On the Nonhydrostatic Atmospheric Models with Inclusion of the Horizontal Component of the Earth's Angular Velocity

Abstract

Two nonhydrostatic effects that have been neglected traditionally in the hydrostatic primitiveequation models are studied in this article. One such effect is due to the vertical acceleration in the vertical equation of motion. The other is due to a Coriolis term involving 2Ω cos (latitude), where Ω is the rate of earth’s rotation, and is referred to here as a cos (latitude) Coriolis term. Cos (latitude) Coriolis terms appear in the vertical and zonal equations of motion. The questions to be investigated are: (1) what are the dynamical consequences of these two nonhydrostatic effects, (2) how the roles of cos (latitude) Coriolis terms can be compared with sin (latitude) Coriolis terms, (3) which nonhydrostatic effect is likely more important, and (4) should these effects be included in atmospheric modeling for describing what kind of motions? These questions are studied quantitatively through a normal mode analysis of compressible, and stratified atmosphere with rotation on a tangent plane in a three-dimensional space that is open horizontally, but bounded by two rigid horizontal planes in the vertical. Numerical results are presented for an isothermal model. Considering the current trend of numerical modeling in permitting to use finer resolutions and to extend the top of model atmosphere higher, it is prudent to include both nonhydrostatic effects in the dynamical core of next generation atmospheric models for all scales of motions.