Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Viscous effects on the Rayleigh-Taylor instability with background
  temperature gradient   The growth rate of the compressible Rayleigh-Taylor instability is studied in
the presence of a background temperature gradient, $\Theta$, using a normal
mode analysis. The effect of $\Theta$ variation is examined for three interface
types corresponding to combinations of the viscous properties of the fluids
(inviscid-inviscid, viscous-viscous and viscous-inviscid) at different Atwood
numbers, $At$, and, when at least one of the fluids' viscosity is non-zero, as
a function of the Grashof number. For the general case, the resulting ordinary
differential equations are solved numerically; however, dispersion relations
for the growth rate are presented for several limiting cases. An analytical
solution is found for the inviscid-inviscid interface and the corresponding
dispersion equation for the growth rate is obtained in the limit of a large
$\Theta$. For the viscous-inviscid case, a dispersion relation is derived in
the incompressible limit and $\Theta=0$. Compared to $\Theta=0$ case, the role
of $\Theta<0$ (hotter light fluid) is destabilizing and becomes stabilizing
when $\Theta>0$ (colder light fluid). The most pronounced effect when
$\Theta\neq 0$ is found at low $At$ and/or at large perturbation wavelengths
relative to the domain size for all interface types. On the other hand, at
small perturbation wavelengths relative to the domain size, the growth rate for
$\Theta<0$ case exceeds the infinite domain incompressible constant density
result. The results are applied to two practical examples, using sets of
parameters relevant to Inertial Confinement Fusion coasting stage and solar
corona plumes. The role of viscosity on the growth rate reduction is discussed
together with highlighting the range of wavenumbers most affected by viscosity.
The viscous effects further increase in the presence of background temperature
gradient, when the viscosity is temperature dependent.

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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: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas