海岸沙坝运动的实验与数值模拟研究
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摘要
沙坝是沙质海滩的重要组成部分之一。在近岸水域内,沙坝的存在会使波浪在离岸较远的地方发生破碎,以减少波浪对岸滩侵蚀,对海岸起到了一定的保护作用。但目前为止,沙坝产生的机理和演化规律仍不清楚。近年来,研究沙坝产生和演化规律已成为海岸工程的一个重要课题,这对研究海岸的演化、防止海岸的冲刷等都具有重要意义。本文通过一系列的物理模型实验和数值模拟对海岸沙坝的产生和运动进行了研究,主要内容包括：
(1)进行了海岸沙坝产生和运动的实验模拟,研究了规则波、波群和不规则波作用下近岸沙坝产生和运动的特征。针对沙坝产生的机理和不稳定性运动,对不同波浪形态(规则波、波群和不规则波)作用下产生的海岸剖面形态进行了研究。实验中发现,在某种波况下,沙坝运动呈向岸、离岸的往复运动,而不是持续向一个方向的运动。通过对实验结果的分析,也进一步表明,沙坝运动不是海床对波浪作用的被动响应,而是更接近于一种海床和波浪之间的相互作用。文中还探讨了波群调制系数对沙坝运动的影响,以及不同波况对海岸剖面形态的影响。通过对沙坝速度的分析,进一步讨论了多种波况作用下沙坝的不稳定运动。最后,通过对这种不稳定运动的分析,并结合线性不稳定的理论,给出了一个初步的理论解释,定性的分析了所观测到的往复运动是一种海床剖面不稳定性导致的运动。
(2)通过对海岸沙坝运动实验的分析可知,本文实验所涉及的海岸属于耗散性海岸,即近岸低频波的影响不可忽视。在波浪条件下,低频波浪对近岸泥沙运动的作用是不容忽视的。为了便于研究低频波浪传播的特性,并且方便验证数学模型中波浪模块对低频波浪的模拟结果,我们也进行了一系列的低频波模型实验研究。低频波浪的模型实验研究包括：实验模型、仪器布置、双波群的生成和实验波况,着重分析了所产生低频波浪的特征,包括反射低频波个数,时间尺度和大小；推导了包含坡度、入射波周期、短波数和波幅的无因次指标M,用于预测反射低频波个数。
(3)在数值模拟方面,本文中分别采用两种数学模型对近岸水动力进行了模拟计算,即波浪平均模型(Wave-averaged model)和短波相位识别模型(Phase-resolving model)。
波浪平均模型的控制方程通过将欧拉方程在短波周期上进行平均得到,然后采用WAF方法进行求解,模拟结果与实验吻合较好。在破碎区,波浪平均计算模型在短波能量的计算方面存在一些误差,主要是由于波浪方程中对耗散项的近似表达引起,也可以由此解释低频波浪波面升高的误差由来,即耗散项的近似表达影响了辐射应力的计算精度,因而影响低频波浪的波面升高。为了更精确的模拟波浪破碎后的低频波波面升高和能量,除了短波平均模型外,我们还采用了短波相位识别模型,即Boussinesq型模型对低频波模型实验进行数值模拟。模型的控制方程采用简化的四阶弱非线性方程和二阶完全非线性方程。
通过与实验结果的对比,分别验证两种模型对低频波浪的模拟效果及精度。虽然波浪平均模型在精确性上不如短波相位识别模型,但是该模型可以单独考虑长波对于近岸输沙的作用,因此,也是本文研究的一个主要内容。而短波相位识别模型的模拟精度更高,且能对短波与低频波浪相互作用进行模拟,有更广泛的适用性。
(4)海底形态的数值模型包括：计算驱动力的水动力模型、计算输沙通量的泥沙模型以及地形变化模型之间的耦合。模型主要采用基于能量考虑的BBB输沙公式及其修正形式；对海岸变形方程的数值求解采用了由Long推导的Euler-WENO格式。
(5)将波浪平均模型应用于海岸演变的数值模拟。将其与近岸输沙和海岸变形方程相耦合,对海岸地形的演变进行了数值模拟。模拟结果与实验结果的对比表明：该模型可以模拟出海岸侵蚀,但不能较好的模拟初始直线型斜坡上近岸沙坝的产生过程。模拟内容包括波群及不规则波作用下的沙坝离岸运动过程,讨论了短波、长波和平均水流共同作用及单独作用下的沙坝运动情况。
(6)将短波相位识别模型应用于海岸演变的数值模拟。将其与输沙和海岸变形模型相耦合,对规则波、波群和不规则波作用下沙坝的产生和运动进行了数值模拟,并与实验结果进行了验证。结果表明：在不同波浪作用下沙坝的产生位置的计算结果和实验结果吻合良好；沙坝的产生主要是由于波浪破碎及其所产生的海底回流所引起的,海底回流所导致的输沙率在空间梯度上的变化是沙坝产生运动的主因。该模型对于预测海岸侵蚀以及沙坝离岸运动能达到很好的结果,并且能够实现对次级沙坝的模拟。
Sandbar is one of the important features of nearshore beach profile. In the nearshore area, the existence of sandbar will make waves break and reduce the erosion of coast beach which is produced by waves and currents. It has an important protective effect for the coast. But so far, the production mechanism of sandbar and its migration is still not clear. In recent years, the sandbar's generation and evolution mechanism has become an important topic in the research of coastal engineering. It has an important significance for preventing coastal area from erosion and siltation. The present study invesgates the generation and evolution of sandbar through a series of physical experiments model and numerical simulations. The main content includes:
(1) A series of physical model experiments were conducted in a wave flume to investigate sandbar movements under various wave conditions. Wave groups, regular and random waves were considered. It was observed that under certain wave conditions sand bars move alternately onshore and offshore, rather than in a single direction. Analysis further shows that the sandbar migration does not seem to be a passive response of the sea bed to wave forcing, but is most likely caused by the feedback interaction between wave and bed topography. A simple theoretical analysis based on linear instability concept is presented which qualitatively establishes that the observed oscillsating movement of a sandbar is a type of instability of sea bed profile.
(2) A series of laboratory experiments were also conducted for the reflection of two wave groups over beach slopes of1:20,1:40,1:60,1:80,1:90,1:100,1:120,1:140and1:160in order to study the characteristics of infragravity waves(LFW). The relation between the number of the reflected LFW and the period of incident wave groups and beach slope is studied and an index for the number of the reflected LFW is introduced for the description of the generation mechanism of LFW on different beach slopes. The experimental results also show that the time intervals between two successive reflected LFW crests and troughs are almost equal to the period of incident wave groups.
(3) Numerical simulations of the observed propagation of LFW in the experiment are also made by using a short wave averaged model and a phase-resolving wave. For the former model, TVD numerical scheme is used to treat the wave breaking of LFW. For the latter model, the simplified version of the fourth-order weakly nonlinear equations and the fourth-order fully nonlinear equations are employed. Eddy Viscosity wave breaking model is included in the model. It is found that by appropriately choosing the model coefficients, agreement with experimental results can be obtained, and the phase-resolving wave model acts better than wave averaged model after wave breaks. The phase-resolving model was also used to simulate some beaches which are not included in experiments,in order to examine the relationship between the number of the reflected LFW and beach slopes.
(4) A numerical model is developed to simulate beach profile changes under different wave conditions. The model consists of wave model, sediment transport rate and profile evolution model. The wave model includes wave-averaged model and Phase-resolving model respectively. The Euler-WENO scheme and instantaneous Bagnold transportation formula are employs in sediment transport model and profile evolution model.
(5) Sediment transport and profile evolution models are coupled with wave-averaged model in order to computing beach profile evolution under waves action. The model is validated against data from laboratory experiments, and the results show that the model can simulate the erosion prossess of beach, but is not efficient for the sandbar formation. The simulation of the sandbar offshore movement under irregular wave actions is also considered, and the effects of waves and mean currents to sandbar migration are invesgated.
