Zonal Flow (or Zonal Wind) is air circulation parallel to the equator and latitudes, i.e., east-to-west or west-to-east. This type of circulation allows stable temperatures along latitudes. Conversely, north-to-south or south-to-north air flow is termed Meridional Flow.
The terms are used to mean regular winds in such a direction (Prevailing Winds), like the Earth's Trade Winds and Westerlies and alternately to mean the east-west component of any wind.
A general zonal flow typically results from the meridional flow that constitutes Hadley Cells and similar circulation-pattern Cells, in conjunction with the Coriolis Effect due to the planet's rotation. This can create a zonal flows in either direction (including Super Rotation, a zonal flow moving Atmosphere faster than the rotation of the planet, such as the Earth's westerlies) depending upon whether the meridional flow generating it is toward or away from its nearer pole. The faster a planet's rotation, the more pronounced the zonal flow and there may be more of them due to more cells.
2ΩR NJets ∝ ( ——— )1/2 NH
A Giant Planet's atmosphere may have layers that are conductive, e.g., with pressure sufficiently high that Hydrogen becomes metallic, and zonal flows in such layers can form Dynamos and associated Magnetic Fields. Conductive fluid layers/regions (gas or liquid) are sometimes called Ionic Oceans.
The term Differential Rotation (often used for the Sun to describe how its apparent rotation at its equator differs from near its poles) means the same thing as zonal flows. In giant planets, and stars, such flows may be at the surface, or may be deep within, or may span from the surface to deep within, e.g., in cylinder-shaped flows encircling the body's axis of rotation.