Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Shear Stress Reynolds' Limit Formula   Historically, meteorological and climate studies have been prompted by the
need for understanding precipitation to have better logistics in food
production. Despite all efforts, nonlinearity in atmosphere dynamics is still a
source of uncertainty. On the other hand, aeronautical science studies the
boundary layer separation through the \emph{shear stress}. In this work, a
mathematical interpretation of methods in classical aerodynamics theory in
terms of successive layers of \emph{diffeomorphisms} over \emph{Lipschitz
domains} allows us to estimate the boundary layer's \emph{shear stress},
$\tau^{*}_d$ and $\tau^{*}_m$, in dry and humid atmospheric conditions without
assuming that there is not a convective derivative term in the conservation of
momentum equation or that the gaseous boundary layer is incompressible: \[
\tau^{*}_d = \frac{U}{h}\ \left(1-\frac{U^2}{2c_{pd}\ T_0}\right)^{19/25},
\hspace{7pt} \tau^{*}_m = \frac{U}{h}\ \left(1-\frac{U^2}{2c_{pm}\
T_0}\right)^{19/25},\] where $h$ is the boundary layer's height, $T_0$ is the
surface temperature, $U$ is the \emph{free stream velocity}; $c_{pd}$ is the
\emph{specific heat at constant pressure for dry air} and $c_{pm}$ is the
\emph{specific heat at constant pressure for moist air}. Furthermore, if
$\hat{R}_m$ is a \emph{gas constant for moist air} and $p_0$ is the pressure at
the surface, the density $\rho \hspace{2pt} \cong \hspace{2pt} p_0 \hspace{2pt}
T_0^{\frac{2b}{b-1}-1} \hspace{2pt} \hat{R}_{m}^{-1} \hspace{2pt}
\left[1-\left(U^2/2c_{ph}T_0\right)\right]^{\frac{b}{(b-1)}-1}$ for $b=1.405$.
Moreover, this opens the possibility of finding a different deterministic
family of atmosphere natural convection models.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th