Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pr...Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and the gradient of horizontal current velocity. A shear stress boundary condition at the wave trough level derived from the momentum balance equation combined with a no-slip condition at the sea bed were applied to solve the vertical structure of undertow. The turbulent eddy viscosity was assumed to be relevant to the breaking energy dissipation and linearly distributed over depth. The wave characteristics as inputs for the present model were obtained by solving an extended wave energy balance equation incorporating the surface roller effect. Numerical results showed generally good agreements with three series of experimental data for various bathymetries and wave conditions. Comparisons indicated that the formula proposed in this paper for the shear stress at wave trough level could reasonably improve the modeled undertow profiles especially outside the surf zone and a little distance shoreward of the breaking point, and revealed that the model performs well in simulating both vertical and horizontal distributions of undertow and is capable of providing hydrodynamic forcing for the cross-shore sediment transport.展开更多
A process-based 3D numerical model for surfzone hydrodynamics and beach evolution was established. Comparisons between the experimental data and model results proved that the model could effectively describe the hydro...A process-based 3D numerical model for surfzone hydrodynamics and beach evolution was established. Comparisons between the experimental data and model results proved that the model could effectively describe the hydrodynamics, sediment transport feature and sandbar migration process in the surfzone with satisfactory precision. A series of numerical simulations on the wave breaking and shoaling up to a barred beach were carried out based on the model system. Analyzed from the model results, the wave-induced current system in the surfzone consists of two major processes, which are the phase-averaged undertow caused by wave breaking and the net drift caused by both of the nonlinear wave motion and surface roller effect. When storm waves come to the barred beach, the strong offshore undertow along the beach suppresses the onshore net drift, making the initial sandbar migrate to the seaside. Under the condition of calm wave environment, both the undertow and net drift flow to the shoreline at the offshore side of the sandbar, and then push the initial sandbar to the shoreline. The consideration of surface roller has significant impact on the modeling results of the sandbar migration. As the roller transfer rate increases, the sandbar moves onshore especially under the storm wave condition.展开更多
Wave shapes that induce velocity skewness and acceleration asymmetry are usually responsible for onshore sediment transport, whereas undertow and bottom slope effect normally contribute to offshore sediment transport....Wave shapes that induce velocity skewness and acceleration asymmetry are usually responsible for onshore sediment transport, whereas undertow and bottom slope effect normally contribute to offshore sediment transport. By incorporating these counteracting driving forces in a phase-averaged manner, the theoretically-based quasi-steady formula of Wang (2007) is modified to predict the magnitude and direction of net cross-shore total load transport under the coaction of wave and current. The predictions show an excellent agreement with the measurement data on medium and fine sand collected by Dohmen-Janssen and Hanes (2002) and Schretlen (2012) in a full-scale wave flume at the Coastal Research Centre in Hannover, Germany. The modified formula can predict the net onshore transport of fine sand in sheet flows. In particular, it can predict the net offshore transport of medium sand in rippled beds through enlarged bed roughness, as well as the net offshore transport of fine-to-coarse sand in sheet flows with the aid of a new criterion to judge the occurrence of net offshore transport.展开更多
For the simulation of the three-dimensional(3D)nearshore circulation,a 3D hydrodynamic model is developed by taking into account the depth-dependent radiation stresses.Expressions for depth-dependent radiation stres...For the simulation of the three-dimensional(3D)nearshore circulation,a 3D hydrodynamic model is developed by taking into account the depth-dependent radiation stresses.Expressions for depth-dependent radiation stresses in the Cartesian coordinates are introduced on the basis of the linear wave theory,and then vertical variations of depth-dependent radiation stresses are discussed.The 3D hydrodynamic model of ELCIRC(Eulerian-Lagrangian CIRCulation)is extended by adding the terms of the depth-dependent or depth-averaged radiation stresses in the momentum equations.The wave set-up,set-down and undertow are simulated by the extended ELCIRC model based on the wave fields provided by the experiment or the REF/DIF wave model.The simulated results with the depth-dependent and depth-averaged radiation stresses both show good agreement with the experimental data for wave set-up and set-down.The undertow profiles predicted by the model with the depth-dependent radiation stresses are also consistent with the experimental results,while the model with the depth-averaged radiation stresses can not reflect the vertical distribution of undertow.展开更多
