Some effects of shearing motion on the propagation of waves in the prevailing westerlie

Abstract

In recent years great interest has developed in the study of the role of the semipermanent centers of action as they affect weather conditions averaged over several days. An examination of the daily synoptic and upper air charts indicates that although these centers of action have closed isobaric systems at the ground (e.g., the Aleutian and Icelandic lows) they often appear at upper levels as sinusoidal disturbances of the average zonal distribution of pressure. It is the primary purpose of this paper to extend the investigations of the horizontal perturbations by determining the effects of shear upon their movements. In treating the case of shear, the method of circulation integrals wil be used. V. Bjerknes first made extensive use of the circulation theorems and some fruitful interpretations of them were made by Hoiland. We will show first how these integrals are to be used by applying them to the cases of the infinite and finite horizontal layers where no shear is present. Then the case of shear will be considered for both infinite and finite layers. The first chapter of the paper deals with the method of circulation integrals, indicating how it is to be applied to wave phenomena. The actual applications of the circulation integral to the single layer of finite and infinite widths, and the double layer are carried out in Chapters II and III. In these chapters, formulas for the velocity, the length of the stationary wave and critical wave length of each case are developed. Tables are computed and diagrams constructed for the more interesting cases of stationary and critical wave lengths.