Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interaction of a rotational motion and an axial flow in small geometries
  for a Couette-Taylor problem   We analyze the stability of a cylindrical Couette flow under the imposition
of a weak axial flow in case of a very short cylinder with a narrow annulus
gap. We consider an incompressible viscous fluid which is contained in the
narrow gap between two concentric short cylinders, where the inner cylinder
rotates with constant angular velocity. The caps of the cylinders have narrow
tubes conically tapering to super narrow slits which allow for an axial flow
along the surface of the inner cylinder. The approximated solution for the
Couette flow for short cylinders was found and used for the stability analysis
instead of the exact but bulky solution. The sensitivity of the Couette flow to
general small perturbations and to the weak axial flow was studied. We
demonstrate that perturbations coming from the axial flow cause the propagation
of dispersive waves in the Taylor-Couette flow. The coexistence of a rotation
and of an axial flow requires to study in addition to the energy and the
angular momentum also the helicity of the flow. The approximated form for the
helicity formula in case of short cylinders was derived. We found that the
axial flow stabilizes the Taylor - Couette flow. The supercritical flow
includes a rich variety of vortical structures including a symmetric pair of
Taylor vortices, an anomalous single vortex and quasi periodic oscillating
vortices. Pattern formation was studied at large for rated ranges of azimuthal
and axial Reynolds numbers. A region where three branches of different states
occur was localized. Numerical simulations in 3D and in axisymmetrical case of
the model flow are presented, which illustrate the instabilities analyzed.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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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: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg