Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closure in Turbulence from first principles   It has been recently demonstrated, [3], that according to the principle of
release of constraints, absence of shear stresses in the Euler equations must
be compensated by additional degrees of freedom, and that led to a
Reynolds-type enlarged Euler equations (EE equations) with a doublevalued
velocity field that do not require any closures. In the first part of the
paper, the theory is applies to turbulent mixing and illustrated by propagation
of mixing zone triggered by a tangential jump of velocity. A comparison of the
proposed solution with the Prandtl's solutions is performed and discussed. In
the second part of the paper, a semi-viscose version of the Navier-Stokes
equations is introduced. The model does not require any closures since the
number of equations is equal to the number of unknowns. Special attention is
paid to transition from laminar to turbulent state. The analytical solution for
this transition demonstrates the turbulent mean velocity profile that
qualitatively similar to the celebrated logarithmic law.

4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th