全水域边缘波动力特性理论解及其数值模拟研究

Edge wave is a "LOCKED" wave propagating alongshore which wave crest line is perpendicular to shoreline and its amplitude decays offshore. Edge wave has important academic and application value and becomes a hot issue in the field of coastal dynamics and morphological dynamics because it influences water levels, wave energy, curriculum system and beach evolution. Nowadays, the mathematical edge wave modeal and its simulations are mainly based on linear shallow water equations, the modified Boussinesq long wave equations and linear mild-slope equations. These models are needed to be further developed for two reasons: (1) it is too simplified (the eigenvalue are too less); (2) their calculations are too complex. Besides, the method to determine the boundary conditions and bottom friction dissipation shall be studied. In this research subject, a linear and second-order nonlinear analytical theoretical solutions of edge waves based on fully water depth on plane sloping bottom are to be established to calculate kinematic-dynamic elements of edge waves to various slope button, wave type and modes; a random edge wave model is established to study the linear and nonlinear spectrum and the change laws of its parameters; a numerical simulation model is established to the fully depth nonlinear edge wave; 3-D physical model experiments are carried out to plane and changed sloping beaches to validate the results of theoretical and numerical solutions. The conclusions of theoretical solutions and simulation results are hope to give a scientific basis to the exploitation and utilization of coastal zone and planning and design of constructions.

边缘波是一种沿平直岸线传播、其波峰线垂直岸线、振幅一般向海衰减的锁闭型波浪。边缘波对近岸水动力和地貌动力作用显著，影响水域水位、波能、环流系统与岸滩演变。边缘波研究一直是海岸和地貌动力学的一个热门课题，具有重要学术与应用价值。目前，基于线性浅水方程及其改进的Boussinesq长波方程、线性缓坡方程的边缘波数学模型与数值模拟或由于较为简化（特征值个数少），或由于计算极为复杂，有待进一步发展完善。边界条件的确定方法、底摩阻耗散影响等也有待探讨。课题拟提出均匀斜坡上边缘波波系线性与二阶非线性解析解系统理论及数值解法，计算分析不同底坡、不同波型、不同模态边缘波水动力的变化特性，建立相应边缘波随机模型，探讨其一阶、二阶谱及其参数变化规律，进行全水非线性边缘波数值模拟，开展均匀斜坡与折坡水域波浪三维物模试验研究，对理论计算与数值模拟予以验证。基于此，以期为海岸带开发利用及工程规划设计提供科学依据。

作为一种沿平直岸线传播、振幅向海衰减的锁闭型波浪，边缘波对近岸水动力条件和地貌塑造有显著的作用，会影响近岸区域水位、波能、环流系统与岸滩演变，其研究具有重要学术与应用价值。本项目提出了全水域边缘波系的运动学动力学特征线性与二阶非线性的解析解并推广于不规则波，建立了边缘波波谱模式。基于所建立的理论模型，对边缘波运动学动力学特征要素进行了系统的计算分析，探讨其随边缘波波态、模态及波参数的变化特性，讨论了不同坡角，不同模态及不同波态的二阶解析解近似适用范围。在数值模式方面，对于均匀斜坡上的边缘波，基于完全频散性非线性统一模型建立了数值模式，对于折坡地形上的边缘波，采用几何光学方法确定了频散关系，并用追赶法进行了稳定快速的数值计算，验证了模拟结果与理论值吻合良好。对于全水域边缘波的物理模型试验，本项目主要在两类地形上进行了试验。对于第一类地形，采用文献中的方法在波浪正向入射的地形上进行了验证性试验，并增加了对波面的观测，将边缘立波的沿岸波长与理论进行了比较。试验结果与理论及文献中的描述基本相符，在两块直墙之间的区域内观察到了稳定存在的边缘立波和伴随出现的裂流现象，裂流位置亦与理论预测相符。第二类地形采用波浪横向入射产生边缘波，用这种方法对推进型边缘波和边缘立波的特性进行了研究。在物模试验结果的基础上对边缘波的模态分离方法进行了初步探讨，采用最小二乘法实测波形进行了模态分离，得到了较为合理的结果。本项目在全水域边缘波理论模型、数值模拟及物理模型试验方面取得的成果可以为海岸带开发利用及工程规划设计提供一定的科学依据。