Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Magnetorotational Instability Prefers Three Dimensions   The magnetorotational instability (MRI) occurs when a weak magnetic field
destabilises a rotating, electrically conducting fluid with inwardly increasing
angular velocity. The MRI is essential to astrophysical disk theory where the
shear is typically Keplerian. Internal shear layers in stars may also be MRI
unstable, and they take a wide range of profiles, including near-critical. We
show that the fastest growing modes of an ideal magnetofluid are
three-dimensional provided the shear rate, $S$, is near the two-dimensional
onset value, $S_c$. For a Keplerian shear, three-dimensional modes are unstable
above $S\approx0.10S_c$, and dominate the two-dimensional modes until
$S\approx2.05S_{c}$. These three-dimensional modes dominate for shear profiles
relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal
laboratory experiments. Significant numbers of rapidly growing
three-dimensional modes remain well past $2.05S_{c}$. These finding are
significant in three ways. First, weakly nonlinear theory suggests that the MRI
saturates by pushing the shear rate to its critical value. This can happen for
systems, like stars and laboratory experiments, that can rearrange their
angular velocity profiles. Second, the non-normal character and large transient
growth of MRI modes should be important whenever three-dimensionality exists.
Finally, three-dimensional growth suggests direct dynamo action driven from the
linear instability.

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The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio