Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resonance phenomenon for the Galerkin-truncated Burgers and Euler
  equations   It is shown that the solutions of inviscid hydrodynamical equations with
suppression of all spatial Fourier modes having wavenumbers in excess of a
threshold $K_G$ exhibit unexpected features. The study is carried out for both
the one-dimensional Burgers equation and the two-dimensional incompressible
Euler equation. For large $K_G$ and smooth initial conditions, the first
symptom of truncation, a localized short-wavelength oscillation which we call a
"tyger", is caused by a resonant interaction between fluid particle motion and
truncation waves generated by small-scale features (shocks, layers with strong
vorticity gradients, etc). Tygers appear when complex-space singularities come
within one Galerkin wavelength $\lambdag = 2\pi/K_G$ from the real domain and
arise far away from preexisting small-scale structures at locations whose
velocities match that of such structures. Tygers are weak and strongly
localized at first - in the Burgers case at the time of appearance of the first
shock their amplitudes and widths are proportional to $K_G^{-2/3}$ and $K_G
^{-1/3}$ respectively - but grow and eventually invade the whole flow. They are
thus the first manifestations of the thermalization predicted by T.D. Lee in
1952.
  The sudden dissipative anomaly - the presence of a finite dissipation in the
limit of vanishing viscosity after a finite time $t_\star$ -, which is well
known for the Burgers equation and sometimes conjectured for the 3D Euler
equation, has as counterpart, in the truncated case, the ability of tygers to
store a finite amount of energy in the limit $K_G\to\infty$. This leads to
Reynolds stresses acting on scales larger than the Galerkin wavelength and
prevents the flow from converging to the inviscid-limit solution. There are
indications that it may eventually be possible to purge the tygers and thereby
to recover the correct inviscid-limit behavior.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat