Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transient Growth in Shear Flows: Linearity vs Nonlinearity   Two approaches to the problem of transition to turbulence of shear flows are
popular in the literature. The first is the linear one of transient growth
which focuses on the likely form of the most 'dangerous' (lowest energy)
turbulence-triggering disturbances. The second is the nonlinear calculation of
the laminar-turbulent boundary which instead focuses on their typical
amplitudes. We look to bridge the gap between these two perspectives by
considering the fully nonlinear transient growth problem to estimate both the
form and amplitude of the most dangerous disturbance. We thereby discover a new
nonlinear optimal disturbance which outgrows the well-known linear optimal for
the same initial energy and is crucially much more efficient in triggering
turbulence. The conclusion is then that the most dangerous disturbance can
differ markedly from what traditional linear transient growth analysis
predicts.

9
The categories of this paper are: nlin
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th