  Torsional Alfv{\'e}n waves propagating in the Earth's core have been inferred
by inversion techniques applied to geomagnetic models. They appear to propagate
across the core but vanish at the equator, exchanging angular momentum between
core and mantle. Assuming axial symmetry, we find that an electrically
conducting layer at the bottom of the mantle can lead to total absorption of
torsional waves that reach the equator. We show that the reflection coefficient
depends on G Br , where Br is the strength of the radial magnetic field at the
equator, and G the conductance of the lower mantle there. With Br = 7e-4 T.,
torsional waves are completely absorbed when they hit the equator if G = 1.3e8
S. For larger or smaller G, reflection occurs. As G is increased above this
critical value, there is less attenuation and more angular momentum exchange.
Our finding dissociates efficient core-mantle coupling from strong ohmic
dissipation in the mantle.
