Non-linear interaction between mean zonal flow and a baroclinic wave is investigated numerically by using a two-layer quasi-geostrophic β-channel model with inclusion of friction and diabatic heating. In a series of experiments, meridional gradient of the heating is varied to elucidate the seasonal variation of the characteristics of non-linear baroclinic waves. Results obtained by these experiments are summarized as follows:
(1) As a result of non-linear interaction, there exists an energy variation with a period of 2-3 weeks as well as 3-4 days.
(2) For small meridional gradient of the diabatic heating, energy variation of 2-3 week period is maintained by the fluctuation of horizontal eddy momentum flux. Namely, the dominant energy process of this frequency range is the barotropic conversion.
(3) The baroclinic energy transfer becomes prominent with increasing the meridional gradient of the heating. The energy cycle is mainly accompanied by the fluctuation of eddy heat flux.
It is suggested that the zonal flow-braoclinic wave interaction is one possible mechanism to explain the quasi-periodic variation in the real atmosphere with time scales of two to three weeks, which is known as the "index cycle" or "tropospheric vacillation" (Webster and Keller, 1975; McGuirk and Reiter, 1976).