Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Turbulent Prandtl number and characteristic length scales in stably
  stratified flows: steady-state analytical solutions   In this study, the stability dependence of turbulent Prandtl number ($Pr_t$)
is quantified via a novel and simple analytical approach. Based on the variance
and flux budget equations, a hybrid length scale formulation is first proposed
and its functional relationships to well-known length scales are established.
Next, the ratios of these length scales are utilized to derive an explicit
relationship between $Pr_t$ and gradient Richardson number. In addition,
theoretical predictions are made for several key turbulence variables (e.g.,
dissipation rates, normalized fluxes). The results from our proposed approach
are compared against other competing formulations as well as published
datasets. Overall, the agreement between the different approaches is rather
good despite their different theoretical foundations and assumptions.

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat