波浪非线性弥散关系及其应用

A wave nonlinear dispersion relation and its application

针对Hedges及Kirby等对Kirby和Dalrymple的非线性弥散关系的修正关系,在小波陡时中等水深范围存在较大偏差的问题,给出了一个新的非线性弥散关系。比较可知,新的关系在小波陡时减小了中等水深范围内50%的误差,而在大波陡时能够保持其单调性,且形式上更为简练。将其应用于含弱非线性效应的缓坡方程进行数值验证,结果表明,采用新的非线性弥散关系得到的计算结果与实测结果更为吻合。

A new nonlinear dispersion relation of wave over the whole range of possible water depths is given in this paper. It reduces the excess phase speed overprediction of both Hedges' modified relation and Kirby and Dalrymple's modified relation in the region of 1<kh<15 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. Making use of the new form along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is obtained and applied to laboratory data for the test. The results show that the model using the new dispersion relation can predict the wave transformation over the complicated bathymetry quite well.