Large-scale rotating flows, like planetary atmospheres, tend to organize themselves into zones. Within a zone, flow remains essentially in an east-west direction and serves as a barrier that keeps heat or other elements from mixing from one zone to another. This is, for example, how the tropical trade winds work here on Earth.
Stars, on the other hand, don’t show this kind of zonal behavior. The reason, it turns out, is their magnetic fields. When there’s no magnetic influence, even weak shear in a rotating flow is enough to start organizing turbulent fluctuations and grow a zonal flow. This tendency toward growth is known as the zonostrophic instability. But when you add a magnetic field, instead of organizing the hydrodynamic disturbances, that weak shear strengthens the magnetic ones, which in turn suppress the flow fluctuations. As a result, the hydrodynamic disturbances cannot grow and no zonal flow forms.
Researchers think this mechanism can explain both why stars have no zonal flows and just how deep zones can penetrate inside the atmospheres of gas giants like Jupiter and Saturn before their planet’s magnetic field suppresses them. (Image credit: NASA; research credit: N. Constantinou and J. Parker, arXiv; via LLNL News; submitted by Stephanie N.)