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该文采用色散性保留到二阶的完全非线性Boussinesq方程,模拟了波群引起的狭长矩形港湾内的非线性共振现象,并使用最小二乘法分析了港湾处于第一共振模态下锁相长波和自由长波的波幅以及它们相对成分随着短波波长的变化。为了进行对比,也模拟了波群未能诱发港湾发生非线性共振的情况,并使用相同的方法对港内低频成分进行分离。研究表明:无论港湾共振与否,锁相长波和自由长波的波幅以及它们的相对成分都与短波波长有着密切的联系。对于该文中所研究的特定港湾以及特定的波群频率范围,港湾处于最低的共振模态时,锁相长波的波幅要小于自由长波波幅,但是在短波的波长大于0.66倍的港湾长度的情况下,锁相长波波幅往往要大于自由长波的1/2;当港湾未处于共振状态且短波波长大于0.56倍的港湾长度时,锁相长波的成分往往要超过自由长波。
In this paper, we use the completely nonlinear Boussinesq equation with dispersion to the second order, and simulate the nonlinear resonance phenomena in the narrow rectangular harbor caused by wave groups. The least-square method is used to analyze the long- And free longwave wave amplitude and their relative composition with the shortwave wavelength changes. For the sake of comparison, it is also simulated that the wave group can not induce non-linear resonance in the harbor and the same method is used to separate the low-frequency components in the harbor. The results show that no matter whether the harbor resonates or not, the amplitudes of the phase-locked and free longwaves and their relative compositions are closely related to the shortwave wavelengths. For the particular harbor studied in this paper and the specific frequency range of the group of waves, when the harbor is in the lowest resonance mode, the amplitude of the locked-in longwave waves is less than the free longwave wave amplitude. However, if the shortwave wavelength is greater than 0.66 times the harbor length , The lock-in long-wave amplitude is often greater than the free long-wave 1/2; when the harbor is not in resonance and the short-wave wavelength is greater than 0.56 times the length of the harbor, the phase-locked long-wave composition tend to exceed free longwave.