The Roles of the Horizontal Component of the Earth's Angular Velocity in Nonhydrostatic Linear Models

Abstract

Roles of the horizontal component of the earth's rotation, which is neglected traditionally in atmospheric and oceanographic models, are studied through the normal mode analysis of a compressible and stratified model on a tangent plane in the domain that is periodic in the zonal and meridional directions but bounded at the top and bottom. As expected, there exist two distinct kinds of acoustic and buoyancy oscillations that are modified by the earth's rotation. When the cos(latitude) Coriolis terms are included, there exists another kind of wave oscillation whose frequencies are very close to the inertial frequency, 2Ω sin(latitude), where Ω is the earth's angular velocity. The objective of this article is to clarify the circumstance in which a distinct kind of wave oscillation emerges whose frequencies are very close to the inertial frequency. Because this particular kind of normal mode appears only due to the presence of boundary conditions in the vertical, it may be appropriate to call these waves boundary-induced inertial (BII) modes as demonstrated through the normal mode analyses of a homogeneous and incompressible model and a Boussinesq model with thermal stratification. Thus, it can be understood that the BII modes can coexist with the acoustic and inertio-gravity modes when the effect of compressibility is added to the effects of buoyancy and complete Coriolis force in the compressible, stratified, and rotating model.