水波色散方程的直接求解方法  

Explicit approximations of water wave dispersion relations

作　　者：张益[1] 刘勇[1] 

机构地区：[1]中国海洋大学工程学院,青岛266100

出　　处：《水道港口》2015年第1期8-11,20,共5页Journal of Waterway and Harbor

基　　金：国家自然科学基金项目(51279224)

摘　　要：在港口与海岸工程设计中,经常要求利用波浪周期和水深来计算波长,这需要迭代求解水波色散方程,不便于实际应用。如何利用波浪周期和水深来直接简单计算波长,是工程实践提出的需要解决的问题。许多学者提出了一些水波色散方程的近似求解方法,可利用波浪周期和水深直接近似求得波长,不需要利用计算机进行迭代计算。文中对已有的色散方程近似直接求解方法进行了总结和评述,并对各近似公式的相对误差进行对比分析。在此基础上,推荐了几种形式简单、精度较高的近似公式来计算波长。For the design of coastal engineering, water wave dispersion relations are usually solved for deter-mining the wavelengths with given wave periods and water depths. The solution procedure requires iterative compu-tations, which is not convenient in practice. Using the wave periods and water depths to quickly and directly calcu-late the wavelengths is significant in engineering applications. Therefore, many scholars proposed some explicit so-lutions of dispersion relation without iterative computations in computers. In this study, a review on published ex-plicit solutions for dispersion relations was presented, and the relative errors of different approximation formulaswere compared. Finally, several simple and accurate approximation formulas for directly calculating the wave-lengths were recommended.

关 键 词：色散方程 直接求解 近似公式 相对误差 

分 类 号：TV143[水利工程—水力学及河流动力学] O242.1[理学—计算数学]