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\begin{document}

\title{Magnetic suppression of zonal flows on a beta plane}



\author[1]{Jeffrey Parker}%
\author[2]{Navid Constantinou}%
\affil[1]{Lawrence Livermore National Laboratory}%
\affil[2]{Australian National University}%


\vspace{-1em}



  
  \date{June 17, 2024}


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\begin{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 Alfv\selectlanguage{ngerman}én frequency is comparable to or larger than the
bare Rossby frequency. However, suppression can occur for even smaller
magnetic field if the resistivity is sufficiently small enough to allow
sizable magnetic fluctuations. Our calculations reproduce the \selectlanguage{greek}η/\selectlanguage{english}B0\^{}2
= 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. These results could provide a plausible
explanation for why the zonal jets in Jupiter go as deep as Juno has
discovered but not any deeper.%
\end{abstract}%



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