  This paper presents an experimental study of different instability scenarios
in a parallelogram-shaped internal wave attractor in a trapezoidal domain
filled with a uniformly stratified fluid. Energy is injected into the system
via the oscillatory motion of a vertical wall of the trapezoidal domain.
Whole-field velocity measurements are performed with the conventional PIV
technique. In the linear regime, the total kinetic energyof the fluid system is
used to quantify the strength of attractors as a function of coordinates in the
parameter spacedefining their zone of existence, the so-called Arnold tongue.
In the nonlinear regime, the choice of the operational point in the Arnold
tongue is shown to have a significant impact on the scenario of the onset of
triadic instability, most notably on the influence of confinement on secondary
waves. The onset of triadic resonance instability may occur as a spatially
localized event similar to Scolan, Ermanyuk and Dauxois (2013) in the case of
strong focusing or in form of growing normal modes as in McEwan (1971) for the
limiting case of rectangular domain. In the present paper, we describe also a
new intermediate scenario for the case of weak focusing. We explore the
long-term behaviour of cascades of triadic instabilities in wave attractors and
show a persistent trend toward formation of standing-wave patterns
corresponding to some discrete peaks of the frequency spectrum. At sufficiently
high level of energy injection the system exhibits a "mixing box" regime which
has certain qualitatively universal properties regardless to the choiceof the
operating point in the Arnold tongue. In particular, for this regime, we
observe a statisticsof events with high horizontal vorticity, which serve as
kinematic indicators of mixing.
