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 viscosity and diffusivity satisfy a precise scaling law in terms of the criticality parameter.