Numerical Analysis for Hydrostatic and Nonhydrostatic Equations of Inertial-Internal Gravity Waves

Abstract

A modified forward-backward scheme applied to the anelastic system is proposed. This modified scheme not only retains all the advantages of the conventional forward-backward scheme but also is more consistent with the original differential equations. This scheme is used to investigate inertial waves and internal gravity waves in three different lattices. It is found that the lattice C proposed by Deardorff is better than either lattice A or lattice B when applied to internal gravity waves and thermal convection in the atmosphere. The difference between a hydrostatic system and a nonhydrostatic system is also discussed in detail in this paper. Here we propose to apply Shuman's smoothing on a hydrostatic system to filter out the undesirably, highly oscillatory short waves, or stroll small-scale convection, so that we may produce reasonable results compared with those of a nonhydrostatic system. The validity of this method has been proved by the numerical results of a study on the mesoscale cloud bands which are produced by the effect of condensation in a conditionally unstable atmosphere with vertical wind shear.