(6) Phase-resolving model is used to predict on-off shore sandbar migration in the coastal region. The wave module is based on the BouN2D4equations, which possesses good dispersion, shoaling and fully nonlinearity characteristics and could take many wave phenomena into account, including wave diffraction, wave refraction and wave breaking. The output of this wave model serves as the input to the sediment transport model. With application of this model, the sandbar formation and evolution can be predicted under different wave actions. It is shown that, undertow which casuses strongh spatial gradient of sediment transport rate, has the most important effect on sandbar generation and evolution. The resulting coupled model can successfully predict beach erosion and sandbar offshore migration.
(1)进行了海岸沙坝产生和运动的实验模拟,研究了规则波、波群和不规则波作用下近岸沙坝产生和运动的特征。针对沙坝产生的机理和不稳定性运动,对不同波浪形态(规则波、波群和不规则波)作用下产生的海岸剖面形态进行了研究。实验中发现,在某种波况下,沙坝运动呈向岸、离岸的往复运动,而不是持续向一个方向的运动。通过对实验结果的分析,也进一步表明,沙坝运动不是海床对波浪作用的被动响应,而是更接近于一种海床和波浪之间的相互作用。文中还探讨了波群调制系数对沙坝运动的影响,以及不同波况对海岸剖面形态的影响。通过对沙坝速度的分析,进一步讨论了多种波况作用下沙坝的不稳定运动。最后,通过对这种不稳定运动的分析,并结合线性不稳定的理论,给出了一个初步的理论解释,定性的分析了所观测到的往复运动是一种海床剖面不稳定性导致的运动。
(2)通过对海岸沙坝运动实验的分析可知,本文实验所涉及的海岸属于耗散性海岸,即近岸低频波的影响不可忽视。在波浪条件下,低频波浪对近岸泥沙运动的作用是不容忽视的。为了便于研究低频波浪传播的特性,并且方便验证数学模型中波浪模块对低频波浪的模拟结果,我们也进行了一系列的低频波模型实验研究。低频波浪的模型实验研究包括：实验模型、仪器布置、双波群的生成和实验波况,着重分析了所产生低频波浪的特征,包括反射低频波个数,时间尺度和大小；推导了包含坡度、入射波周期、短波数和波幅的无因次指标M,用于预测反射低频波个数。
(3)在数值模拟方面,本文中分别采用两种数学模型对近岸水动力进行了模拟计算,即波浪平均模型(Wave-averaged model)和短波相位识别模型(Phase-resolving model)。
波浪平均模型的控制方程通过将欧拉方程在短波周期上进行平均得到,然后采用WAF方法进行求解,模拟结果与实验吻合较好。在破碎区,波浪平均计算模型在短波能量的计算方面存在一些误差,主要是由于波浪方程中对耗散项的近似表达引起,也可以由此解释低频波浪波面升高的误差由来,即耗散项的近似表达影响了辐射应力的计算精度,因而影响低频波浪的波面升高。为了更精确的模拟波浪破碎后的低频波波面升高和能量,除了短波平均模型外,我们还采用了短波相位识别模型,即Boussinesq型模型对低频波模型实验进行数值模拟。模型的控制方程采用简化的四阶弱非线性方程和二阶完全非线性方程。
通过与实验结果的对比,分别验证两种模型对低频波浪的模拟效果及精度。虽然波浪平均模型在精确性上不如短波相位识别模型,但是该模型可以单独考虑长波对于近岸输沙的作用,因此,也是本文研究的一个主要内容。而短波相位识别模型的模拟精度更高,且能对短波与低频波浪相互作用进行模拟,有更广泛的适用性。
(4)海底形态的数值模型包括：计算驱动力的水动力模型、计算输沙通量的泥沙模型以及地形变化模型之间的耦合。模型主要采用基于能量考虑的BBB输沙公式及其修正形式；对海岸变形方程的数值求解采用了由Long推导的Euler-WENO格式。
(5)将波浪平均模型应用于海岸演变的数值模拟。将其与近岸输沙和海岸变形方程相耦合,对海岸地形的演变进行了数值模拟。模拟结果与实验结果的对比表明：该模型可以模拟出海岸侵蚀,但不能较好的模拟初始直线型斜坡上近岸沙坝的产生过程。模拟内容包括波群及不规则波作用下的沙坝离岸运动过程,讨论了短波、长波和平均水流共同作用及单独作用下的沙坝运动情况。
(6)将短波相位识别模型应用于海岸演变的数值模拟。将其与输沙和海岸变形模型相耦合,对规则波、波群和不规则波作用下沙坝的产生和运动进行了数值模拟,并与实验结果进行了验证。结果表明：在不同波浪作用下沙坝的产生位置的计算结果和实验结果吻合良好；沙坝的产生主要是由于波浪破碎及其所产生的海底回流所引起的,海底回流所导致的输沙率在空间梯度上的变化是沙坝产生运动的主因。该模型对于预测海岸侵蚀以及沙坝离岸运动能达到很好的结果,并且能够实现对次级沙坝的模拟。
Sandbar is one of the important features of nearshore beach profile. In the nearshore area, the existence of sandbar will make waves break and reduce the erosion of coast beach which is produced by waves and currents. It has an important protective effect for the coast. But so far, the production mechanism of sandbar and its migration is still not clear. In recent years, the sandbar's generation and evolution mechanism has become an important topic in the research of coastal engineering. It has an important significance for preventing coastal area from erosion and siltation. The present study invesgates the generation and evolution of sandbar through a series of physical experiments model and numerical simulations. The main content includes:
(1) A series of physical model experiments were conducted in a wave flume to investigate sandbar movements under various wave conditions. Wave groups, regular and random waves were considered. It was observed that under certain wave conditions sand bars move alternately onshore and offshore, rather than in a single direction. Analysis further shows that the sandbar migration does not seem to be a passive response of the sea bed to wave forcing, but is most likely caused by the feedback interaction between wave and bed topography. A simple theoretical analysis based on linear instability concept is presented which qualitatively establishes that the observed oscillsating movement of a sandbar is a type of instability of sea bed profile.
