viscosity profile across the outer core. We find the variation to be closely
log-linear between the measured boundary values. The close agreement of the
boundary values of viscosity, found by Arrhenius extrapolation of laboratory
experiments, with those found from the free core nutations, and the inner core
translational modes, suggests that core flows are laminar and that the returned
viscosities are measures of their molecular values. This would not be the case
in the presence of the vigorous turbulent convection sometimes postulated by
dynamo theorists. The local Ekman number is found to range from 10^-2 at the
bottom of the outer core to 10^-10 at the top. Except in the very lower part of
the outer core, Ekman numbers are in the range 10^-4 to 10^-5, or below, in
which the laminar flows of numerical dynamos and laboratory rotating fluids
experiments occur.
