Eur. Phys. J. B 9, 731-738 (1999)
https://doi.org/10.1007/s100510050818

On the analogy between gravity modes and inertial modes in spherical geometry

¹ Observatoire Midi-Pyrénées, 14 avenue Édouard Belin, 31400 Toulouse, France
² École Normale Supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France

Corresponding author: ^a rieutord@obs-mip.fr

Received: 2 July 1998
Published online: 15 June 1999

Abstract

Analysing similarities and differences between gravity modes and inertial modes, we derive the analytic expression of gravity modes in an axisymmetric ellipsoid for a diffusionless fluid. We also give the expression of the dispersion relation for these modes in such a geometry. The case of a spherical shell is then considered. After deriving a class of analytical solutions, we exhibit the analogous structure of singular gravity modes and singular inertial modes. Finally, we show why singular modes should play an important part in the transport properties of a stratified or rotating fluid.