QUASI-RESONANCE OF BAROCLINIC ATMOSPHERIC WAVES AND EXTRATROPICAL LOW-FREQUENCY OSCILLATION^*

In operating the quasi-geostrophic two-layer model,the quasi-resonance occurs possibly in two cases:(1)pure barotropic waves;(2) two baroclinic and one barotropic waves.For case (2),we find the analytical solution of triad amplitude of quasi-resonance and approximate expression for the period of wave energy variation.Both the approximate expression and numerical calculation indicate that this period tends to approach the period (2πε)/(△ω) of the quasi-resonance frequency mismatch △ω itself for the baroclinic atmosphere than for the barotropic atmosphere.Physically,there is a feedback mechanism between the wave phase and amplitude,and the slowly varying phase difference between the barotropic wave and the baroclinic wave causes the conversion of kinetic energy and available potential energy,which gives rise to the wave-related low-frequency oscillation alternatively strengthening and weakening with the oscillation period identical to the above approximate formula.For △ω～(0.1-0.02) 0(ωj),the averaged energy period is 12-43 days and when △ω=0,it is 366 days.Therefore,the occurrence of frequency mismatch △ω is probably a new important mechanism for the formation of extratropical low-frequency oscillation in baroclinic atmosphere as well.