PLANETARY WAVES IN THE ATMOSPHERE

Abstract

A numerical method is presented for solving the non-linear barotropic vorticity equation in spherical coordinates. It is shown that, when the stream function is expressed as a sum of surface spherical harmonics, the barotropic vorticity equation gives rise to harmonic tendency equations which express the time rate of change of the harmonic coefficients as functions of all the harmonic coefficients. The harmonic tendency equations may be used in an iterative process to find the flow pattern at a future time from a knowledge of the harmonic coefficients at an initial time. The amount of computation is reduced greatly if the planetary waves are regarded as composed of perturbations superimposed on a steady zonal flow in which the angular velocity varies with colatitude. An example based on an actual synoptic situation is given. The effect of large scale lateral mixing is to curb the development of harmonics of large degree.