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
In this paper, the large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling lead...In this paper, the large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling leads to the increase of wave height, and then at a certain position, the wave will be breaking. The breaking wave is a powerful agent for generating turbulence, which plays an important role in most of the fluid dynamic processes throughout the surf zone, Such as transformation of wave energy, generation of near-shore current and diffusion of materials. So a proper numerical model for describing the turbulence effect is needed. In this paper, a revised Smagorinsky subgrid-scale model is used to describe the turbulence effect. The present study reveals that the coefficient of the Smagorinsky model for wave propagation or breaking simulation may be taken as a varying function of the water depth and distance away from the wave breaking point. The large eddy simulation model presented in this paper has been used to study the propagation of the solitary wave in constant water depth and the shoaling of the non-breaking solitary wave on a beach. The model is based on large eddy simulation, and to track free-surface movements, the Tokyo University Modified Marker and Cell (TUMMAC) method is employed. In order to ensure the accuracy of each component of this wave mathematical model, several steps have been taken to verify calculated solutions; with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a constant depth and on a beach. Application of the model to cnoidal wave breaking in the surf zone shows that the model results are in good agreement with analytical solution and experimental data. From the present model results, it can be seen that the turbulent eddy viscosity increases from the bottom to the water surface in surf zone. In the eddy viscosity curve, there is a turn-point obviously, dividing water depth into two parts, in the upper part, the eddy viscosity becomes very large near the wave breaking position.展开更多
The purpose of this paper is to extend the validity of Li's parabolic model (1994) by incorporating a combined energy factor in the mild-slope equation and by improving the traditional radiation boundary condition...The purpose of this paper is to extend the validity of Li's parabolic model (1994) by incorporating a combined energy factor in the mild-slope equation and by improving the traditional radiation boundary conditions. With wave breaking and energy dissipation expressed in a direct form in the equation, the proposed model could provide an efficient numerical scheme and accurate predictions of wave transformation across the surf zone. The radiation boundary conditions are iterated in the model without use of approximations. The numerical predictions for wave height distributions across the surf zone are compared with experimental data over typical beach profiles. In addition, tests of waves scattering around a circular pile show that the proposed model could also provide reasonable improvement on the radiation boundary conditions for large incident angles of waves.展开更多
The wave characteristics affecting coastal sediment transport include wave height, wave period and breaking wave direction. Wave height is a critical factor in determining the amount of sediment transport in the coast...The wave characteristics affecting coastal sediment transport include wave height, wave period and breaking wave direction. Wave height is a critical factor in determining the amount of sediment transport in the coastal area. The force of sediment transport is much more intense under breaking waves than under non-breaking waves. Breaking waves exhibit various patterns, principal- ly depending on the incident wave steepness and the beach slope. Based on the equations of con- servation of mass, momentum and energy, a theoretical model for wave deformation in and outside the surf zone was obtained, which is used to calculate the wave shoaling, wave set-up and set- down and wave height distributions in and outside the surf zone. The analysis and comparison were made about the breaking point location and the wave height decay caused by the wave breaking and the bottom friction. Flume experiments relating to the spilling wave height distribution across the surf zone were conducted to verify the theoretical model. Advanced wave maker, data sampling de- vices and data processing system were utilized in the flume experiments with a slope covered by sands of different diameters to facilitate the observation and research on the wave transformation and breaking. The agreement between the theoretical and experimental results is good.展开更多
The experiments on pollutant movement in surf zone were conducted on the two gentle beaches(with slope of 1:100 and 1:40, respectively), for diverse wave cases. The movement contours and direction of pollutants, under...The experiments on pollutant movement in surf zone were conducted on the two gentle beaches(with slope of 1:100 and 1:40, respectively), for diverse wave cases. The movement contours and direction of pollutants, under the action of regular and random waves with diverse wave amplitudes, were provided and studied in this paper. It was shown that, due to complicated hydrodynamics in surf zone, the pollutant movement state is quite complicated and different from that in pure current zone.展开更多
