运动物体生成内波的一类非线性谱方程组  

A Kind of Nonlinear Equations of Internal Waves Generated by Body-Source

作　　者：徐肇廷[1] 徐昊 

机构地区：[1]中国海洋大学物理海洋研究所,物理海洋实验室青岛266003 [2]美国密西根大学大气海洋空间科学系,mi48105

出　　处：《青岛海洋大学学报（自然科学版）》2003年第4期503-511,共9页Journal of Ocean University of Qingdao

基　　金：国家自然科学基金项目 (4 0 2 76 0 0 8);高等学校博士点专项基金项目 (2 0 0 0 0 4 2 30 9);海洋科学与设估模拟国家海海局重点实验室基金项目 (990 3)部分资助

摘　　要：本文给出了由运动物体所生成内波的基本方程组和对应的谱方程组。该方程组的线性部分是一具有体积源 (其下简称为体源 )的 Sturm- Liouville本征值问题 ,而它的非线性部分是由体源与线性波场相互作用的谱表示。在这类强迫方程的源项中包含了 10类内波谱 ,这些谱最终均可利用内波的振幅谱表示。本文给出了线性波场波要素的谱表示和运动物体生成内波的非线性谱方程可解性的讨论。为了检验所得到的谱方程组 ,文中又进行了该谱方程组线性部分的数值计算。A basic equation of internal waves generated by moving body and its corresponding spectrum equation are presented in this paper. Linear part of this spectrum equation is a Sturm-Liouville eigenvalue problem with a body-source. And its nonlinear part is a spectra equation denoted by interactions between the linear wave fields and the body-source. There exist 10 spectra in the source terms of the nonlinear spectra equation, and all the unknown spectrum can be denoted in terms of the amplitude spectrum. At the same time, the spectrum expressions of the wave properties for the linear wave field are given and the solvability of the spectrum equations of the internal waves excited by the body-sources is also discussed. Finally, in order to examine the spectrum equations, a computation of its linear part is also carried out in this paper.

关 键 词：内波 波要素 Sturm-Liouvlle本征值问题 运动物体 非线性谱方程组 数值计算 海洋水文学 

分 类 号：P731.24[天文地球—海洋科学]