考虑振幅弥散影响的波浪变形模型

Wave propagation model with the consideration of amplitude dispersion

本文给出了一个精度高于Zhao和Anastasiou (1993)显式近似Kirby和Dalrymple的非线性经验弥散关系的显式表达式 ,该显式表达式与Kirby和Dalrymple的非线性经验弥散关系吻合很好。用本文给出的非线性弥散关系显式表达式 ,结合含弱非线性经效应的缓坡方程的前进波折近似方程组 ,建立了一个考虑振幅弥散影响的波浪变形模型 ,用文中模型对波浪的变形进行了计算 ,将计算结果和试验数据 (试验数据采用Berkhoff等 (1982 )验证数学模型可信性试验 )进行了比较。结果表明 ,采用本文的波浪变形模型 ,所得计算结果与试验结果更为吻合。

In the present study, an explicit non linear dispersion expression approximated to the nonlinear dispersion relation developed by Kirby and Dalrymple (1986) was deduced. This explicit expression which gives the simplification to facilitate the calculation of nonlinear terms in the mild slope equation was proved to have much better agreement with the dispersion relation of Kirby and Dalrymple than that of Zhao and Anastasiou (1993). Usig this mild slope equation and experimented data of Berkhoff et al.(1982) for the case of submerged elliptical island on a slope, a wave propagation model with amplitude dispersion was established. The results show that it is better to use a set of progress wave approximation to mide slope equation with some weak non linearity than that with linearity. It is advantageous and feasible to use a mild slope equation with weakly non linear effect for modeling the non linear of wave propagation.