Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Epi-two-dimensional flow and generalized enstrophy   The conservation of the enstrophy ($L^2$ norm of the vorticity $\omega$)
plays an essential role in the physics and mathematics of two-dimensional (2D)
Euler fluids. Generalizing to compressible ideal (inviscid and barotropic)
fluids, the generalized enstrophy $\int_{\Sigma(t)} f(\omega/\rho)\rho\, d^2
x$, ($f$ an arbitrary smooth function, $\rho$ the density, and $\Sigma(t)$ an
arbitrary 2D domain co-moving with the fluid) is a constant of motion, and
plays the same role. On the other hand, for the three-dimensional (3D) ideal
fluid, the helicity $\int_{M} {V}\cdot\omega\,d^3x$, ($V$ the flow velocity,
$\omega=\nabla\times V$, and ${M}$ the three-dimensional domain containing the
fluid) is conserved. Evidently, the helicity degenerates in a 2D system, and
the (generalized) enstrophy emerges as a compensating constant. This transition
of the constants of motion is a reflection of an essential difference between
2D and 3D systems, because the conservation of the (generalized) enstrophy
imposes stronger constraints, than the helicity, on the flow. In this paper, we
make a deeper inquiry into the helicity-enstrophy interplay: the ideal fluid
mechanics is cast into a Hamiltonian form in the phase space of Clebsch
parameters, generalizing 2D to a wider category of epi-2D flows (2D embedded in
3D has zero helicity, while the converse is not true -- our epi-2D category
encompasses a wider class of zero-helicity flows); how helicity degenerates and
is substituted by a new constant is delineated; and how a further generalized
enstrophy is introduced as a constant of motion applying to epi-2D flow is
described.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas