Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Unified Transition Stages in Linearly Stable Shear Flows   Abrupt transition to turbulence may occur in pipe and channel flows at
moderate flow rates, an unexpected event according to linear stability theory,
and has been an open problem in fluid dynamics for more than a century.
Extensive numerical simulations and statistical analyses of the
plane-Poiseuille flow have been performed. A sequence of transition stages,
which includes the equilibrium localized turbulence, the temporally persistent
turbulence and the uniform turbulence, is identified. The spread of turbulent
band is mainly caused by an oblique extension at moderate Reynolds numbers and
band splitting at high Reynolds numbers. The small scale regime of a turbulent
band coincides with the oblique swirl region of the mean flow in planes
parallel to the walls. Furthermore, this transition scenario is shown
quantitatively to be universal for channel and pipe flows in terms of a locally
defined Reynolds number.

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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
31
The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: math
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The categories of this paper are: astro-ph