二维与三维随机波浪对半圆型防波堤作用的研究
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摘要
斜向与多向不规则波浪对半圆型防波堤作用的研究此前尚未见文献报道。
综合考虑波陡H／L(π_1)、相对波高H／d(π_2)、堤顶相对水深d_1／d(π_3′)、波浪入射角或波浪主方向θ_0(π_4)和波浪方向分布参数s(π_5)等5个主要影响半圆型防波堤波浪荷载的因子，基于二维水槽和三维水池物理模型试验，对二维(规则波与不规则波)和三维(斜向规则波、斜向不规则波和多向不规则波)波浪条件下半圆型防波堤的受力特性及其机理作了较系统的试验研究和数值计算。给出了不同波浪条件下半圆型防波堤的波浪压力分布特征及单位堤长、单元堤长波浪力的计算方法。
半圆型防波堤波浪压力分布的基本特征受π_3′影响比较大。除π_3′外，π_1和π_2对压力分布的影响也不能忽略。规则波、不规则波和多向波作用下半圆型防波堤的波浪压力分布的基本特征无定性的差别。
在π_2和π_3′一定的条件下，正向水平波浪力、垂向波浪力和底板浮托力随着π_1的减小而增大；负向水平波浪力则随单因子π_1变化的趋势较缓；在π_1和π_3′一定的条件下，正向水平波浪力、垂向波浪力和底板浮托力随π_2的增大而增大；在π_1和π_2一定的条件下，无因次总水平力(正向与负向)随着π_3′的增大而减小。实验范围内，给出了单位堤长上半圆型防波堤的负向水平力大于正向水平力的以π_1、π_2和π_3′分界的临界指标。
斜向和多向波作用下单位堤长上波浪总力随主要影响因子π_1、π_2的变化规律与正向波浪作用时无定性的差别。但斜向波浪入射角度和多向波主波向的变化将会引起堤前波浪形态的变化(产生短峰波)，进而导致波浪力的变化。实验范围内，斜向波浪入射角度在15°～45°范围内变化时，不排除单位堤长正向水平波浪力大于正向波浪作用时正向水平力的可能性；单位堤长上负向水平力总体上不大于正向波浪作用时的负向水平力。当主波向方向θ_0=0°和θ_0=30°时，在s=2～70范围内，多向不规则波作用时单位堤长上波浪力基本不受方向分布宽度参数的影响。π_3′一定的条件下，单位堤长波浪力的折减系数K_(θ_0)与π_1和π_2有关。试验给出了单位堤长波浪力的折减系数K_(θ_0)。
波浪力的纵向分布受控于π_4和π_5。纵向分布的特征变化基本不受π_1和π_2的影响。波浪力的纵向分布是相对堤长L_c~*sinθ_0／L_p的函数。波浪能量的方向分布越宽，波浪力沿纵向的分布越不均匀。斜向波力纵向分布的不均匀性大于多向波的纵向分布的不均匀性。
Few experimental and numerical results have been found so far in the literature to study the effects of wave obliquity and multi-directionality on the wave forces acting on semicircular breakwaters.
Based on 2-d and 3-d random wave physical model tests, the hydraulic characteristics of the semicircular breakwater are studied in this paper. The variations of wave forces on unit length of semicircular breakwater with the main effective factors including wave steepness H/L (π_1), relative wave height H/ d (π_2), relative water depth above the crown of semicircular breakwater d_1/d (π_3') , the angle of incidence θ_0( π_4 ) and spreading parameters s (π_5) are studied. A simplified formula for calculating crests values and troughs values of the total horizontal wave forces on the submerged, alternately submerged, and emerged semicircular breakwater is suggested.
The π_3' is the most important factor for the pressure distribution on the semicircular breakwater, besides π_1 and π_2 The characteristics of the pressure distribution have no significant difference when the semicircular breakwater is subjected to regular waves, irregular waves and multi-directional waves.
The analysis was made with the forces normalized. The crests values of the dimensionless total horizontal wave force P_h~+ the total vertical wave force P_v and the uplift force applied to the bottom slab P_u increase obviously with decreasing π_1 with π_2 and π_3' fixed. The troughs values of the dimensionless total horizontal wave forces P_h~+ are not vary much with the π_1; P_h~+, P_v and P_u increase with increasing π_2 when π_2 and π_3' were kept constant and decrease with increasing π_3' when π_2 and π_2 fixed. The conditions for trough values of the total horizontal wave forces are larger than crest values are discussed.