The effects of surf zone eddy generated by alongshore currents on the deformation and transport of dye are still poorly understood,and related tracer release experiments are lacking.Therefore,a tracer release laborato...The effects of surf zone eddy generated by alongshore currents on the deformation and transport of dye are still poorly understood,and related tracer release experiments are lacking.Therefore,a tracer release laboratory experiment was conducted under monochromatic,unidirectional incident waves with a large incident angle(30°)on a plane beach with a 1:100 slope in a large wave basin.A charge-coupled device suspended above the basin recorded the dye patch image.The evolution of eddy dye patch was observed and the transport and diffusion were analyzed based on the collected images.Subsequently,a linear instability numerical model was adopted to calculate the perturbation velocity field at the initial stage.The observation and image processing results show that surf zone eddy patches occurred and were separated from the original dye patches.Our numerical analysis results demonstrate that the structure of the perturbation velocity field is consistent with the experimental observations,and that the ejection of eddy patches shoreward or offshore may be ascribed to the double vortex.展开更多
In this paper, the distribution characteristics of the breaking wave current and suspended load transport in the surf zone are discussed in main. Based on the measured data of the waves, the form of breaking wave, the...In this paper, the distribution characteristics of the breaking wave current and suspended load transport in the surf zone are discussed in main. Based on the measured data of the waves, the form of breaking wave, the breaking wave current and the sediment concentration of suspended load in the offshore surf zone near Nouakchott, the Islamic Republic of Mauritania, the author has analized the law governing the distribution of longshore current and sediment concentration of suspended load by means of statistical method, and presented a calculation method for the longshore sediment transport in offshore surf zone.展开更多
This study examines the effects of Stokes drift on pollutant transport within the surf zone on a plane beach both numerically and experimentally. Firstly, the numerical model is described. The wave-induced current is ...This study examines the effects of Stokes drift on pollutant transport within the surf zone on a plane beach both numerically and experimentally. Firstly, the numerical model is described. The wave-induced current is modeled using the concept of the radiation stress. The wave propagation model is based on the wave energy conservation equation. And the advective diffusion model including the Stokes drift is used to describe the pollutant transport in the surf zone. Model validation was achieved in this case versus an analytical solution for an instantaneous point source in a uniform horizontal flow. This study also describes a laboratory experiment on dye release in the surf zone over a plane beach. We examined the final inclination angle required by a continuously released pollutant plume to reach the shoreline under both cases, and transport velocities in the alongshore and cross- shore directions were estimated by linearly fitting the location of a dye-patch front at different time. Results show that this dye patch moved shoreward with an approximate speed of 0.05 m/s (0.017 m/s) between 10 s and 40 s and 0.001 m/s (0.011 m/s) after 40 s for Case 1 (2). This model was then used to simulate pollutant transport in the surf zone on a plane beach as reproduced in the current experiment. Comparisons between our dye transport experiment and numerical results were then also conducted;the data showed that the numerical results including Stokes drift agreed more closely with experimental results than those without it. The data showed that the pollutant was generally transported obviously shoreward in addition to its expected drift along the shore. We also suggest that Stokes drift plays an important role in pollutant movement in the surf zone, especially shoreward.展开更多
Time-averaged suspended sediment concentration profiles across the surf zone were measured in a large-scale three-dimensional movable bed laboratory facility (LSTF:Large-scale Sediment Transport Facility). Sediment su...Time-averaged suspended sediment concentration profiles across the surf zone were measured in a large-scale three-dimensional movable bed laboratory facility (LSTF:Large-scale Sediment Transport Facility). Sediment suspension under two different types of breaking waves, spilling and plunging breakers, was investigated. The magnitudes and shapes of the concentration profiles varied substantially at different locations across the surf zone, reflecting the different intensities of breaking-induced turbulence. Sediment sus- pension at the energetic plunging breaker-line was much more active, resulting in nearly homogeneous concentration profiles throughout most of the water column, as compared to the reminder of the surf zone and at the spilling breaker-line. Four suspended sediment concentration models were examined based on the LSTF data, including the mixing turbulence length approach, segment eddy viscosity model, breaking-induced wave-energy dissipation approach, and a combined breaking and turbulence length model developed by this study. Neglecting the breaking-induced turbulence and subsequent sediment mixing, suspended sediment concentration models failed to predict the across-shore variations of the sediment suspension, especially at the plunging breaker-line. Wave-energy dissipation rate provided an accurate method for estimating the intensity of turbulence generated by wave breaking. By incorporating the breaking-induced turbulence, the combined breaking and turbulence length model reproduced the across-shore variation of sediment suspension in the surf zone. The combined model reproduced the measured time-averaged suspended sediment concentration profiles reasonably well across the surf zone.展开更多
