Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The global picture of self-similar and not self-similar decay in Burgers
  Turbulence   This paper continue earlier investigations on the decay of Burgers turbulence
in one dimension from Gaussian random initial conditions of the power-law
spectral type $E_0(k)\sim|k|^n$. Depending on the power $n$, different
characteristic regions are distinguished. The main focus of this paper is to
delineate the regions in wave-number $k$ and time $t$ in which self-similarity
can (and cannot) be observed, taking into account small-$k$ and large-$k$
cutoffs. The evolution of the spectrum can be inferred using physical arguments
describing the competition between the initial spectrum and the new frequencies
generated by the dynamics. For large wavenumbers, we always have $k^{-2}$
region, associated to the shocks. When $n$ is less than one, the large-scale
part of the spectrum is preserved in time and the global evolution is
self-similar, so that scaling arguments perfectly predict the behavior in time
of the energy and of the integral scale. If $n$ is larger than two, the
spectrum tends for long times to a universal scaling form independent of the
initial conditions, with universal behavior $k^2$ at small wavenumbers. In the
interval $2<n$ the leading behaviour is self-similar, independent of $n$ and
with universal behavior $k^2$ at small wavenumber. When $1<n<2$, the spectrum
has three scaling regions : first, a $|k|^n$ region at very small $k$\ms1 with
a time-independent constant, second, a $k^2$ region at intermediate
wavenumbers, finally, the usual $k^{-2}$ region. In the remaining interval,
$n<-3$ the small-$k$ cutoff dominates, and $n$ also plays no role. We find also
(numerically) the subleading term $\sim k^2$ in the evolution of the spectrum
in the interval $-3<n<1$. High-resolution numerical simulations have been
performed confirming both scaling predictions and analytical asymptotic theory.

20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an