波浪作用下建筑物周围的泥沙冲刷及海床演变
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摘要
本文利用数值方法研究了海上建筑物周围的泥沙冲刷和海床演变，建立了用于模拟建筑物周围海床演变的数值模型。由于直接利用三维模型计算量非常大，为了提高计算速度和节省计算机存储量，本文利用深度平均的二维模型计算波浪场和水流场，并利用在海底边界层内对动量方程进行垂向积分的数值模型计算海底剪切应力。本文中所有的数值方法利用有限元方法实现。
本文提出的数值模型主要用于模拟大尺度建筑物周围的泥沙冲刷情况，所以在计算时必须考虑波浪对建筑物的绕射和反射。在本文中首先分别利用有限元方对缓坡方程和Boussinesq方程进行了数值求解，并在此基础上分别建立了基于缓坡方程和Boussinesq方程的波浪作用下建筑物周围的海床演变数值计算模型。在求解波浪方程时应用了边界处利用解析解拟合和内部边界造波、边界阻尼层消波的方法，避免了利用数值方法近似处理边界条件引起的误差。在求解波浪引起的水流场时利用二维浅水方程，将辐射应力梯度项加入浅水方程中以考虑波浪对水流的影响。计算海底剪切应力时应用波流共同作用模型，而不是纯波浪和纯水流两种情况下的剪切应力的叠加。计算了波浪周期内各个时刻瞬时的悬移质和推移质泥沙输沙率，并对输沙率进行时间平均求得时间平均的输沙率。计算输沙率时考虑了Lagrangian漂移速度和由于波浪边界层不均匀产生的竖向流速的影响，在计算海底地形演变时通过求解用输沙率表示的泥沙质量守恒方程来实现。推导出了利用波面随时间的分布来表示的辐射应力计算公式。对泥沙在斜坡上运动时的临界Shields数进行了修正，并将其应用于本文提出的数值模型中。利用本文数值模型的计算结果与他人的数值结果和试验结果进行了比较。利用数值方法研究了KC数、泥沙粒径和模型比尺对圆柱周围的泥沙冲刷情况的影响。
本文利用物理模型试验对波流共同作用下大尺度圆柱周围的泥沙冲刷进行了研究，研究了在波流作用下不同直径的圆柱周围的泥沙冲刷情况，并建立了用于模拟波流共同作用下建筑物周围的泥沙冲刷的数值模型，将此数值模型的计算结果与物理模型试验中的实测值进行了比较。由于实际工程中水流速度相对波浪水质点速度很小，所以在数值模型中忽略了水流对波浪的影响，而考虑波浪辐射应力对水流的影响。
The local scour and topographical change around offshore structures are studied numerically in this thesis. The numerical models are established for simulating the topographical change around structures. Because the computation using 3D numerical models is time-consuming, the depth-averaged 2D numerical models are applied in the calculation of wave and current fields for saving computer memory and increasing the computing speed. The shear stress at the sea bed is calculated by solving the depth-integrated momentum equation over the thickness of the boundary layer near the bed. The numerical models are implemented by finite element method.
The numerical models proposed in this thesis are applied to simulate the local scour around the large-scale structures and the wave reflection and diffraction around structures can be computed. The finite element models for solving the Mild-slope equation and Boussinesq equations are firstly established in this thesis. The methods of coupling with an analytical solver, inner wave generation and wave absorption using spongy layer are applied to the boundaries in calculation of the wave field for reducing the numerical errors. The wave-induced current is calculated by solving a set of 2D shallow water equations in the horizontal plane. The gradients of radiation stress components are added to the shallow water equations to take into account the affect of waves on current. The combined wave-current models are applied to the calculation of bed shear stress instead of the simple addition of wave and current. The instantaneous sediment transport
of suspended and bed load are computed, and the sediment transport rates are time-averaged over one wave period. The Lagrangian drift velocity and the bed shear stress due to streaming are considered when calculating the suspended sediment transport rate. A conservation equation of sediment mass expressed by time-averaged sediment transport rates is solved for simulating the topographical evolution. Equations expressed by the time series of wave surface elevation for computing the radiation stress components are proposed. The critical shields parameter is modified when the sediment grain moving on a slope beach and the modified shields parameter is applied to the numerical model. The computation results using the models in this thesis are compared with experimental data and other numerical results. The influence of KC number, sediment grain size, and scale affect on process of scour are examinated numerically in this thesis.
The local scour around a large-scale vertical cylinder due to wave and current is studied experimentally and numerically. The scour processes of wave and current acting on cylinders with various diameter are tested. The numerical model for simulating the scour process around large-scale structures due to wave and current is established, and the numerical results are compared to with experimental data. Because the current velocity is smaller than the wave particle velocity in real coastal engineering, the affect of current on waves is neglected in the numerical model, but the affect of radiation stress of waves on current was considered.
