FRICTIONAL DISSIPATION AND NONLINEAR BAROTROPIC INSTABILITY

Based on the nonlinear quasi-geostrophic barotropic vorticity equation with Ekman friction, the criteria for nonlinear barotropic stability of the zonal basic flows are derived using Serrin-Joseph energy approach and through total energy, total enstrophy and their linear combination, separately, in terms of variational principle. Since the new transformation for Euler equation is utilized, the estimation of eigenvalue is more accurate, and the previous results of the author are improved very well.     

摩擦耗散和非线性正压不稳定

本文从含Ekman摩擦的非线性准地转正压涡度方程出发,应用Serrin-Joseph的能量方法,按变分原理,分别用总能量、总涡度拟能和两者的线性组合,导得纬向基流的非线性正压稳定性判据。由于采用了对Euler方程作新的变换,使本征值的估计更为精确,较好地改善了作者以前的部分结果。     

正压大气波动准共振与中纬低频振荡

本文从准地转正压涡度方程出发,在准共振条件K_1+K_2+K_3=0和ω_1+ω_2+ω_3=Δω下,求得准共振三波振幅的解析解为椭圆函数.并在一定的条件下求得波能量变化周期的近似式.此近似式和数值计算结果两者都表明,能量变化周期趋于准共振频率偏离Δω自身对应的周期1/Δω,特别当Δω～(0.1—0.025)O(ω_j)时,能量变化周期分别趋于12—46天,而当Δω=0时,周期为25—568天.因此,频率偏离Δω的出现可能是产生中纬低频振荡的一种新的重要机制.这还可以较好地解释Egger所作的著名的两个地形驻波和一个自由慢波准共振产生阻塞的数值试验结果.     

Ageostrophic Generalized E－P Flux in Baroclinic Atmosphere

Aimed at limitation and deficiency of the traditional Eliassen-Palm (E-P) flux associated with wave-meanflow interaction and its subsequent generalization based on the Boussinesq approximation or quasi-geostrophic approximation, we develop an ageostrophic Generalized E-P flux in baroclinic stratified atmosphere. This generalized E-P flux can be conveniently used to diagnose and analyse some important phenomena related to wave-meanflow interaction of the baroclinic atmosphere with observational data, such as the upper-level jet acceleration, gravity wave breaking-up and stratospheric erupt warming.     

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

It is proved, based on the quasi--geostropic barotropic vortex equation and the quasi-resonance conditions K_1+ K_2+ K_3=0 and ω_1 +ω_1 +ω_3 =Δω, that the analytic solution ofthe 3--wave amplitude of quasi--resonance is an elliptical function. The approximate expressionfor the periodic variation of wave energy is thus obtained under certain conditions. Boththe approximate expression and numerical calculation indicate that the period of energyvariation approaches the period 1/Δω corresponding to the quasi--resonance frequency biasΔω itself. When Δω～(0.1--0.025)o(ω_j), the energy variation period is 12---46 days andwhen Δω=0, it is 25--568 days. Therefore, the occurrence of frequency bias Δω is probablya 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 causedby the resonance of two topographic stationary waves and one free slow wave.