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An exact analytical solution for gravity wave expansion of the compressible, non-hydrostatic Euler equations on the sphere

Presented by: 
Michael Baldauf Deutscher Wetterdienst (DWD)
Date: 
Thursday 27th September 2012 - 16:35 to 17:00
Venue: 
INI Seminar Room 1
Session Title: 
From Dynamical Cores to Operational Models
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.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons