Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Averaging of thermoacoustic azimuthal instabilities   We consider the acoustic flow field of rotationally symmetric systems, like
an annular combustor and the flow in a round duct, in absence of a mean
azimuthal flow field. We focus on azimuthal instabilities, which manifest as
either spinning (rotating) waves or standing waves, or a linear combination of
the two. These instabilities are often excited by some level of background
noise that makes the system randomly change between spinning and standing
states, undergo amplitude variations and changes to the azimuthal orientation
of the solution. To account for this random change, we make use of a novel
ansatz to track as a function of time the amplitude, orientation, nature
(standing/spinning) and temporal phase of these instabilities. To capture the
effect of the background noise, we apply stochastic averaging on the governing
equations and obtain a novel differential equation. The equation allows to
study the effects of acoustic sources and sinks on the statistics of the
solution, and of explicit and spontaneous symmetry breaking and noise
intensity. We focus on this last effect and show how the noise intensity
affects the system preference for spinning and/or standing states. We find for
example that, when present, background noise pushes the system away from
spinning states and towards standing states, consistently with experiments and
numerical simulations.

32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat