A SIMPLE THREE-DIMENSIONAL MODEL FOR THE STUDY OF LARGE-SCALE EXTRATROPICAL FLOW PATTERNS

Abstract

A study is made of the hydrostatic and quasi-geostrophic motion of two superimposed layers of homogeneous and incompressible fluids of different densities, these fluids being contained between two rigid, horizontal plates. It is found that the local time derivatives of the pressure heights in the two layers and the height of their interface can be determined from partial differential equations similar to those developed by Charney for the equivalent-barotropic model. The possibility of using this two-layer model to represent motions of a continuously stratified, baroclinic troposphere is explored by comparing the behavior of small perturbations superimposed on a zonal current in the two-layer model with the results of the continuous baroclinic perturbation theories of Eady and Fjørtoft. The remarkable similarity of behavior of the two-layer and the continuous perturbation models, which appears from this comparison, suggests that if the initial flow patterns of the two-layer model are determined from the initial flow patterns of the troposphere in a specified manner the later flow patterns in the troposphere can be inferred from the forecast flow patterns of the two-layer model. This hypothesis is subjected to a preliminary test by computing the instantaneous sea-level pressure tendencies and vertical motions (in the middle troposphere) at the beginning of the severe storm of 24–25 November 1950 over eastern North America. The order of magnitude of the predicted quantities and their general distribution agree in many respects with the observed pressure changes and hydrometeors, but some disagreement exists. It is suggested that a part of this disagreement may be due to the effect of large normal accelerations on the validity of the quasi-geostrophic assumption.