波面位移非线性特征数值研究

Numerical study on the nonlinear behaviors of wave surface elevation

基于Longuest-Higgins(1963)非线性海浪模型,在有限水深且存在均匀背景流的条件下,根据Song(2006)给出的波面位移二阶表达式,采用Combi海浪频谱计算了海表面定点波面位移时间序列和波面位移概率统计分布。分析了波面位移统计分布随风速、水深、反波龄和均匀背景流的变化特征和规律以及不同海况条件下二阶非线性项对波面位移统计分布的影响。结果表明:二阶非线性项使波面位移分布偏离正态分布,二阶非线性作用受风速、水深、反波龄和均匀背景流的影响。风速增大、水深降低、反波龄减小或者均匀背景流和风速传播方向相反均使波面位移二阶非线性项的作用加强,无因次波面位移概率密度分布的偏度和峰度随之增大,反之则二阶非线性项作用减弱。当均匀背景流和风速相同时,虽然使非线性项的作用减弱,但平均波面位移反而比静止水平面降低。当均匀背景流和风速相反时,虽然使非线性作用增强,但平均波面位移反而趋于静止水平面。得到如下结论:二阶非线性项对于波面位移有显著影响,数值模拟波面位移需要增加二阶非线性项。通过以上研究,提高了数值模拟波面位移的准确性,而波面位移是海浪最基本的特征量,从而增强了海浪模拟和预报的准确性,对海洋工程、海–气相互作用、上层海洋动力学等具有重要意义。

Based on a previously published nonlinear wave-surface model, we have calculated the time series of wave-surface elevations and their statistical distribution with Combi wave spectra under conditions of a steady background current in a finite water depth. This is in, accordance with the second-order expression of wave-surface elevation. We also analyzed the changing characteristics of the wave-surface elevation distribution by wind speed, water depth, inverse wave age, and steady background current. The effects made by second-order nonlinearity on the wave-surface elevation distribution under various ocean conditions have also been discussed in this article. According to our analyses, second-order nonlinearity leads to a non-Gaussian distribution of wave-surface elevation. Indeed, second-order nonlinearity is affected by wind speed, water depth, inverse wave age, and a steady background current. Increasing the wind speed and inverse wave age, decreasing the water depth, or when the steady background current is against the wind direction, the effect of second-order nonlinearity will increase. This, leads to an increase of the skewness and kurtosis of the dimensionless wave-surface elevation distribution, however, the effect of the second-order nonlinearity will decrease. When the steady background current spreads in the same direction as the wind, although the effect of second-order nonlinearity decreases, the average wave-surface elevation is lower than the static water surface. When the steady background current is against the wind, although the effect of second-order nonlinearity increases, the average wave-surface elevation is inclined to the static water-surface. In conclusion, second-order nonlinearity has significant effects on wave-surface elevation, and it is necessary to add second-order nonlinearity to numerical simulations of wave-surface elevation. According to the analyses mentioned above, since the wave-surface is the most basic characteristic of an ocean wave, the addition of second-order nonlinearity will improve the numerical accuracy of wave-surface and ocean wave stimulations. This, will improve forecast accuracy, making significant differences in ocean engineering, air-sea interactions, and the dynamics of the upper ocean.