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An analytical solution for linear gravity and sound waves on the sphere as a test for compressible, non‐hydrostatic numerical models
Author(s) -
Baldauf Michael,
Reinert Daniel,
Zängl Günther
Publication year - 2014
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2277
Subject(s) - hydrostatic equilibrium , compressibility , euler equations , physics , mechanics , classical mechanics , polytropic process , nonlinear system , compressible flow , advection , mathematical analysis , perturbation (astronomy) , mathematics , thermodynamics , quantum mechanics
An analytical solution for the expansion of gravity and sound waves for the linearized form of the fully compressible, non‐hydrostatic, shallow atmosphere Euler equations on the sphere is derived. The waves are generated by a weak initial temperature and density perturbation of an isothermal atmosphere. The derived analytical solution can be used as a benchmark to assess dynamical cores of global models based on the above‐mentioned (in general nonlinear) equation system. Three different test configurations, with or without Coriolis force or additional advection, are discussed. Convergence studies of the newly developed ICOsahedral Non‐hydrostatic global model (ICON) against this solution are performed.