Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear and nonlinear optimal growth mechanisms for generating turbulent
  bands   Linear and nonlinear energy optimizations in a tilted domain are used to
unveil the main mechanisms allowing the creation of a turbulent band in a
channel flow. Linear optimization predicts an optimal growth for streamwse and
spanwise wavenumbers $k_x = 1.2$, $k_z = - 1.75$, corresponding to the peak
values of the premultiplied energy spectra of direct numerical simulations. At
target time, the linear optimal perturbation is composed by oblique streaks,
which, for a sufficiently large initial energy, induce turbulence in the whole
domain, due to the lack of spatial localization. When localization is achieved
by adding nonlinear effects to the optimization, or by artificially confining
the linear optimal to a localized region in the spanwise direction, a
large-scale flow is created, which leads to the generation of a localised
turbulent band. These results suggest that inducing transition towards
turbulent bands in a tilted domain, two main elements are needed: a linear
energy growth mechanism such as the lift-up for generating large-amplitude flow
structures which produce inflection points; large-scale vortices ensuring
spatial localisation. Remarkably, these two elements alone are able to generate
an isolated turbulent band also in a large, non-tilted domain.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an