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Changes in wavelength of wave propagation over a sandy seabed
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摘要: 沙质海床具有渗透性，会引起波浪的波长变化。基于线性波浪理论，采用Mendez提出的摄动方法，在已知波浪周期、水深和海床渗透系数的条件下，数值求解了渗透海床上的波浪色散方程，得到相应的波长，进而研究不同渗透系数和相对水深的沙质海床上波长的变化规律。结果表明，波浪在沙质海床上传播时的波长大于海床不可渗透的情况，且随着渗透系数的增大而增大；波浪在向岸传播过程中会发生浅水变形而波长减小，相比海床不可渗透的情况，沙质海床上的波长减小程度相对较小，这种现象随着相对水深的减小而愈加明显。因此，沙质海床的渗透性对波长的影响相当于1个“海床水深”Δh，它随渗透系数的增大和相对水深的减小而增大，当波浪在水深为h的沙质海床上传播时，其波长等于水深为h+Δh的不可渗透海床的波长。Abstract: A sandy seabed is permeable, and it will cause the changes in wavelength. Based on the linear wave theory, a perturbation method proposed by Mendez is applied to solving the dispersion equation for waves over the porous bottom numerically, obtaining the wavelength under the given conditions of wave period, water depth and permeability coefficients. And then the changes in wavelength of the wave propagation over the sandy seabeds with different permeability coefficients and water depths are studied. The research results indicate that: ① the wavelength on the sandy seabed is longer than that on an impermeable bottom, and it will increase with the increase of the permeability coefficients; ② when waves propagate toward the shore, the decreasing degree of the wavelength by wave shoaling on the sandy seabed is smaller compared with the impermeable bottom, and the differences are more remarkable in a shallower water depth. Therefore, the effect of the permeable sandy bottom on the wavelength is equivalent to a variable Δh, namely the water depth of the seabed, which increases with the increase in the permeability coefficients and decrease in the water depth. As a result, the wavelength of the wave propagation over the sandy seabed with a water depth h equals that over the impermeable bottom with a water depth h+Δh.
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Key words:
- sandy seabed /
- permeability /
- dispersion equation /
- water depth on seabed
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图 1 相对波长L/L0随渗透系数的变化
Figure 1. Changes of wavelength ratio L/L0 versus permeability coefficients
图 2 相对波长L/L0和L/LI随相对水深的变化
Figure 2. Changes of wavelength ratio L/L0and L/LI versus non-dimensional wave depth h/L
表 1 不同区间数时计算结果的相对误差
Table 1. Relative calculation errors with different interval number N
渗透系数Ks/(m·s-1) 波浪周期/s 区间数N 本文计算结果k 迭代法计算结果k 衰减系数相对误差/% 0.01 3 10 0.456 973+0.000 040i 0.456 973+0.000 036i 10.00 0.01 3 15 0.456 973+0.000 038i 0.456 973+0.000 036i 6.67 0.01 3 50 0.456 973+0.000 037i 0.456 973+0.000 036i 2.00 0.01 3 150 0.456 973+0.000 036i 0.456 973+0.000 036i 0.67 0.01 3 200 0.456 973+ 0.000 036i 0.456 973+ 0.000 036i 0.50 0.08 5 10 0.207 437+0.000 766i 0.207 437+0.000 696i 10.00 0.08 5 15 0.207 437+0.000 742i 0.207 437+0.000 696i 6.67 0.08 5 50 0.207 437+0.000 710i 0.207 437+0.000 696i 2.00 0.08 5 150 0.207 437+0.000 700i 0.207 437+0.000 696i 0.67 0.08 5 200 0.207 437+ 0.000 699i 0.207 437+0.000 696i 0.50 
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