Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak turbulence theory for rotating magnetohydrodynamics and planetary
  dynamos   A weak turbulence theory is derived for magnetohydrodynamics under rapid
rotation and in the presence of a large-scale magnetic field. The angular
velocity $\Omega_0$ is assumed to be uniform and parallel to the constant
Alfv\'en speed ${\bf b_0}$. Such a system exhibits left and right circularly
polarized waves which can be obtained by introducing the magneto-inertial
length $d \equiv b_0/\Omega_0$. In the large-scale limit ($kd \to 0$; $k$ being
the wave number), the left- and right-handed waves tend respectively to the
inertial and magnetostrophic waves whereas in the small-scale limit ($kd \to +
\infty$) pure Alfv\'en waves are recovered. By using a complex helicity
decomposition, the asymptotic weak turbulence equations are derived which
describe the long-time behavior of weakly dispersive interacting waves {\it
via} three-wave interaction processes. It is shown that the nonlinear dynamics
is mainly anisotropic with a stronger transfer perpendicular ($\perp$) than
parallel ($\parallel$) to the rotating axis. The general theory may converge to
pure weak inertial/magnetostrophic or Alfv\'en wave turbulence when the large
or small-scales limits are taken respectively. Inertial wave turbulence is
asymptotically dominated by the kinetic energy/helicity whereas the
magnetostrophic wave turbulence is dominated by the magnetic energy/helicity.
For both regimes a family of exact solutions are found for the spectra which do
not correspond necessarily to a maximal helicity state. It is shown that the
hybrid helicity exhibits a cascade whose direction may vary according to the
scale $k_f$ at which the helicity flux is injected with an inverse cascade if
$k_fd < 1$ and a direct cascade otherwise. The theory is relevant for the
magnetostrophic dynamo whose main applications are the Earth and giant planets
for which a small ($\sim 10^{-6}$) Rossby number is expected.

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The categories of this paper are: cs
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph