CAJ | 학술논문

针对Hedges、Kirby、李瑞杰提出的修正非线性弥散关系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相对波速具有单值性的新的非线性弥散关系。它在深水区与二阶Stokes波的弥散关系相一致，在浅水区较前人的修正式与Hedges经验弥散关系更加吻合，在中等水深区域与二阶Stokes波的弥散关系及Hedges经验弥散关系的偏差也达到最小。为了避免非线性弥散关系引入缓坡方程而导致的迭代，采用显式形式近似表达该非线性弥散关系，得到与其精度几乎完全相同的显式表达式。用该显式表达式，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数学模型。用该模型对复杂地形进行模拟，计算结果与实测值吻合很好。
침대Hedges、Kirby、리서걸제출적수정비선성미산관계재천수구존재교대편차적문제，급출료일개재정개수심범위내상대파속구유단치성적신적비선성미산관계。타재심수구여이계Stokes파적미산관계상일치，재천수구교전인적수정식여Hedges경험미산관계경가문합，재중등수심구역여이계Stokes파적미산관계급Hedges경험미산관계적편차야체도최소。위료피면비선성미산관계인입완파방정이도치적질대，채용현식형식근사표체해비선성미산관계，득도여기정도궤호완전상동적현식표체식。용해현식표체식，결합약비선성효응적완파방정，득도고필비선성미산영향적파랑변형수학모형。용해모형대복잡지형진행모의，계산결과여실측치문합흔호。
Due to the larger deviation in shallow water of the nonlinear dispersion relations modified by Hedg-es, Kirby and Li Ruijie, a new nonlinear dispersion relation, whose relative wave velocity was monotonic in the en-tire depth, was presented in this paper. It is consistent with the dispersion relation of second order stokes wave in deep water, and is closer to Hedges′empirical one than previous modified relations in shallow water. In moderate depth water, its deviation is also minimal. In order to avoid iterations due to the introduction of nonlinear dispersion relation to the mild slope equation, an explicit form was adopted to approximately express the new nonlinear disper-sion relation. And the accuracy of the two was almost identical. The explicit expression, along with the mild slope equation, could constitute a wave transformation model, which included nonlinear dispersion effects. Using the new model to simulate a complicated seabed, the calculation results are in good agreement with the measured values.