Simple Tests of a Semi-Implicit Semi-Lagrangian Model on 2D Mountain Wave Problems

The fully compressible 3D nonhydrostatic semi-implicit semi-Lagrangian MC2 (mesoscale compressible community) model described by Tanguay et al. has been modified in order to incorporate orography through the Gal-Chen and Somerville transformation of the vertical coordinate by Denis. In this study, a 2D version of the model is tested against classical solutions covering various mountain-wave regimes for continuously stratified flows. A close inspection of the propagation of the vertical momentum flux is performed to asses the accuracy and stability of the numerical method. The study emphasizes also the fact that a correct representation of forced hydrostatic gravity waves is reliable for Courant numbers less than 0.5. This limitation may be less severe as the flow becomes more nonhydrostatic. Furthermore, the sensitivity of the isothermal reference state for flows with realistic static stability and over steep slope mountain is explored.