Free oscillations of deep nonhydrostatic global atmospheres: Theory and a test of numerical schemes

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.