The regularity of oblique and multi-directional wave force on the semicircular breakwater with the main effecting factors are not vary much from the head-on wave forces. But short-crest waves will be produce in the water field just in front of the semicircular breakwater, and lead to the variety of the wave forces. Within the experimental consideration in this study, the angle of incidence of oblique wave varies in a range of 15° ~ 45°. P_h~+ does not decrease with increasing angle of attack θ_0 as the modified Goda's formulae related. It is clear that oblique incident waves often impose larger forces than head-on waves do. In general, the P_h~- under oblique waves is less
综合考虑波陡H／L(π_1)、相对波高H／d(π_2)、堤顶相对水深d_1／d(π_3′)、波浪入射角或波浪主方向θ_0(π_4)和波浪方向分布参数s(π_5)等5个主要影响半圆型防波堤波浪荷载的因子，基于二维水槽和三维水池物理模型试验，对二维(规则波与不规则波)和三维(斜向规则波、斜向不规则波和多向不规则波)波浪条件下半圆型防波堤的受力特性及其机理作了较系统的试验研究和数值计算。给出了不同波浪条件下半圆型防波堤的波浪压力分布特征及单位堤长、单元堤长波浪力的计算方法。
半圆型防波堤波浪压力分布的基本特征受π_3′影响比较大。除π_3′外，π_1和π_2对压力分布的影响也不能忽略。规则波、不规则波和多向波作用下半圆型防波堤的波浪压力分布的基本特征无定性的差别。
在π_2和π_3′一定的条件下，正向水平波浪力、垂向波浪力和底板浮托力随着π_1的减小而增大；负向水平波浪力则随单因子π_1变化的趋势较缓；在π_1和π_3′一定的条件下，正向水平波浪力、垂向波浪力和底板浮托力随π_2的增大而增大；在π_1和π_2一定的条件下，无因次总水平力(正向与负向)随着π_3′的增大而减小。实验范围内，给出了单位堤长上半圆型防波堤的负向水平力大于正向水平力的以π_1、π_2和π_3′分界的临界指标。
斜向和多向波作用下单位堤长上波浪总力随主要影响因子π_1、π_2的变化规律与正向波浪作用时无定性的差别。但斜向波浪入射角度和多向波主波向的变化将会引起堤前波浪形态的变化(产生短峰波)，进而导致波浪力的变化。实验范围内，斜向波浪入射角度在15°～45°范围内变化时，不排除单位堤长正向水平波浪力大于正向波浪作用时正向水平力的可能性；单位堤长上负向水平力总体上不大于正向波浪作用时的负向水平力。当主波向方向θ_0=0°和θ_0=30°时，在s=2～70范围内，多向不规则波作用时单位堤长上波浪力基本不受方向分布宽度参数的影响。π_3′一定的条件下，单位堤长波浪力的折减系数K_(θ_0)与π_1和π_2有关。试验给出了单位堤长波浪力的折减系数K_(θ_0)。
波浪力的纵向分布受控于π_4和π_5。纵向分布的特征变化基本不受π_1和π_2的影响。波浪力的纵向分布是相对堤长L_c~*sinθ_0／L_p的函数。波浪能量的方向分布越宽，波浪力沿纵向的分布越不均匀。斜向波力纵向分布的不均匀性大于多向波的纵向分布的不均匀性。
Few experimental and numerical results have been found so far in the literature to study the effects of wave obliquity and multi-directionality on the wave forces acting on semicircular breakwaters.
Based on 2-d and 3-d random wave physical model tests, the hydraulic characteristics of the semicircular breakwater are studied in this paper. The variations of wave forces on unit length of semicircular breakwater with the main effective factors including wave steepness H/L (π_1), relative wave height H/ d (π_2), relative water depth above the crown of semicircular breakwater d_1/d (π_3') , the angle of incidence θ_0( π_4 ) and spreading parameters s (π_5) are studied. A simplified formula for calculating crests values and troughs values of the total horizontal wave forces on the submerged, alternately submerged, and emerged semicircular breakwater is suggested.
The π_3' is the most important factor for the pressure distribution on the semicircular breakwater, besides π_1 and π_2 The characteristics of the pressure distribution have no significant difference when the semicircular breakwater is subjected to regular waves, irregular waves and multi-directional waves.
The analysis was made with the forces normalized. The crests values of the dimensionless total horizontal wave force P_h~+ the total vertical wave force P_v and the uplift force applied to the bottom slab P_u increase obviously with decreasing π_1 with π_2 and π_3' fixed. The troughs values of the dimensionless total horizontal wave forces P_h~+ are not vary much with the π_1; P_h~+, P_v and P_u increase with increasing π_2 when π_2 and π_3' were kept constant and decrease with increasing π_3' when π_2 and π_2 fixed. The conditions for trough values of the total horizontal wave forces are larger than crest values are discussed.
The regularity of oblique and multi-directional wave force on the semicircular breakwater with the main effecting factors are not vary much from the head-on wave forces. But short-crest waves will be produce in the water field just in front of the semicircular breakwater, and lead to the variety of the wave forces. Within the experimental consideration in this study, the angle of incidence of oblique wave varies in a range of 15° ~ 45°. P_h~+ does not decrease with increasing angle of attack θ_0 as the modified Goda's formulae related. It is clear that oblique incident waves often impose larger forces than head-on waves do. In general, the P_h~- under oblique waves is less
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