A three-dimensional nearshore circulation model was developed by coupling CH3D, a three-dimensional hydrodynamic model and REF/DIF, a nearshore wave transformation model. The model solves the three-dimensional wave-av...A three-dimensional nearshore circulation model was developed by coupling CH3D, a three-dimensional hydrodynamic model and REF/DIF, a nearshore wave transformation model. The model solves the three-dimensional wave-averaged equations of motion. Wave-induced effects on circulation were introduced in the form of radiation stresses, wave-induced mass transport, wave-induced enhancement of bottom friction and wave-induced turbulent mixing. Effects of breaking waves were considered following Svendsen (1984a and 1984b) and Stive and Wind (1986). The model was successfully tested against the analytical solution of longshore currents by Longuet and Higgins (1970). The model successfully simulated the undertow as observed in a laboratory experiment by Stive and Wind (1982). In addition, the model was applied to a physical model by Mory and Hamm (1997) and successfully reproduced the eddy behind a detached breakwater as well as the longshore current on the open beach and the contiguous eddy in the open area of the wave tank. While the qualitative agreement between model results and experimental observations was very good, the quantitative agreement needs to be further improved. Albeit difficult to explain every discrepancy between the model results and observations, in general, sources of errors are attributed to the lack of understanding and comprehensive description of following processes: (1)the horizontal and vertical distribution of radiation stress, especially for breaking waves;(2)the detailed structure of turbulence;(3)Wave-current interaction (not included at this moment); and (4)the wave-current boundary layer and the resulting bottom shear stress.展开更多
By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical so...By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.展开更多
基金The National Natural Science Foundation of China under contract No 50979033the Program for New Century Excellent Talents in University of China No NCET-07-0255the Special Fund of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering under contract No 2009585812
文摘Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and the gradient of horizontal current velocity. A shear stress boundary condition at the wave trough level derived from the momentum balance equation combined with a no-slip condition at the sea bed were applied to solve the vertical structure of undertow. The turbulent eddy viscosity was assumed to be relevant to the breaking energy dissipation and linearly distributed over depth. The wave characteristics as inputs for the present model were obtained by solving an extended wave energy balance equation incorporating the surface roller effect. Numerical results showed generally good agreements with three series of experimental data for various bathymetries and wave conditions. Comparisons indicated that the formula proposed in this paper for the shear stress at wave trough level could reasonably improve the modeled undertow profiles especially outside the surf zone and a little distance shoreward of the breaking point, and revealed that the model performs well in simulating both vertical and horizontal distributions of undertow and is capable of providing hydrodynamic forcing for the cross-shore sediment transport.
基金financially supported by the National Key Research and Development Program of China(Grant No.2016YFC0402603)the National Natural Science Foundation of China(Grant Nos.51779112,51509119,and 51609029)+2 种基金the Project of Tianjin Natural Science Foundation(Grant No.16JCQNJC06900)the Open Project of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering(Grant No.2014492211)the Fundamental Research Funds for the Central Public Welfare Research Institutes(Grant Nos.TKS170101and TKS170202)
文摘A process-based 3D numerical model for surfzone hydrodynamics and beach evolution was established. Comparisons between the experimental data and model results proved that the model could effectively describe the hydrodynamics, sediment transport feature and sandbar migration process in the surfzone with satisfactory precision. A series of numerical simulations on the wave breaking and shoaling up to a barred beach were carried out based on the model system. Analyzed from the model results, the wave-induced current system in the surfzone consists of two major processes, which are the phase-averaged undertow caused by wave breaking and the net drift caused by both of the nonlinear wave motion and surface roller effect. When storm waves come to the barred beach, the strong offshore undertow along the beach suppresses the onshore net drift, making the initial sandbar migrate to the seaside. Under the condition of calm wave environment, both the undertow and net drift flow to the shoreline at the offshore side of the sandbar, and then push the initial sandbar to the shoreline. The consideration of surface roller has significant impact on the modeling results of the sandbar migration. As the roller transfer rate increases, the sandbar moves onshore especially under the storm wave condition.
