半地转近似下的混合Rossby－重力椭圆余弦波

在半地转近似[1]下,利用层结大气中的涡度方程、散度方程、连续方程和绝热方程结合行波解的方法得到了关于垂直速度的单一变量方程。这是与KdV方程相应的非线性常微分方程,可得到椭圆余弦波或弧立波。此波动的频率有两种,表明层结大气中存在着两种性质不同的非线性波动。其一是东传的惯性重力椭圆余弦波,另一是混合Rossby-重力椭圆余弦波,其性质介于Rossby椭圆余弦波与西传的惯性重力椭圆余弦波之间。这两种非线性波的相速不但与波数和振幅有关,而且与β因子和静力稳定度有关,即纬度越低,则传播越慢;大气越稳定,则传播越快。

MIXED ROSSBY-GRAVITY CNOIDAL WAVE UNDER THE CONDITION OF SEMI-GEOSTROPHIC APPROXIMATION

Under the codition of semi-geostrophic approximation,incorporating the travelling wave solution,the single variable equation of the verticle velocity is obtained by use of the vorticity equation,divergence equation,continuity equation and adiabatic equation in the stratified atmosphere. To find the solution of the single varible equation which can be reduced to the KdV equation,the nonlinear cnoidal wave and solitary wave are obtained. These waves have two frequences,so it can be seen that there are two nonlinear waves in the stratified atmosphere,one is the inertial gravity cnoidal wave which propagates eastwardly,the other is the mixed Rossby-gravity cnoidal wave which character is situated between the Rossby cnoidal wave and the inertial gravity cnoidal wave which propagates westwardly. The phase velocities of these cnoidal waves have relations with not only their wave numbers and amplitudes,but also the β effect and the static stabilities. The lower the latitude,the slower the phase velocity of the waves is;the more stable the atmospheric stratification,the faster the phase velocity is.