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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.