中文摘要：

建立了基于高阶Boussinesq水波方程的一维波浪破碎数值模型。基于一组具有二阶完全非线性特征的Boussinesq水波方程，建立了交错网格下的高精度差分格式，推导了适用于该组方程的永形波解析解，其和松弛造波技术相结合实现了数值波浪水槽中（强）非线性波浪的无反射入射。通过模拟封闭容器内水体晃动问题对数值格式进行了验证，通过模拟孤立波在斜坡海岸上的浅化过程说明了将方程从弱非线性发展到完全非线性的必要性。采用涡粘方法处理波浪破碎，利用物理模型实验数据，分析了模型中各波浪破碎参数对数值结果的影响并对参数进行了率定。应用该模型对规则波在斜坡海岸上的传播、变浅以及破碎过程进行了数值模拟研究，数值结果同实验数据吻合良好，验证了模型的有效性。

英文摘要：

A 1 D wave breaking model is developed based on an existing set of second-order fully nonlinearity Boussinesq equations.The discretized equations are solved numerically on a staggered grid using a higher-order finite difference scheme.The non-reflective boundary condition for incident wave is achieved by deriving a standing wave solution of the equations and using a relaxation wave generation technique.The 1 D wave breaking model is used to solve the problem of water sloshing in a closed container.The shoaling of a solitary wave on a plane beach is simulated by the model in an effort to illustrate the importance of retaining full nonlinearity.The shoaling and breaking of regular waves on a sloping plane beach is studied numerically using the model.The result shows that there is a satisfactory agreement between the numerical simulation and the experimental data,which demonstrates the effectiveness of the 1 D wave breaking model.