本文提出的数值模型主要用于模拟大尺度建筑物周围的泥沙冲刷情况，所以在计算时必须考虑波浪对建筑物的绕射和反射。在本文中首先分别利用有限元方对缓坡方程和Boussinesq方程进行了数值求解，并在此基础上分别建立了基于缓坡方程和Boussinesq方程的波浪作用下建筑物周围的海床演变数值计算模型。在求解波浪方程时应用了边界处利用解析解拟合和内部边界造波、边界阻尼层消波的方法，避免了利用数值方法近似处理边界条件引起的误差。在求解波浪引起的水流场时利用二维浅水方程，将辐射应力梯度项加入浅水方程中以考虑波浪对水流的影响。计算海底剪切应力时应用波流共同作用模型，而不是纯波浪和纯水流两种情况下的剪切应力的叠加。计算了波浪周期内各个时刻瞬时的悬移质和推移质泥沙输沙率，并对输沙率进行时间平均求得时间平均的输沙率。计算输沙率时考虑了Lagrangian漂移速度和由于波浪边界层不均匀产生的竖向流速的影响，在计算海底地形演变时通过求解用输沙率表示的泥沙质量守恒方程来实现。推导出了利用波面随时间的分布来表示的辐射应力计算公式。对泥沙在斜坡上运动时的临界Shields数进行了修正，并将其应用于本文提出的数值模型中。利用本文数值模型的计算结果与他人的数值结果和试验结果进行了比较。利用数值方法研究了KC数、泥沙粒径和模型比尺对圆柱周围的泥沙冲刷情况的影响。
本文利用物理模型试验对波流共同作用下大尺度圆柱周围的泥沙冲刷进行了研究，研究了在波流作用下不同直径的圆柱周围的泥沙冲刷情况，并建立了用于模拟波流共同作用下建筑物周围的泥沙冲刷的数值模型，将此数值模型的计算结果与物理模型试验中的实测值进行了比较。由于实际工程中水流速度相对波浪水质点速度很小，所以在数值模型中忽略了水流对波浪的影响，而考虑波浪辐射应力对水流的影响。
The local scour and topographical change around offshore structures are studied numerically in this thesis. The numerical models are established for simulating the topographical change around structures. Because the computation using 3D numerical models is time-consuming, the depth-averaged 2D numerical models are applied in the calculation of wave and current fields for saving computer memory and increasing the computing speed. The shear stress at the sea bed is calculated by solving the depth-integrated momentum equation over the thickness of the boundary layer near the bed. The numerical models are implemented by finite element method.
The numerical models proposed in this thesis are applied to simulate the local scour around the large-scale structures and the wave reflection and diffraction around structures can be computed. The finite element models for solving the Mild-slope equation and Boussinesq equations are firstly established in this thesis. The methods of coupling with an analytical solver, inner wave generation and wave absorption using spongy layer are applied to the boundaries in calculation of the wave field for reducing the numerical errors. The wave-induced current is calculated by solving a set of 2D shallow water equations in the horizontal plane. The gradients of radiation stress components are added to the shallow water equations to take into account the affect of waves on current. The combined wave-current models are applied to the calculation of bed shear stress instead of the simple addition of wave and current. The instantaneous sediment transport
of suspended and bed load are computed, and the sediment transport rates are time-averaged over one wave period. The Lagrangian drift velocity and the bed shear stress due to streaming are considered when calculating the suspended sediment transport rate. A conservation equation of sediment mass expressed by time-averaged sediment transport rates is solved for simulating the topographical evolution. Equations expressed by the time series of wave surface elevation for computing the radiation stress components are proposed. The critical shields parameter is modified when the sediment grain moving on a slope beach and the modified shields parameter is applied to the numerical model. The computation results using the models in this thesis are compared with experimental data and other numerical results. The influence of KC number, sediment grain size, and scale affect on process of scour are examinated numerically in this thesis.
The local scour around a large-scale vertical cylinder due to wave and current is studied experimentally and numerically. The scour processes of wave and current acting on cylinders with various diameter are tested. The numerical model for simulating the scour process around large-scale structures due to wave and current is established, and the numerical results are compared to with experimental data. Because the current velocity is smaller than the wave particle velocity in real coastal engineering, the affect of current on waves is neglected in the numerical model, but the affect of radiation stress of waves on current was considered.
引文
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2． Keulegan,G.H.,Carpenter,L.H.Forces on cylinders and plates in an oscillating fluid.J.Reseach of the National Bureau of Standards Research Paper,1958,60 (5) : 423-440．
3． Sumer,B.M.,Fredsee,J.Wave scour around structures.Advances in Coastal Ocean Engineering,1999,4: 191-249．
4． Saito,E.,Sato S.,Shibayama T.Local scour around a large circular cylinder due to wave action,Proc.22nd Int.Coastal Engineering Conference,ASCE,Delft,the Netherlands,1990,2: 1795-1804．
5． Sumer,B.M.,Fredsoe J.Scour around a large vertical circular cylinder in waves.16th Int.Conference on Offshore Mechanics and Arctic Engineering,Yokohama,Japan,1997,April 13-18．
6． Katsui H.,Toue T.Bottom stress in coexistent field of superimposed waves and current and scouring around a large-scale circular cylinder,Coastal Engineering in Japan,1992,35 (1) ,93-110
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