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Analytical calculation of cnoidal wave diffracted force on a V-shaped breakwater
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摘要: 应用椭圆余弦波理论，给出了V形薄壁防波堤的浅水波绕射理论解，对现有Airy微幅波理论进行了有效拓展。通过对V形防波堤的浅水波浪力进行试算，揭示了椭圆余弦波对防波堤的作用规律。计算结果表明：椭圆余弦波理论计算的V形防波堤的最大无量纲波浪力明显大于相同浅水条件下Airy微幅波理论的对应结果，该方法有效拓展了无限长直立薄壁堤的反射波理论。此外，浅水波入射角、V形堤张角和防波堤臂长与水深比等参数的变化均将对V形堤的波浪作用产生相关影响，而V形堤的实际绕射波浪力幅值将随浅水波特征参数值的增大而增大。Abstract: With the use of cnoidal wave theory, the theoretical solutions to shallow water wave diffraction by a V-shaped breakwater are derived, so the existing Airy small amplitude wave theory is effectively extended. By calculating the shallow water wave forces on the V-shaped breakwater, the law of cnoidal wave action on the breakwater has been revealed. The results show that the maximum dimensionless wave forces on the breakwater are obviously larger than those predicted by small amplitude wave theory under the same shallow water conditions. The reflected wave theory on the infinite long vertical thin-walled breakwater is effectively extended by using the method in the paper. The variation of incident wave angle, breakwater angle and ratio of breakwater arm length and water depth may have some related influence on wave effects and the practical maximum diffracted wave forces will increase as the shallow water wave characteristic parameter value increases.
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Key words:
- cnoidal wave /
- V-shaped breakwater /
- wave force /
- wave diffraction
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图 2 与无限长密实直墙堤的中心线剖面的比较
Figure 2. Comparation of central profile with infinite long solid wall (
$\lambda = 1, \;a = 1\;000,\; d = 2,\; \alpha = {\text{π}},\; \beta= {\text{π}}/2$ )
图 3 不同臂长水深比下最大无量纲波浪力随
$kd$ 的变化Figure 3. Maximum dimensionless wave force for different arm length-water depth ratio
$\left( {\beta = {\text{π}}/3,\;\lambda {\rm{ = }}3,\;\alpha {\rm{ = }}2{\text{π}}/3} \right)$ 
图 4 不同臂长水深比下最大无量纲波浪力随
$kd$ 的变化Figure 4. Maximum dimensionless wave force for different arm length-water depth ratios
$\left( {\beta = {\text{π}}/2,\;\lambda {\rm{ = }}3,\;\alpha = {\text{π}}} \right)$ 
图 5 不同来波入射角下最大无量纲波浪力随
$kd$ 的变化Figure 5. Maximum dimensionless wave force for different incident angles
$\left( {\lambda = 3,\;d/a = 1/5,\;\alpha = 2{\text{π}}/3} \right)$ 
图 6 不同入射角下最大无量纲波浪力随
$kd$ 的变化Figure 6. Maximum dimensionless wave force for different incident angles
$\left( {\lambda = 3,\;d/a = 1/5,\;\alpha = {\text{π}}} \right)$ 
图 7 不同张角下V形堤的最大无量纲波浪力随
$kd$ 的变化Figure 7. Maximum dimensionless wave force for different opening angles of the breakwater (λ
=3, d/a=1/5, β=π/4, π/3, π/2) 
图 8 不同
$kd$ 下最大无量纲波浪力随浅水波特征参数$\lambda $ 的变化Figure 8. Maximum dimensionless wave force for different characteristic parameters of shallow water (β=π/3, α=2π/3, d/a=1/5)
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