edu.ucar.opensky::technotes:461 UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact 2025-12-26T16:01:06.926648 ISO 19115-2 Geographic Information - Metadata - Part 2: Extensions for Imagery and Gridded Data ISO 19115-2:2009(E) https://n2t.org/ark:/85065/d73r0sbn Free oscillations of deep nonhydrostatic global atmospheres: Theory and a test of numerical schemes 2004-01-01T00:00:00Z publication https://n2t.org/ark:/85065/d73r0sbn https://doi.org/10.5065/D6F18WP2 Kasahara, Akira author UCAR/NCAR - Library publisher This report describes a method of calculating the modes of small-amplitude free oscillations of a compressible, stratified, nonhydrostatic, rotating deep atmosphere, confined between two concentric spheres, including sin q and cos e Coriolis terms, where q is the latitude. Unlike the Laplace-Taylor problem for the hydrostatic primitive equations that can be solved by the separation of variables, the present problem is non-separable. In this study, normal mode solutions are obtained numerically by setting up an eigenvalueeigenfunction matrix problem by the combination of a spherical harmonics expansion in the horizontal direction and a finite-difference discretization in the radial direction. A Test of the numerical schemes is conducted for an isothermal basic state with a constant gravitational acceleration. In order to identify the species of solutions, a shallow atmosphere version of the same formulation is considered in parallel. Because the shallow nonhydrostatic normal mode problem can be solved also by the separation of variables, two different approaches to the shallow problem provide an aid to verify the numerical schemes of the deep normal mode problem. Numerical results are presented for the frequencies and eigen-structures of various kinds of normal modes in the deep model and compared with those from the shallow model. UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact PDF Text theme Resource Type 2016-01-01T00:00:00Z publication Weather research/forecast models theme U.S. National Aeronautics and Space Administration Global Change Master Directory GCMD 2021-09-17 revision 11.2 NASA Global Change Master Directory originator Valids List: Science and Services Keywords Copyright Author(s). This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. None eng geoscientificInformation