On the Dynamics of Ultralong Waves in the Troposphere and Lower Stratosphere

A linear nonstationary quasi-geostrophic model is considered with extevnal and internal heating and for-ing. First, a stationary problem is solved. As it is slipposed that the nonstationary component of the ultra!ong wave is mainly generated by the nonlinear interaction of cyclonic waves, initially it is taken to be the same at all atmospheric levels, with the amplitude and phase being equal to the stationary solution a t 700 mb. The total ultralong wave (stationary plus nonstationary components) is taken as the initial value of geopotential in integrating the equations for 90 days. Typically for quasi-stationary ultralong waves, fluctuations at 700 mb and specific (cascade), rather large changes of the amplitudes a t the upper levels are obtained. Integral characteristics are quoted that strikingly agree with similar values studied from the real data over the periods of sudden stratospheric warmings and with the results of theoretical investigations of this phenomenon.