内波垂向结构的分段求解方法

A Subsection Solution to the Vertical Structure of Internal Waves

为了掌握海洋内波的特性,针对内波垂向结构的数值解法进行了严谨的分析推导,提出了分段求解方法.将数理方程中的Sturm Liouville本征值问题应用到内波方程,可获得标准化的两种方法,进而探讨了这两种方法的统一性及实用性.计算结果表明,对半日潮的低频情况内波可存在于整个水深,而对周期为20分钟的较高频情况则内波只存在于垂向的有限范围内,在上下两层,其垂向速度的衰减很快.该方法应用于实际海洋中,可以获得一般情况下内波函数的广义Fourier级数,从理论上可以证明解函数的完备性.

In order to master the characteristics of ocean internal waves,a numerical eigenvalue solution to the vertical structure of internal waves is strictly deduced and a subsection solution method is proposed.Based on Sturm-Liouville equation,two methods of standardization are obtained. Discussion on their sameness and practicability is presented. The results show that internal waves will exist in the whole depth for low frequency(half day tide) case, and it only exists in finite vertical range for high frequency (20 min).And the vertical velocity decaies very quickly in upper and lower layers. Applying the method mentioned in this paper to the case of real ocean,a generalized Fourier series of internal wave function could be obtained.The series are proved to be self-contained theoretically.