中文摘要：

作者在采用刚盖近似并忽略海底地形和风应力的情况下,用Boussinesq方程组研究了海洋内部波动的波谱和谱函数.在一定条件下对该方程组线性化并取标准模后,可将此初边值问题转化为矩阵的广义特征值问题来数值求解,这样就可知原问题波谱和谱函数的性质.当无基本流且取地转参数、层结参数为常数时,可求得其波谱和谱函数的解析解.此时该模式中仅包含有一对重力惯性内波模态,且各模态均是简谐波;模态越高,垂直波数越大则波动传播得越慢,所有的模态均为离散谱,并存在聚点.本文用该解析解与相应的数值解作了对比,结果表明,该数值求解方案合理可行,对不太高的模态其精度也令人满意.当考虑了层结垂直变化后,一般无法求取解析解,为此作了数值求解.这时该模式仍仅包含有一对重力惯性内波的离散谱模态,不过由于层结参数不是常数,各模态结构与简谐波出现了偏差.

英文摘要：

The spectrum and spectral function of the wave in ocean have been studied based on non-geostatic Boussinesq equations. The equations are linearized at certain conditions and in general solved by using numerical method. In case without flow as well as with constant stratification parameter and Coriolis parameter, analytical solution of the spectra and spectral function can be obtained. Comparisons between the results from analytical and numerical solution have been carried out. It shows that the numerical method can provide satisfied accuracy in the cases with lower mode. If the parameter structure of stratification is non-constant, the numerical method have to be applied. All the results are discussed in the paper.