数值研究非平底地形对畸形波能量结构的影响

摘要

A numerical model that solves the Reynolds time-averaged N-S equations by the finite-difference method was built with the k-εmodel for the turbulence closure and the volume of fluid (VOF)method for tracking the free surface.The model was implemented to simulate the freak waves over non-flat bottom to-pography.With the time-frequency energy spectrum of the freak waves that was calculated by the wavelet analysis method the effects of non-flat bottom topography on the energy focusing and high frequency ener-gy were analyzed.It is concluded that the non-flat bottom topography has a insignificant effect on the time-frequency energy spectrums for the slope that is less than 1 ∶ 10 and the topography whose normalized change in water depth is smaller than 0.333,but the influence of the non-flat bottom topography is consid-erable for the slope that is more than 1∶10 and the topography whose normalized change in water depth is greater than 0.333.With the increasing slope and normalized change in water depth,the energy shifts to high frequency endwhich makes the frequency domain of the energy distribution broaden,and the peak val-ue of the time-frequency spectrum density decreases.On the other hand,the non-flat bottom topography has a indifferent effect on the parameters of energy focusing.%采用流体体积(VOF)方法捕捉自由表面，结合有限差分方法求解 N-S(Navier-Stokes)方程、k-ε模型封闭，建立数值模型，并使用该模型模拟非平底地形条件下畸形波的生成。采用小波分析方法计算模拟结果的时频能量谱，基于计算结果分析非平底地形对畸形波能量集中程度和高频能量的影响。主要结论为：坡度小于1∶10的斜坡地形和无量纲水深变化小于0.333的曲线地形对畸形波时频能量谱的影响不显著；坡度大于1∶10的斜坡地形和无量纲水深变化大于0.333的曲线地形会显著影响畸形波的时频能量谱，随着坡度和无量纲水深变化的增加，时频能量谱中畸形波发生时刻附近，能量向高频方向移动，使得能量在高频端的分布范围增大，时频谱密度峰值减小；斜坡和曲线地形的特征变化对于畸形波能量集中度参数的影响不显著。