Magnetic suppression of zonal flows on a beta plane

TL;DR

This paper provides a theoretical explanation for how magnetic fields suppress zonal flows in a beta plane, relevant to astrophysical systems, by showing magnetic fluctuations counteract flow growth, with suppression depending on magnetic and resistive parameters.

Contribution

The paper introduces a novel theoretical framework explaining magnetic suppression of zonal flows, extending Kelvin-Orr analysis and employing CE2 to connect magnetic fluctuations with flow suppression.

Findings

Magnetic fluctuations absorb energy from zonal flows.

Suppression occurs when Alfvén frequency exceeds Rossby frequency.

Resistivity influences the amplitude of magnetic fluctuations and flow suppression.

Abstract

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 has not yet been explained. In the idealized setting of a magnetized beta plane, we provide a theoretical explanation that shows how magnetic fluctuations directly counteract the growth of weak zonal flows. Two distinct calculations yield consistent conclusions. The first, which is simpler and more physically transparent, extends the Kelvin-Orr shearing wave to include magnetic fields and shows that weak, long-wavelength shear flow organizes magnetic fluctuations to absorb energy from the mean flow. The second calculation, based on the quasilinear, statistical CE2 framework, is valid for arbitrary wavelength zonal flow and predicts a self-consistent growth rate of the zonal flow. We find that a background magnetic field suppresses zonal flow if the bare Alfven frequency is comparable to or larger than the bare Rossby frequency. However, suppression can occur for even smaller magnetic fields if the resistivity is sufficiently small enough to allow sizable magnetic fluctuations. Our calculations reproduce the $\eta/B_0^2 = \text{const.}$ scaling that describes the boundary of zonation, as found in previous work, and we explicitly link this scaling to the amplitude of magnetic fluctuations.