波浪的非线性显式弥散关系

波浪的非线性弥散关系在应用于求解波浪的变形问题时很不方便，需要与含非线性效应的缓坡方程一起进行迭代运算，往往导致数值计算的计算量太大，计算过于复杂。采用显式形式表达非线性弥散关系，可以克服上述缺点，大为简化波浪变形数值计算的计算量。本文通过将现有的非线性弥散关系进行分析比较，给出了一个更为一般的非线性弥散关系及其显式表达式，经比较可知，该显式弥散关系与相对应非线性弥散关系吻合的很好。本文最后用该显式结合含弱非线性效应的缓坡方程，对复式浅滩地形上的波浪折射绕射进行了计算。结果表明，考虑弱非线性可以得出与实验数据更为相符的结果，而采用显式弥散关系可以有效提高计算效率,在波浪的非线性计算中不失为一种切实有效的方法。

WAVE EXPLICIT NONLINEAR DISPERSION RELATION

A general explicit nonlinear dispersion relation which can overcome the defect of the common nonlinear dispersion relations is derived in this paper. To solve wave transformation, the common nonlinear dispersion relations need to be used in connection with the mild slope equation, and complex iterative computations have to be conducted. The explicit nonlinear dispersion relation can simplify the computation of wave transformation. The several mostly often used common nonlinear dispersion relations are all included in the general explicit nonlinear dispersion relation derived in this paper which highly agree with those common nonlinear dispersion relations. Making use of the explicit nonlinear formulation derived in this paper and the mild slope equation with weak non-linearity calculations are conducted for wave transformation in the compound shoals. The results show that the present model is rational and in good agreement with experiment data and that nonlinearity should be considered in this case.