THE FORMATION OF THE SEMIPERMANENT CENTERS OF ACTION IN RELATION TO THE HORIZONTAL SOLENOIDAL FIELD

Abstract

The perturbation of the middle cell of the general circulation in a baroclinic atmosphere is investigated under the assumption of horizontal, divergence-free, isothermal motion. With the introduction of the horizontal solenoidal field the velocity of the trough does not differ very much from that obtained by Rossby, but the existence of a critical wave length, beyond which the perturbation will become unstable, explains to some extent the flow pattern of upper-air motions during weak-circulation weather and also provides a means of explaining how the large-scale mixing process of air masses between different latitudes takes place. It is shown that the assumption of non-divergent flow does not greatly affect the investigation of the disturbance of the horizontal motion. The inclusion of the divergence term in the perturbation equation adds to the frequency equation a term which may affect the magnitude of the critical wave length and the velocity of the disturbance by roughly ten per cent. The approximate solution of a two-layer system leads to a trough velocity which, in weather of high zonal circulation, is greater than the zonal wind speed in the lower layer and less than the zonal wind speed in the upper layer, a phenomenon often observed in synoptic analysis. The phase relationship between isobars and isotherms derived here is the same as that obtained by Rossby. The coincidence of the isobars and isotherms in the stationary disturbance eliminates any horizontal solenoidal field and leads to a stationary wave length equivalent to that in an autobarotropic atmosphere, namely L = 2π U/?. Here U is the speed of the undisturbed westerly flow and ? is the derivative of the Coriolis parameter with respect to horizontal distance northward. In the consideration of energy transformation an interrelationship between meridional and zonal circulation is established which is in fair accordance with the synoptic and statistical calculations by various authors.