Equatorial meridional flows: Rotationally induced circulations

This study examines two-dimensional large-scale atmospheric circulations that are centered over the equator. The influence of terms that contain the Coriolis parameter f' = 2 Omega cos Theta is highlighted in a simple linear inviscid equatorial beta model. Two general types of oscillatory circulations are identified within the y-z plane. In a neutral or stably stratified atmosphere one circulation is expressed in terms of an analytic solution that contains Hermite polynomials, while a second solution is described in terms of a Bessel function. In the more traditional Hermite polynomial solution the influence of f' is small as suggested by scale analysis. Neutral stability provides the only exception. In contrast to these findings, the Bessel solution contains frequencies with semiannual periods that depend entirely on f' not equal 0. This solution describes cross-equatorial flow with a maximum meridional velocity at the equator. Consequently, this indicates that to model the atmosphere it is necessary to include in the model equations all terms containing f', since they influence oscillatory circulations that describe internal waves with periods that vary from a few days to semiannual.