  We consider torsional Alfv\'en waves which may be excited in Jupiter's
metallic hydrogen region. These axisymmetric zonal flow fluctuations have
previously been examined for incompressible fluids in the context of Earth's
liquid iron core. Theoretical models of the deep-seated Jovian dynamo,
implementing radial changes of density and electrical conductivity in the
equilibrium model, have reproduced its strong, dipolar magnetic field.
Analysing such models, we find anelastic torsional waves travelling
perpendicular to the rotation axis in the metallic region on timescales of at
least several years. Being excited by the more vigorous convection in the outer
part of the dynamo region, they can propagate both inwards and outwards. When
being reflected at a magnetic tangent cylinder at the transition to the
molecular region, they can form standing waves. Identifying such reflections in
observational data could determine the depth at which the metallic region
effectively begins. Also, this may distinguish Jovian torsional waves from
those in Earth's core, where observational evidence has suggested waves mainly
travelling outwards from the rotation axis. These waves can transport angular
momentum and possibly give rise to variations in Jupiter's rotation period of
magnitude no greater than tens of milliseconds. In addition these internal
disturbances could give rise to a 10% change over time in the zonal flows at a
depth of 3000 km below the surface.
