  We present an experimental analysis of the linear and non-linear regimes of
an attractor of inertial waves in a trapezoidal cavity under rotation. Varying
the rotation rate and the forcing amplitude and wavelength, we identify the
scaling laws followed by the attractor amplitude and wavelength in both
regimes. In particular, we show that the non-linear scaling laws can be well
described by replacing the fluid viscosity in the linear model by a turbulent
viscosity, a result that could help extrapolating attractor theory to
geo/astrophysically relevant situations. We further study the triadic resonance
instability of the attractor which is at the origin of the turbulent viscosity.
We show that the typical frequencies of the subharmonic waves produced by the
instability behaves very differently from previously reported numerical results
and from the prediction of the theory of triadic resonance. This behavior might
be related to the deviation from horizontal invariance of the attractor in our
experiment in relation with the presence of vertical walls of the cavity, an
effect that should be at play in all practical situations.