(2) A series of laboratory experiments were also conducted for the reflection of two wave groups over beach slopes of1:20,1:40,1:60,1:80,1:90,1:100,1:120,1:140and1:160in order to study the characteristics of infragravity waves(LFW). The relation between the number of the reflected LFW and the period of incident wave groups and beach slope is studied and an index for the number of the reflected LFW is introduced for the description of the generation mechanism of LFW on different beach slopes. The experimental results also show that the time intervals between two successive reflected LFW crests and troughs are almost equal to the period of incident wave groups.
(3) Numerical simulations of the observed propagation of LFW in the experiment are also made by using a short wave averaged model and a phase-resolving wave. For the former model, TVD numerical scheme is used to treat the wave breaking of LFW. For the latter model, the simplified version of the fourth-order weakly nonlinear equations and the fourth-order fully nonlinear equations are employed. Eddy Viscosity wave breaking model is included in the model. It is found that by appropriately choosing the model coefficients, agreement with experimental results can be obtained, and the phase-resolving wave model acts better than wave averaged model after wave breaks. The phase-resolving model was also used to simulate some beaches which are not included in experiments,in order to examine the relationship between the number of the reflected LFW and beach slopes.
(4) A numerical model is developed to simulate beach profile changes under different wave conditions. The model consists of wave model, sediment transport rate and profile evolution model. The wave model includes wave-averaged model and Phase-resolving model respectively. The Euler-WENO scheme and instantaneous Bagnold transportation formula are employs in sediment transport model and profile evolution model.
(5) Sediment transport and profile evolution models are coupled with wave-averaged model in order to computing beach profile evolution under waves action. The model is validated against data from laboratory experiments, and the results show that the model can simulate the erosion prossess of beach, but is not efficient for the sandbar formation. The simulation of the sandbar offshore movement under irregular wave actions is also considered, and the effects of waves and mean currents to sandbar migration are invesgated.
(6) Phase-resolving model is used to predict on-off shore sandbar migration in the coastal region. The wave module is based on the BouN2D4equations, which possesses good dispersion, shoaling and fully nonlinearity characteristics and could take many wave phenomena into account, including wave diffraction, wave refraction and wave breaking. The output of this wave model serves as the input to the sediment transport model. With application of this model, the sandbar formation and evolution can be predicted under different wave actions. It is shown that, undertow which casuses strongh spatial gradient of sediment transport rate, has the most important effect on sandbar generation and evolution. The resulting coupled model can successfully predict beach erosion and sandbar offshore migration.
引文
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