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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新的非线性弥散关系。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Dalrymple的修正表达式与Hedges的关系式更加吻合的优点 ,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。数值验证结果表明 ,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
Aiming at the problem that the modified formulas of nonlinear dispersive relations proposed by Hedges, Kirby and Dalrymple have large deviations in shallow water regions, a new nonlinear dispersion relation with singular value in the entire water depth is given. Compared with Hedges, Hedges, Kirby and Dalrymple have better dispersion relations in shallow water than those in Hedges, and their forms are concise. By using the explicit expression approximate to the nonlinear dispersion relationship and combining with the gentle slope equation of weak nonlinear effect, the wave deformation model considering the influence of nonlinear dispersion is obtained. The numerical results show that the model obtained from the new nonlinear dispersion relationship is in good agreement with the measured results of the complex terrain