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Numerical study on resonance response of a combined harbor to a solitary wave
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摘要: 港池受到孤立波入射时会在港池内激发多种模态的共振响应。为进一步研究不同平面布置形式港池的响应特性和共振规律，建立不同内外港池长度和连接位置的组合型港池，采用基于Boussinesq方程的波浪数值模型MIKE 21-BW模拟了孤立波作用下组合型港池的共振响应，对数值模拟的结果进行频谱分析和波幅分布测定并与现有理论值比较。结果表明，孤立波正向入射组合型港池激发的主要响应模态的频率和与其长度相等的细长港池的理论固有频率接近，各主要共振模态的振幅与内外港池的长度和两港池口门的距离有密切关系；波浪入射方向和港池内边界反射条件的改变对狭长组合型港池中形成的各共振模态的形状影响不大，但是增大港池宽度会使港池内激发明显的横向共振。最后提出了消减港湾共振的平面布置形式，可为实际工程设计提供指导。Abstract: The muti-modal resonant response will be excited in the harbor during the solitary wave affection. A further research is carried out to study the response characteristics and resonance laws. Firstly, harbors in plan layouts are established with different inner and outer harbor lengths and connecting positions. Then, MIKE 21-BW, a wave numerical model based on Boussinesq equation, is applied to simulate the resonance response of the harbor under solitary waves action. Finally, as compared with the existing theoretical values, the numerical simulation results, especially the amplitude distribution, are analyzed by spectrum method. The results show that the main response frequency of a combined harbor excited by the normal incident solitary wave is close to the theoretical natural frequency of the slender harbor with the same length. Meanwhile, the amplitudes of the main resonance modes are closely related to the length of the inner and outer harbors as well as the distances between two entrances. On the other hand, the directional change of the incident wave and the reflection condition of the boundary within the harbor have little effect on the shaping of each resonance mode in a narrow and long combined harbor. However, with the increasing of the harbor width, transverse resonance becomes obvious at docking zone. Based on the above, a layout plan is proposed to decrease harbor resonance, which would provide guidance for practical engineering design.
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Key words:
- solitary wave /
- harbor resonance /
- combined harbor /
- MIKE21-BW /
- natural frequency
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图 3 内外港池长度变化下组合型港池平面布置
Figure 3. Layout of combined harbor with change of length of inner and outer harbors
图 4 内外港池长度变化下各测点的共振模态的响应频率和振幅
Figure 4. Response frequency and amplitude of resonance modes at each measurement point under changes of length of inner and outer harbors
图 6 内外港池长度变化时其他类型共振的波幅分布
Figure 6. Amplitude distribution of other types of resonances with change of length of inner and outer harbors
图 7 连接位置变化下组合型港池平面布置
Figure 7. Layout of combined harbor with change of connecting position
图 8 连接位置变化下测点1和测点2前两个共振模态的响应频率和振幅
Figure 8. Response frequency and amplitude of first two resonant modes at point 1 and point 2 with change of connecting position
图 10 连接位置变化时其他类型共振的波幅分布
Figure 10. Amplitude distribution of other types of resonances with change of connecting position
图 12 全反射与部分反射边界有效波高差值(单位：cm)
Figure 12. Significant wave height difference between total reflection and partial reflective boundary(unit: cm)
图 14 港池宽度变化下各测点的共振模态的响应频率和振幅
Figure 14. Response frequency and amplitude of resonance modes at each measurement point under changes in width of harbor
图 15 宽度为4.8 m的组合型港池中测点1和测点3波浪频谱比较
Figure 15. Comparison of wave spectra of measuring points 1 and 3 in combined harbor with a width of 4.8 m
图 16 不同宽度港池中横向共振的波幅分布
Figure 16. Amplitude distribution of transverse resonance in harbors with different widths
表 1 细长港池测点1的响应频率和理论共振频率
Table 1. Response frequency and natural frequency at point 1 in the narrow long harbor
共振模态 模拟频率fy/Hz 理论频率fm/Hz 相对误差ε =|fy-fm|/fy×100% 第1共振模态 0.035 0.033 5.98 第2共振模态 0.107 0.102 4.12 第3共振模态 0.179 0.173 3.08 
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表 2 内外港池长度变化时其他类型共振的响应频率和理论共振频率
Table 2. Response frequency and theoretical resonance frequency of other types of resonances with changes of length of inner and outer harbors
位置 共振模态n 模拟频率fy/Hz 理论频率fm/Hz 相对误差ε=|fy-fm|/fy×100% 壁面1-2 (c=5.7 m) 3 0.554 0.557 0.54 壁面1-2 (c=6.7 m) 3 0.510 0.506 0.78 壁面1-2 (c=8.0 m) 4 0.546 0.554 1.47
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表 3 连接位置变化时其他类型共振的响应频率和理论共振频率
Table 3. Response frequency and theoretical resonance frequency of other types of resonances with change of connecting position
位置 共振模态n 模拟频率fy/Hz 理论频率fm/Hz 相对误差ε=|fy-fm|/fy×100% 壁面1-2 (e=1.0 m) 3 0.351 0.358 1.99 壁面1-2 (e=0.5 m) 4 0.450 0.451 0.22 壁面1-2 (e=0.5 m) 5 0.523 0.530 1.34 壁面1-3 (e=3.0 m) 2 0.215 0.203 5.58 壁面1-3 (e=5.0 m) 2 0.186 0.180 3.23
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表 4 不同波浪入射方向下组合型港池主要共振模态的频率
Table 4. Frequency of main resonant modes of a combined harbor in different wave directions
Hz 入射波方向与
岸线夹角c=10.0 m c=16.0 m e=5.8 m 第1共振模态 第2共振模态 第3共振模态 第1共振模态 第2共振模态 第3共振模态 第1共振模态 第2共振模态 45° 0.035 0.107 0.176 0.035 0.104 0.172 0.044 0.092 60° 0.035 0.108 0.176 0.035 0.105 0.174 0.043 0.092 120° 0.035 0.107 0.176 0.037 0.104 0.172 0.044 0.092 135° 0.035 0.107 0.176 0.035 0.105 0.174 0.044 0.093
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表 5 不同反射边界条件下内部港池长度c=10.0 m的组合型港池共振模态比较
Table 5. Comparison of resonant modes of combined harbor with inner pool length c=10.0 m under different reflective boundary conditions
边界条件 第1共振模态 第2共振模态 第3共振模态 振幅/cm 频率/Hz 振幅/cm 频率/Hz 振幅/cm 频率/Hz 部分反射(反射系数0.4) 1.76 0.035 0.86 0.108 0.28 0.177 全反射 1.79 0.035 0.88 0.107 0.28 0.176
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表 6 不同反射边界条件下偏移量e =2.0 m的组合型港池共振模态比较
Table 6. Comparison of resonant modes of the combined harbor with offset e=2.0 m under different reflective boundary conditions
边界条件 测点1 测点2 第1共振模态 第2共振模态 第1共振模态 第2共振模态 振幅/cm 频率/Hz 振幅/cm 频率/Hz 振幅/cm 频率/Hz 振幅/cm 频率/Hz 部分反射(反射系数0.4) 1.48 0.037 1.15 0.107 1.09 0.037 0.97 0.107 全反射 1.57 0.038 1.12 0.111 1.14 0.038 0.95 0.111
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