Abstract
The simplified system of dynamic equation is solved by use of the first and the third kind of elliptic functions, to study the non-linear feed-back mechanism in the barotropic atmosphere.
These solutions show that there is n o shorter period than 5 days in the barotropic variations, unless due to linear effect, that the influences of small-scale disturbances upon the large-scale ones are not so large with respect to the period of variation, that the magnitude of exchange of kinetic energy among disturbances of close scales is larger than the other couple, and that accordingly the contributions of smaller-scale disturbances to the time change of the zonal flow decreases rapidly with the increasing wave number.
It may further be concluded that the per i o d of variation becomes longer the nearer the representative scale approaches the middle scale, and is in inverse proportion to the total kinetic energy. It has been suggested from the above that the domain of wave number less than m=12, nm=15 is enough for long-range prediction and time intervals Δt=12 hours used for integration of equation may be permitted.
