On the motion of various vertical modes of transient, very long waves II. The Spherical Case¹

1 Publication No. 188 from the Department of Meteorology and Oceanography, The University of Michigan. Research supported by the National Science Foundation under Grant GA-16166.

Abstract

The problem of motion of atmospheric waves superimposed on a basic state of no motion and a constant temperature lapse rate has been solved. It is found that there exists several vertical modes. For each of the vertical modes there exists several horizontal modes, each moving with a separate speed and having a certain south-north variation of the amplitudes of the geopotential, the stream function and the velocity potential.

The solution is obtained by expanding each variable for each vertical mode in a truncated series of associated Legendre functions. It is found that the waves connected with the first vertical mode behave as waves in a homogeneous fluid with a free surface, while the waves connected with the second and third vertical modes move with a much smaller speed. All waves move from east to west. The structure of the waves is compared with the structure as obtained from atmospheric observations with fair agreement.

The solutions are compared with the motion of transient, very long waves as obtained from a quasi-geostrophic model.

Notes

1 Publication No. 188 from the Department of Meteorology and Oceanography, The University of Michigan. Research supported by the National Science Foundation under Grant GA-16166.