  Internal waves are believed to be of primary importance as they affect ocean
mixing and energy transport. Several processes can lead to the breaking of
internal waves and they usually involve non linear interactions between waves.
In this work, we study experimentally the parametric subharmonic instability
(PSI), which provides an efficient mechanism to transfer energy from large to
smaller scales. It corresponds to the destabilization of a primary plane wave
and the spontaneous emission of two secondary waves, of lower frequencies and
different wave vectors. Using a time-frequency analysis, we observe the time
evolution of the secondary waves, thus measuring the growth rate of the
instability. In addition, a Hilbert transform method allows the measurement of
the different wave vectors. We compare these measurements with theoretical
predictions, and study the dependence of the instability with primary wave
frequency and amplitude, revealing a possible effect of the confinement due to
the finite size of the beam, on the selection of the unstable mode.
