Abstract

For the development and assessment of dynamical cores for atmospheric simulation models, suitable idealized test setups with known solutions are very useful. But only in rare cases exact analytical solutions exist for the underlying equation systems. In this work a slightly modified version of the original idea of Skamarock, Klemp (1994) is proposed: the quasi linear expansion of sound and gravity waves on a sphere induced by a weak warm bubble. For this case an exact analytical solution for the compressible, non-hydrostatic Euler equations was found for a shallow atmosphere and optionally with inclusion of Coriolis effects for a ‘spherical f-plane-approximation’.

This solution can be used as reference for convergence studies of global models. ‘Small earth’ convergence tests with the ICON model of the Deutscher Wetterdienst (DWD) and the Max-Planck Institut of Meteorology (MPI) are shown.