Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Cooling Box Problem: Convection with a quadratic equation of state   We investigate the convective cooling of a fluid with a quadratic equation of
state by performing three-dimensional direct numerical simulations of a flow
with a fixed top-boundary temperature, which is lower than the initial fluid
temperature. We consider fluid temperatures near the density maximum, where the
nonlinearity is expected to be important. When the equation of state is
nonlinear, the resultant vertical transport of heat is fundamentally different
and significantly lower than the predictions derived for a linear equation of
state. Further, three dimensionless groups parameterize the convective system:
the Rayleigh number ($\hbox{Ra}_0$), the Prandtl number (Pr), and the
dimensionless bottom water temperature $(T_B)$. We further define an effective
Rayleigh number ($\hbox{Ra}_{eff} = Ra_0 \ T_B^2$), which is equivalent to the
traditional Rayleigh number used with a linear equation of state. We present a
predictive model for the vertical heat flux, the top boundary-layer thickness,
and the turbulent kinetic energy of the system. We show that this model agrees
well with the direct numerical simulations. This model could be used to
understand how quickly freshwater lakes cool in high latitude environments.

8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat