Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersive Hydrodynamics in Viscous Fluid Conduits   The evolution of the interface separating a conduit of light, viscous fluid
rising buoyantly through a heavy, more viscous, exterior fluid at small
Reynolds numbers is governed by the interplay between nonlinearity and
dispersion. Previous authors have proposed an approximate model equation based
on physical arguments, but a precise theoretical treatment for this two fluid
system with a free boundary is lacking. Here, a derivation of the interfacial
equation via a multiple scales, perturbation technique is presented.
Perturbations about a state of vertically uniform, laminar conduit flow are
considered in the context of the Navier-Stokes equations with appropriate
boundary conditions. The ratio of interior to exterior viscosities is the small
parameter used in the asymptotic analysis, which leads systematically to a
maximal balance between buoyancy driven, nonlinear self-steepening and viscous,
interfacial stress induced, nonlinear dispersion. This results in a scalar,
nonlinear partial differential equation describing large amplitude dynamics of
the cross-sectional area of the intrusive fluid conduit, in agreement with
previous derivations. The leading order behavior of the two fluid system is
completely characterized in terms of the interfacial dynamics. The regime of
model validity is characterized and shown to agree with previous experimental
studies. Viscous fluid conduits provide a robust setting for the study of
nonlinear, dispersive wave phenomena.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph