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

Linear boundary layer analysis of the near-critical reflection of internal gravity waves with different sizes of viscosity and diffusivity