QUASI-RESONANCE OF BAROTROPIC ATMOSPHERIC WAVE MOTION AND MIDLATITUDE LOW-FREQUENCY OSCILLATION

It is proved, based on the quasi-geostropic barotropic vortex equation and the quasi-resonance conditions K1 + K2 + K3 = 0 and omega1 + omega2 + omega3 = DELTAomega, that the analytic solution of the 3-wave amplitude of quasi-resonance is an elliptical function. The approximate expression for the periodic variation of wave energy is thus obtained under certain conditions. Both the approximate expression and numerical calculation indicate that the period of energy variation approaches the period 1/DELTAomega corresponding to the quasi-resonance frequency bias DELTAomega itself. When DELTAomega approximately (0.1-0.025)o(omega(j)), the energy variation period is 12-46 days and when DELTAomega = 0, it is 25-568 days. Therefore, the occurrence of frequency bias DELTAomega is probably a new important mechanism for the formation of mid-latitude low-frequency oscillation. This also accounts for the result of the numerical test Egger (1978) did on blocking caused by the resonance of two topographic stationary waves and one free slow wave.