  The shear resulting from internal wave reflections can play a crucial role in
the transport and resuspension of sediments in oceanic conditions. In
particular, when these waves undergo a \textit{critical reflection} phenomenon,
the reflected wave can produce a very large shear. Separating the reflected
wave from the incident wave is a technical challenge since the two waves share
the same temporal frequency. In our study, we present a series of experimental
measurements of internal waves in \textit{critical reflection} configuration
and we analyze them using the 2D-VMD-prox decomposition method. This
decomposition method was adapted to specifically decompose waves in an internal
wave critical reflection, showing an improvement in its performance with
respect to preexisting internal wave decomposition methods. Being able to
confidently isolate the reflected wave allowed us to compare our results to a
viscous and non-linear model for critical reflection, that correctly describes
the dependence of the shear rate produced in the boundary as a function of the
experimental parameters.
