非线性弥散效应及其对波浪变形的影响

针对Hedges,Kirby和Dalrymple提出的非线性弥散关系的修正式在浅水区存在的较大偏差的问题，给出了一个在整个水深范围内具有单值性的非线性弥散关系。比较可知，它具有在深水与中等水深逼近二阶Stokes波的弥散关系式，在浅水较Hedges,Kirby和Dalymple的修正表达式与Hedges的关系更加吻合的优点，且形式简练，用近似该非线性弥散关系的显式表达式，结合弱非线性效应的缓坡方程，得到考虑非线性弥散影响的波浪变形模型。数值模拟结果表明，用新的非线性弥散关系得到的模型对复杂地形进行模拟的结果和实测结果吻合很好。

Nonlinear dispersion effect on wave transformation

A new nonlinear dispersion relation is given in this paper. It can modify the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple and have a better approximation to Hedges' empirical one than the modified relation by Hedges, Kirby and Dalrymple in shallow water. It has a simpler expression which can be used more easyly in practice. Meanwhile, an explicit approximation to the new dispersion relation is given. The use of the explicit approximation is along with the mild slope equation. Taking into account weakly nonlinear effects, a mathematical model is obtained and applied to laboratory data. The results show that the new dispersion relation employed by the model can predict the wave transformation over a complicated seabed quite well.