Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How does flow in a pipe become turbulent?   The transition to turbulence in pipe flow does not follow the scenario
familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile
is stable against infinitesimal perturbations for all Reynolds numbers.
Moreover, even when the flow speed is high enough and the perturbation
sufficiently strong such that turbulent flow is established, it can return to
the laminar state without any indication of the imminent decay. In this
parameter range, the lifetimes of perturbations show a sensitive dependence on
initial conditions and an exponential distribution. The turbulence seems to be
supported by three-dimensional travelling waves which appear transiently in the
flow field. The boundary between laminar and turbulent dynamics is formed by
the stable manifold of an invariant chaotic state. We will also discuss the
relation between observations in short, periodically continued domains, and the
dynamics in fully extended puffs.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci