Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear dynamics induced by linear wave interactions in multi-layered
  flows   Using simple kinematics, we propose a general theory of linear wave
interactions between the interfacial waves of a two dimensional (2D), inviscid,
multi-layered fluid system. The strength of our formalism is that one does not
have to specify the physics of the waves in advance. Wave interactions may lead
to instabilities, which may or may not be of the familiar "normal-mode" type.
Contrary to intuition, the underlying dynamical system describing linear wave
interactions is found to be non-linear. Specifically, a saw-tooth jet profile
with three interfaces possessing kinematic and geometric symmetry is explored.
Fixed points of the system for different ranges of a Froude number like control
parameter $\gamma$ are derived, and their stability evaluated. Depending upon
the initial condition and $\gamma$, the dynamical system may reveal transient
growth, weakly positive Lyapunov exponents, as well as different non-linear
phenomena such as formation of periodic and pseudo-periodic orbits. All these
occur for those ranges of $\gamma$ where normal-mode theory predicts neutral
stability. Such rich non-linear phenomena is not observed in 2D dynamical
system resulting from the $2$-wave problem, which only reveals stable and
unstable nodes.

20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th