Magnetic suppression of zonal flows on a beta plane*

Zonal flows in rotating systems have been previously shown to be suppressed by the imposition of a background magnetic field aligned with the direction of rotation. Understanding the physics behind the suppression may be important in systems found in astrophysical fluid dynamics, such as stellar interiors. However, the mechanism of suppression is not yet explained. We provide a theoretical explanation that shows how magnetic fluctuations directly counteract the growth of weak zonal flows. Using the quasilinear, statistical CE2 framework we predict a self-consistent growth rate of the zonal flow. We find that a background magnetic field suppresses zonal flow if the bare Alfvén frequency is comparable to or larger than the bare Rossby frequency.  However, suppression occurs for even weaker magnetic fields if the resistivity η is small enough to allow sizable magnetic fluctuations. Our calculations reproduce the η/B₀² = const. scaling that describes the boundary of zonation, as found in previous work, and we explicitly link this scaling to the amplitude of magnetic fluctuations.