The purpose of the present paper is to examine the possibility of numerical prediction by Fourier Series and to analyse the atmospheric structure.
Let us multiply the vorticity equation by a periodic function and integrate it from 0 to 2π (along a latitude circle), and we can obtain certain equations. Namely, the following results could be derived from numerical calculation on the barotropic model, i. e.
1) Numerical prediction is possible by the Fourier Series with the harmonics from
n=1 to
n=9.
2) Correlation between the zonal flow of
component-wave vorticitv by the mean flow and the meridional flow of absolute mean flow vorticity by that component wave is negative at middle latitudes from 55°N to 40°N, and positive at 60°N.
3) The same relation as in 2) can be found in the interaction between the component waves.
4) The non-linear effect at lower latitudes than 55°N is reverse to that at 60°N, which, coupled with that shown in 2) and 3), tells us that 55°N latitude circle, roughly speaking, forms a kind of nodal line.
5) Magnitude of time change of amplitudes of long waves can not be explained by the barotropic and non-divergent model, perhaps due to the upward motion and horizontal stability changes caused by the topography.
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