摘要
推导了由一阶色散项Ｏ（β２）表示的Ｂｏｕｓｉｎｅｓｑ类方程，方程中保留了一阶非线性项Ｏ（α）及四阶色散项Ｏ（β８），其中α＝Ａ／ｈ０，β＝ｈ０／Ｌ，Ａ为特征波高，Ｌ为特征波长，ｈ０为特征水深从理论上证明了Ｂｏｕｓｉｎｅｓｑ改善型方程对色散性精度的提高，阐明了此类方程对色散项所保留的精度为Ｏ（β８），而并非是此类方程推导之初的假设为Ｏ（β２）这一点。
In this paper, the Boussinesq-type equations with first-order O(α) of nonlinearity and fourth-order O(β 8) of dispersion is derived, in which, α=A/h 0 , β=h 0/L , A, L and h 0 is typical value of wave amplitude, wavelength and water depth By using the transforming velcity, the linear dispersion relation of our equations is consistent with fourth order pade approximation of the exact linear dispersion relation for Airy waves, this make the equations applicable to a wider range of water depths Our results also proved that the accuracy of Schaffer′s (1995) Boussinesq-type equations is the order of O(β 8, α) , in which O(α)=O(β 8) , not O(α)=O(β 2)
出处
《力学学报》
EI
CSCD
北大核心
1998年第5期531-539,共9页
Chinese Journal of Theoretical and Applied Mechanics
关键词
一阶非线性项
四阶色散项
B类方程
波浪理论
first order of nonlinearity, fourth order of dispersion, Boussinesq type equations
