Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of a Symmetry leading to an Inertial Range Similarity Theory
  for Isotropic Turbulence   We present a theoretical attack on the classical problem of intermittency and
anomalous scaling in turbulence. Our focus is on an ideal situation: high
Reynolds number isotropic turbulence driven by steady large scale forcing.
Moreover, the fluid is incompressible and no confining boundaries are present.
We start from a good set of basis functions for the velocity field. These are
real and divergence-free. To each wave-vector k in Fourier space there is one
pair of basis functions with respectively left and right-handed polarity.
Isotropy makes all k on the shell of constant |k| statistically equivalent.
Consequently, the coefficients, X+ and X-, to the basis functions in that shell
become two random variables whose joint pdf describes the statistics at scale L
=2*pi/|k|. Moreover, (X+)**2+(X-)**2 becomes a random variable for the energy.
Switching to polar coordinates, the joint pdf expands in azimuthal modes. We
focus on the axisymmetric mode which is itself a pdf and characterized by it
radial profile P(r;L). Observations from both shell model and DNS data indicate
that (1) the moments of P(r;L) scale as power laws in L, and (2) the profile
obeys an affine symmetry P(r;L)=C(L)*f((lnr-mu(L))/sigma(L)). We raise the
question: What statistics agree with both observation? The answer is pleasing.
We find the functions f, mu, sigma C analytically in terms of a few constants.
Moreover, we obtain closed form expressions for both scaling exponents and
coefficients in the power laws. A virtual origin also emerges as an intrinsic
length scale L0 for the inertial range.

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The categories of this paper are: math
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th