Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applicability of Boussinesq approximation in a turbulent fluid with
  constant properties   The equations of motion describing buoyant fluids are often simplified using
a set of approximations proposed by J. Boussinesq one century ago. To resume,
they consist in assuming constant fluid properties, incompressibility and
conservation of calories during heat transport. Assuming fulfilment of the
first requirement (constant fluid properties), we derive a set of 4 criteria
for assessing the validity of the two other requirements in turbulent
Rayleigh-B\'enard convection. The first criterion $\alpha \Delta \ll 1 $ simply
results from the incompressibility condition in the thermal boundary layer
($\alpha$ and $\Delta$ are the thermal expansion coefficient and the
temperature difference driving the flow). The 3 other criteria are proportional
or quadratic with the density stratification or, equivalently with the
temperature difference resulting from the adiabatic gradient across the cell
$\Delta_{h}$. Numerical evaluations with air, water and cryogenic helium show
that most laboratory experiments are free from such Boussinesq violation as
long as the first criterion is fulfilled. In ultra high Rayleigh numbers
($Ra>10^{16}$) experiments in He, one of the stratification criteria, scaling
with $\alpha \Delta_{h}$, could be violated. This criterion garanties that
pressure fluctuations have a negligible influence both on the density variation
and on the heat transfer equation through compression/expansion cycles.
Extrapolation to higher $Ra$ suggests that strong violation of Boussinesq
approximation could occur in atmospheric convection.

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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: math
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga