Interactions between stationary planetary waves in the stratosphere

The interactions between stationary planetary waves 1 and 2 are investigated using a truncated quasi-geostrophic model in a midlatitude beta channel. The model includes eight interacting horizontal modes with three zonal wave numbers and two meridional scales in a quasi-geostrophic beta channel 40 deg wide; all wave-wave interactions in the model are a result of dissipation. The procedures for solving the model equations are examined. The theory of dissipation-induced interactions is discussed in terms of interactions between weak waves under severe truncation. The behavior of small amplitude waves 1 and 2 in basic states is discussed; it is observed that wave 1 is amplified in a wave 2 basic state, and a wave 2 disturbance in a wave 1 basic state is affected by the relative phases of the waves. The dynamics of these wave interactions are analyzed using potential enstrophy budgets of the waves. The relevance of the waves to the atmosphere is studied. It is noted that the wave behavior is a combination of the linear results with an amplification of wave 1 and a strong dependence on the relative phases of waves 1 and 2 in the stratosphere.