Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero-Prandtl-number convection with slow rotation   We present the results of our investigations of the primary instability and
the flow patterns near onset in zero-Prandtl-number Rayleigh-B\'enard
convection with uniform rotation about a vertical axis. The investigations are
carried out using direct numerical simulations of the hydrodynamic equations
with stress-free horizontal boundaries in rectangular boxes of size $(2\pi/k_x)
\times (2\pi/k_y) \times 1$ for different values of the ratio $\eta = k_x/k_y$.
The primary instability is found to depend on $\eta$ and $Ta$. Wavy rolls are
observed at the primary instability for smaller values of $\eta$ ($1/\sqrt{3}
\le \eta \le 2$ except at $\eta = 1$) and for smaller values of $Ta$. We
observed K\"{u}ppers-Lortz (KL) type patterns at the primary instability for
$\eta = 1/\sqrt{3}$ and $ Ta \ge 40$. The fluid patterns are found to exhibit
the phenomenon of bursting, as observed in experiments [Bajaj et al. Phys. Rev.
E {\bf 65}, 056309 (2002)]. Periodic wavy rolls are observed at onset for
smaller values of $Ta$, while KL-type patterns are observed for $ Ta \ge 100$
for $\eta =\sqrt{3}$. In case of $\eta = 2$, wavy rolls are observed for
smaller values of $Ta$ and KL-type patterns are observed for $25 \le Ta \le
575$. Quasi-periodically varying patterns are observed in the oscillatory
regime ($Ta > 575$). The behavior is quite different at $\eta = 1$. A time
dependent competition between two sets of mutually perpendicular rolls is
observed at onset for all values of $Ta$ in this case. Fluid patterns are found
to burst periodically as well as chaotically in time. It involved a homoclinic
bifurcation. We have also made a couple of low-dimensional models to
investigate bifurcations for $\eta = 1$, which is used to investigate the
sequence of bifurcations.

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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol