  An analytical linear solution of the fully compressible Euler equations is
found, in the particular case of a stationary two dimensional flow that passes
over an orographic feature with small height-width ratio. A method based on the
covariant formulation of the Euler equations is used, and the analytical
vertical velocity as well as the horizontal velocity, density and pressure, are
obtained. The analytical solution is tested against a numerical model in three
different regimes, hydrostatic, non-hydrostatic and potential flow. The model
used is a non-hydrostatic spectral semi-implicit model, with a height-based
vertical coordinate. It is shown that there is a clear and consistent
convergence of the numerical solution towards the analytical solution, when the
resolution increases. The method described is intended to be used as an
idealized test for numerical weather models.
