斜压大气中尺度扰动的有限振幅对称不稳定

THE FINITE-AMPLITUDE SYMMETRIC INSTABILITY OF MESOSCALE DISTURB-ANCE IN BAROCLINIC ATMOSPHERE

本文通过一个非地转、非静力的Eady模式讨论了斜压粘性流中的非线性对称不稳定。采用具有常值水平和垂直切变的基本场,考虑扰动沿基本气流方向不变,应用摄动方法,得到了非线性情况下扰动振幅的特性方程。结果表明,当δ>0时(δ是进行稳定性分析时所选取的无量纲小参数),振幅|A(T)|存在两个有意义的平衡点|A|_(b1)=0和|A|_(b2)=(-μ_2/μ_1)^(1/2)(μ_1,μ_2是和流体性质、区域大小以及波参数有关的量),|A|_(b1)为不稳定平衡点,|A|_(b2)为稳定平衡点。因此,不论初态如何,终态都趋于稳定平衡点,出现有限振幅现象。当δ<0时,振幅|A(T)|仅有一个有意义的平衡点|A|_(b1)=0,且为稳定平衡点。线性分析所得结果为非线性结果的特例。

By utilizing a non.-geostrophic and non-hydrostatic EADY's model, the non-linear symmetric instability in the viscous baroclinic current is discussed. It is considered that the basic field has constant vertical and horizontal shear and the disturbance field does not change in the direction of the basic current. By using the perturbation method, the disturbance amplitude equation in the nonlinear case is obtained. The results show that the amplitude |A(T)| has twomeaningful equilibrium points |A|b1=0 and when δ>0(δis a non-dimensional parameter, μ1 and μ2 are parameters concerning the fluid, area and wave parameter). |A|b1 is an unstable equilibrium point and |A|b2 is a stable one. Hence, the final state tends to the stable equilibrium point, i.e. finite-amplitude phenomenon whatever the initial value. The amplitude |A| has noly a meaningful equilibrium point |A|b1=0 which is stable when δ<0. The linear case is a special case of nonlinear case.