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

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 $ν$ and the size of diffusivity $κ$ 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.

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