  The aim of this work is to make a further step towards the understanding of
the near-critical reflection of internal gravity waves from a slope in the more
general and realistic context where the size of viscosity $\nu$ and the size of
diffusivity $\kappa$ are different. In particular, we provide a systematic
characterization of boundary layers (boundary layer wave packets) decays and
sizes depending on the order of magnitude of viscosity and diffusivity. We can
construct an $L^2$ stable approximate solution to the linear near-critical
reflection problem under the scaling assumption of Dauxois \& Young JFM 1999,
where either viscosity of diffusivity satisfies a precise scaling law in terms
of the criticality parameter.

Analysis of PDEs