  Jupiter's weather layer exhibits long-term and quasi-periodic cycles of
meteorological activity that can completely change the appearance of its belts
and zones. There are cycles with intervals from 4 to 9 years, dependent on the
latitude, which were detected in 5$\mu$m radiation, which provides a window
into the cloud-forming regions of the troposphere; however, the origin of these
cycles has been a mystery. Here we propose that magnetic torsional
oscillations/waves arising from the dynamo region could modulate the heat
transport and hence be ultimately responsible for the variability of the
tropospheric banding. These axisymmetric waves are magnetohydrodynamic waves
influenced by the rapid rotation, which have been detected in Earth's core, and
have been recently suggested to exist in Jupiter by the observation of magnetic
secular variations by Juno. Using the magnetic field model JRM33, together with
the density distribution model, we compute the expected speed of these waves.
For the waves excited by variations in the zonal jet flows, their wavelength
can be estimated from the width of the alternating jets, yielding waves with a
half period of 3.2-4.7 years in 14-23$^\circ$N, consistent with the intervals
with the cycles of variability of Jupiter's North Equatorial Belt and North
Temperate Belt identified in the visible and infrared observations. The nature
of these waves, including the wave speed and the wavelength, is revealed by a
data-driven technique, dynamic mode decomposition, applied to the
spatio-temporal data for 5$\mu$m emission. Our results imply that exploration
of these magnetohydrodynamic waves may provide a new window to the origins of
quasi-periodic patterns in Jupiter's tropospheric clouds and to the internal
dynamics and the dynamo of Jupiter.
