  Recent developments of the weak turbulence theory applied to internal waves
exhibit a power-law solution of the kinetic energy equation close to the
oceanic Garrett \& Munk spectrum, confirming weakly nonlinear wave interactions
as a likely explanation of the observed oceanic spectra. However, finite-size
effects can hinder wave interactions in bounded domains, and observations often
differ from theoretical predictions. This article studies the dynamical regimes
experimentally developing in a stratified fluid forced by internal gravity
waves in a pentagonal domain. We find that by changing the shape and increasing
the dimensions of the domain, finite-size effects diminish and wave turbulence
is observed. In this regime, the temporal spectra decay with a slope compatible
with the Garrett-Munk spectra. Different regimes appear by changing the forcing
conditions, namely discrete wave turbulence, weak wave turbulence, and strongly
stratified turbulence. The buoyancy Reynolds number $Re_b$ marks well the
transitions between the regimes, with weak wave turbulence occurring for
$1\lesssim Re_b\lesssim 3.5$ and strongly non-linear stratified turbulence for
higher $Re_b$.
