  Inertia-gravity waves (IGWs) play an essential role in the terrestrial
atmospheric dynamics as they can lead to energy and momentum flux when
propagating upwards. An open question is to which extent IGWs contribute to the
total energy and to flattening of the energy spectrum observed at the
mesoscale. In this work, we present an experimental investigation of the energy
distribution between the large-scale balanced flow and the small-scale
imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are
observed in the differentially heated rotating annulus experiment. Similar to
the atmospheric spectra, the experimental kinetic energy spectra reveal the
typical subdivision into two distinct regimes with slopes $k^{-3}$ for the
large scales and $k^{-5/3}$ for the small scales. By separating the spectra
into the vortex and the wave component, it emerges that at the large-scale end
of the mesoscale the gravity waves observed in the experiment cause a
flattening of the spectra and provide most of the energy. At smaller scales,
our data analysis suggests a transition towards a turbulent regime with a
forward energy cascade up to where dissipation by diffusive processes occurs.
