An analytic solution for linear gravity waves in a channel as a test for numerical models using the non‐hydrostatic, compressible Euler equations

A slightly modified version of the idealized test set-up used by Skamarock and Klemp is proposed: the quasi linear two-dimensional expansion of sound and gravity waves in a flat channel induced by a weak warm bubble. For this test case an exact analytic solution of the linearized compressible, non-hydrostatic Euler equations for a shallow atmosphere has been derived. This solution can be used as a benchmark to assess compressible, non-hydrostatic dynamical cores which are the basis for many of today's, and probably most of the future, atmospheric models. Comparisons and convergence studies of two quite differently designed numerical limited-area simulation models, COSMO and DUNE, against this analytic solution are performed.