Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert Statistics of Vorticity Scaling in Two-Dimensional Turbulence   In this paper, the scaling property of the inverse energy cascade and forward
enstrophy cascade of the vorticity filed $\omega(x,y)$ in two-dimensional (2D)
turbulence is analyzed. This is accomplished by applying a Hilbert-based
technique, namely Hilbert-Huang Transform, to a vorticity field obtained from a
$8192^2$ grid-points direct numerical simulation of the 2D turbulence with a
forcing scale $k_f=100$ and an Ekman friction. The measured joint probability
density function $p(C,k)$ of mode $C_i(x)$ of the vorticity $\omega$ and
instantaneous wavenumber $k(x)$ is separated by the forcing scale $k_f$ into
two parts, which corresponding to the inverse energy cascade and the forward
enstrophy cascade. It is found that all conditional pdf $p(C\vert k)$ at given
wavenumber $k$ has an exponential tail. In the inverse energy cascade, the
shape of $p(C\vert k)$ does collapse with each other, indicating a
nonintermittent cascade. The measured scaling exponent $\zeta_{\omega}^I(q)$ is
linear with the statistical order $q$, i.e., $\zeta_{\omega}^I(q)=-q/3$,
confirming the nonintermittent cascade process.
  In the forward enstrophy cascade, the core part of $p(C\vert k)$ is changing
with wavenumber $k$, indicating an intermittent forward cascade.
  The measured scaling exponent $\zeta_{\omega}^F(q)$ is nonlinear with $q$ and
can be described very well by a log-Poisson fitting:
$\zeta_{\omega}^F(q)=\frac{1}{3}q+0.45\left(1-0.43^{q}\right)$. However, the
extracted vorticity scaling exponents $\zeta_{\omega}(q)$ for both inverse
energy cascade and forward enstrophy cascade are not consistent with
Kraichnan\rq{}s theory prediction. New theory for the vorticity field in 2D
turbulence is required to interpret the observed scaling behavior.

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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc