一种改进的近岸波浪破碎数值模型

Improved numerical model for nearshore wave breaking

提出一种基于完全非线性Boussinesq方程的改进波浪破碎模型,用于模拟近岸浅水波浪破碎。模型借助水滚的概念,提出一种确定k方程紊动模式中紊动源项的计算公式,通过解k方程计算Boussinesq方程中的涡黏系数,实现对破碎波的模拟。岸边界采用窄缝法,使得模型可用于波浪爬坡的计算。用实验室实测波高和增减水资料对模型进行了验证,得到了一致的结果。紊动源、紊动动能以及紊动耗散率的计算结果表明:①在破波点处紊动源项值最大,随着波浪向岸边传播,逐渐减小;②破波点处,水平方向的对流和扩散在紊动能量输移中发挥重要作用;③岸边附近紊动源与紊动耗散接近平衡。

This paper aims at proposing an improved numerical model based on the full-nonlinear Boussinesq equations for simulating wave breaking in the surf zone. A new formula is proposed based on the concept of surface roller to determine the production term in the k equation of turbulent model. Consequently the eddy viscosity in the Boussinesq equations, which gives the attenuation effect of the waves in the surf zone, can be calculated by solving the k equation. The slot method is used in the model to simulate wave movement in the swash zone. The model is verified by the experimental data in terms of wave height and setup and setdown. Comparison of modeled results with measurements shows a reasonable agreement. Modeled results of the turbulent production, the turbulent energy and the dissipation rate of turbulent energy indicate: (1) the turbulent production peaks at the breaking point and decreases gradually as the wave approaches the shoreline; (2) at the incipient regime of wave breaking, the advection and the diffusion effects play an important role in the transport process of the turbulent energy; and (3)as waves approach the shoreline, the turbulent production and the dissipation are almost balanced each other.