  Jupiter and Saturn exhibit alternating east-west jet streams as seen from
surface. The origin of these zonal flows has been debated for decades. The
high-precision gravity measurements by Juno mission and the grand finale of
Cassini mission have revealed that the zonal flows observed at the surface may
extend several thousand kilometres deep and stop around the transition region
from molecular to metallic hydrogen, suggesting the magnetic braking effect on
zonal flows. In this study, we perform a set of magnetohydrodynamic simulations
in a spherical shell with radially variable electrical conductivity to
investigate the interaction between magnetic fields and zonal flows. A key
feature of our numerical models is that we impose a background dipole magnetic
field on the anelastic rotating convection. By varying the strength of the
imposed magnetic field and the vigor of convection, we investigate how the
magnetic field interacts with the convective motions and the convection-driven
zonal flows. Our simulations reveal that the magnetic field tends to destroy
zonal flows in the metallic hydrogen and suppress zonal flows in the molecular
envelope, while the magnetic field may enhance the radial convective motions.
We extract a quantitative relation between the magnetic field strength and the
amplitude of zonal flows at the surface through our simulations, which roughly
matches the observed magnetic field and zonal wind speed of Jupiter and Saturn.
This discovery provides support from a new perspective for the scenario of deep
convection-driven zonal winds which are confined to the molecular hydrogen
layers in giant planets.