基金supported by the National Natural Science Foundation of China(Grant No.51179211)
文摘Wave shapes that induce velocity skewness and acceleration asymmetry are usually responsible for onshore sediment transport, whereas undertow and bottom slope effect normally contribute to offshore sediment transport. By incorporating these counteracting driving forces in a phase-averaged manner, the theoretically-based quasi-steady formula of Wang (2007) is modified to predict the magnitude and direction of net cross-shore total load transport under the coaction of wave and current. The predictions show an excellent agreement with the measurement data on medium and fine sand collected by Dohmen-Janssen and Hanes (2002) and Schretlen (2012) in a full-scale wave flume at the Coastal Research Centre in Hannover, Germany. The modified formula can predict the net onshore transport of fine sand in sheet flows. In particular, it can predict the net offshore transport of medium sand in rippled beds through enlarged bed roughness, as well as the net offshore transport of fine-to-coarse sand in sheet flows with the aid of a new criterion to judge the occurrence of net offshore transport.
基金supported bythe National Natural Science Foundation of China(Grant No.50279029)
文摘For the simulation of the three-dimensional(3D)nearshore circulation,a 3D hydrodynamic model is developed by taking into account the depth-dependent radiation stresses.Expressions for depth-dependent radiation stresses in the Cartesian coordinates are introduced on the basis of the linear wave theory,and then vertical variations of depth-dependent radiation stresses are discussed.The 3D hydrodynamic model of ELCIRC(Eulerian-Lagrangian CIRCulation)is extended by adding the terms of the depth-dependent or depth-averaged radiation stresses in the momentum equations.The wave set-up,set-down and undertow are simulated by the extended ELCIRC model based on the wave fields provided by the experiment or the REF/DIF wave model.The simulated results with the depth-dependent and depth-averaged radiation stresses both show good agreement with the experimental data for wave set-up and set-down.The undertow profiles predicted by the model with the depth-dependent radiation stresses are also consistent with the experimental results,while the model with the depth-averaged radiation stresses can not reflect the vertical distribution of undertow.
文摘A three-dimensional nearshore circulation model was developed by coupling CH3D, a three-dimensional hydrodynamic model and REF/DIF, a nearshore wave transformation model. The model solves the three-dimensional wave-averaged equations of motion. Wave-induced effects on circulation were introduced in the form of radiation stresses, wave-induced mass transport, wave-induced enhancement of bottom friction and wave-induced turbulent mixing. Effects of breaking waves were considered following Svendsen (1984a and 1984b) and Stive and Wind (1986). The model was successfully tested against the analytical solution of longshore currents by Longuet and Higgins (1970). The model successfully simulated the undertow as observed in a laboratory experiment by Stive and Wind (1982). In addition, the model was applied to a physical model by Mory and Hamm (1997) and successfully reproduced the eddy behind a detached breakwater as well as the longshore current on the open beach and the contiguous eddy in the open area of the wave tank. While the qualitative agreement between model results and experimental observations was very good, the quantitative agreement needs to be further improved. Albeit difficult to explain every discrepancy between the model results and observations, in general, sources of errors are attributed to the lack of understanding and comprehensive description of following processes: (1)the horizontal and vertical distribution of radiation stress, especially for breaking waves;(2)the detailed structure of turbulence;(3)Wave-current interaction (not included at this moment); and (4)the wave-current boundary layer and the resulting bottom shear stress.
基金financially supported by the the National Natural Science Foundation of China(Grant No.51709054)the Public Science and Technology Research Funds Projects of Ocean(Grant Nos.201405025 and 201505019)
文摘By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.