Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Statistical Theory of Homogeneous Isotropic Turbulence   The present work proposes a theory of isotropic and homogeneous turbulence
for incompressible fluids, which assumes that the turbulence is due to the
bifurcations associated to the velocity field. The theory is formulated using a
representation of the fluid motion which is more general than the classical
Navier-Stokes equations, where the fluid state variables are expressed in terms
of the referential coordinates.
  The theory is developed according to the following four items: 1) Study of
the route toward the turbulence through the bifurcations analysis of the
kinematic equations. 2) Referential description of the motion and calculation
of the velocity fluctuation using the Lyapunov analysis of the local
deformation. 3) Study of the mechanism of the energy cascade from large to
small scales through the Lyapunov analysis of the relative kinematics equations
of motion. 4) Determination of the statistics of the velocity difference with
the Fourier analysis. Each item contributes to the formulation of the theory.
  The theory gives the connection between number of bifurcations, scales and
Reynolds number at the onset of the turbulence and supplies an explanation for
the mechanism of the energy cascade which leads to the closure of the von
K\'arm\'an-Howarth equation. The theory also gives the statistics of the
velocity difference fluctuation and permits the calculation of its PDF.
  The presented results show that the proposed theory describes quite well the
properties of the isotropic turbulence.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex