  The outer areas of Jupiter and Saturn have multiple zonal winds, reaching the
high latitudes, that penetrate deep into the planets' interiors, as suggested
by gravity measurements. These characteristics are replicable in numerical
simulations by including both a shallow stably stratified layer, below a
convecting envelope, and increasing electrical conductivity. A dipolar magnetic
field, assumed to be generated by a dynamo below our model, is imposed. We find
that the winds' depth into the stratified layer depends on the local product of
the squared magnetic field strength and electrical conductivity. The key for
the drop-off of the zonal winds is a meridional circulation which perturbs the
density structure in the stable layer. In the stable region its dynamics is
governed by a balance between Coriolis and electromagnetic forces. Our models
suggest that a stable layer extending into weakly conducting regions could
account for the observed deep zonal wind structures.
