中文摘要：

本文在基于能量平衡方程考虑绕射项的多向随机波数学模型的研究基础上，将非线性弥散关系和底摩擦能量耗散引入原模型中，以提高模型计算波浪浅水域变形的精度。另外，在输入方向谱上，加入我国《海港水文规范》推荐的文氏谱和改进的光易型方向分布函数，使模型的应用范围更广。改进后的模型考虑了波浪的浅化、折射、绕射、反射、破碎、底摩擦以及非线性。选择椭圆形浅滩地形和莱州湾海域地形，分别利用改进前和改进后的模型对多向随机波传播变形进行数值模拟。通过对计算结果的比较分析证明，改进后的模型更具适用性与合理性。

英文摘要：

Based on an energy-balance-equation mathematical model with diffraction term for multi-di- rectional random wave, the present paper introduces nonlinear dispersion relationship and energy dissi- pation induced by bottom friction to the original model in order to make the model compute wave trans- formation over the shallow water area more accurately. In addition, Wen spectrum and improved Mitsuyasu type directional distribution function recommended by ffChinese Code of Hydrology for Sea Harbor}are added as the input directional spectrum to widen the applied range of the model. Improved model accounts for the shoaling, refraction, diffraction, reflection, breaking, bottom friction and nonlinearity. The original model and improved model are implied to simulate the multi-directional random wave transformation over the bathymetry with an ellipse shoal and Laizhou Bay. The improved model is proved more applicable and reasonable through the comparison and analysis to the computation results