中文摘要：

设计了一个热带赤道β-平面的两层海洋模式，在准长波近似下，应用最大截断模分析赤道波的基本形态，指出无论是正压模或斜压模Kelvin波、Rossby波及基本流所对应的“地形Rossby波”是最基本的波系，在基本流的一定切变条件下，它们之间可以耦合出一类不稳定波。在浅混合层近似和“快波近似”下，正压模和斜压模是可以分离的，因此可以分别分析它们的色散特征，由于它们的特征量不同，在同样波长（扰动的纬向尺度）下，扰动的增长率也不同，通过分析得出在一定参数下，斜压模扰动增长率为正压模的2倍。近似分析表明，混合层中流场的增长要快于温跃层，但温跃层的温度增长要比混合层明显。

英文摘要：

A two-layer equatorial ocean model on the beta-plane is first derived, which consists of a mixed layer and a thermocline with different temperatures and densities, and then with the quasi-long-wave approximation, via low-order symmetrical truncation method, the basic mode of equatorial waves is studied. Research indicates that no matter for barotropic or baroclinic mode, the basic low-frequency waves in the tropics include Kelvin wave, Rossby wave, and topographic Rossby wave which depends on the basic flow; and under certain shear conditions there exists one kind of instability wave-coupled Kelvin-Rossby wave. With the approximation of the shallow mixed layer and the approximation of ＂fast wave＂, barotropic and baroclinic modes can be easily separated, and therefore their dispersion characteristics analyzed, respectively. Because of different values of characteristic parameter, the growth rates of the perturbations with the same wavelength （namely latitudinal scale of the perturbation） differ for barotropic and baroclinic modes, and under certain parameter value, the growth rate of perturbation for baroclinic mode is twice that for barotropic mode. Further research indicates that the growth of the flow field in the mixed layer is faster than that in the thermocline while the growth of temperature in the thermoeline is more remarkable than that in the mixed layer, which provides theoretical basis for analyzing evolution of ENSO using subsurface temperature anomalies as done in recent years by many authors.