Surf-zone hydrodynamics forced by oblique wave shoaling and breaking on beach slopes were investigated.The results showed that in wave-basin experiments with incident angles in the range of 15°-30°,wave brea...Surf-zone hydrodynamics forced by oblique wave shoaling and breaking on beach slopes were investigated.The results showed that in wave-basin experiments with incident angles in the range of 15°-30°,wave breaking was initiated at a breaker coefficient of around 0.67,which was significantly less than that predicted from empirical relations based on normally incident waves for a given beach slope and deep-water wave steepness.The measurements also showed that subsequent saturated breaking occurred at a breaker coefficient of around 0.47 that was inde-pendent of beach slope in the range of 1∶10 to 1∶100.This result is likely applicable to both oblique and normally incident waves.It is shown that the measured wave heights and longshore velocity profiles in wave-basin studies can be reasonably well predicted by theory with proper ad-justments to the process parameters.Best-match formulations were identified for quantifying bottom friction,eddy viscosity,and energy loss due to surface rollers.展开更多
A nonlinear short-wave-averaged (surf beat) model is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the so-called weighted-averaged flux (WAF) ...A nonlinear short-wave-averaged (surf beat) model is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the so-called weighted-averaged flux (WAF) method (eg Watson et al., 1992), with time-operator splitting used for the treatment of some of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modelling breaking long waves. The short-wave (or primary-wave) energy equation is solved using a more traditional Lax-Wendroff technique. Results of validation indicate that the model performs satisfactorily in most respects.展开更多
When waves propagate from deep water to shallow water, wave heights and steepness increase and then waves roll back and break. This phenomenon is called surf. Currently, the present statistical calculation model of su...When waves propagate from deep water to shallow water, wave heights and steepness increase and then waves roll back and break. This phenomenon is called surf. Currently, the present statistical calculation model of surf was derived mainly from the wave energy conservation equation and the linear wave dispersion relation, but it cannot reflect accurately the process which is a rapid increasing in wave height near the broken point. So, the concept of a surf breaking critical zone is presented. And the nearshore is divided as deep water zone, shallow water zone, surf breaking critical zone and after breaking zone. Besides, the calculation formula for the height of the surf breaking critical zone has founded based on flume experiments, thereby a new statistical calculation model on the surf has been established. Using the new model, the calculation error of wave height maximum is reduced from 17.62% to 6.43%.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This research project was supported by the National Natural Science Foundation of China and The Hong Kong Research Grants under contracts No. 59809006 and No. 59890200, also by the Science Foundation of Tianjin Municipality under contract No. 9837020
文摘In this paper, the large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling leads to the increase of wave height, and then at a certain position, the wave will be breaking. The breaking wave is a powerful agent for generating turbulence, which plays an important role in most of the fluid dynamic processes throughout the surf zone, Such as transformation of wave energy, generation of near-shore current and diffusion of materials. So a proper numerical model for describing the turbulence effect is needed. In this paper, a revised Smagorinsky subgrid-scale model is used to describe the turbulence effect. The present study reveals that the coefficient of the Smagorinsky model for wave propagation or breaking simulation may be taken as a varying function of the water depth and distance away from the wave breaking point. The large eddy simulation model presented in this paper has been used to study the propagation of the solitary wave in constant water depth and the shoaling of the non-breaking solitary wave on a beach. The model is based on large eddy simulation, and to track free-surface movements, the Tokyo University Modified Marker and Cell (TUMMAC) method is employed. In order to ensure the accuracy of each component of this wave mathematical model, several steps have been taken to verify calculated solutions; with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a constant depth and on a beach. Application of the model to cnoidal wave breaking in the surf zone shows that the model results are in good agreement with analytical solution and experimental data. From the present model results, it can be seen that the turbulent eddy viscosity increases from the bottom to the water surface in surf zone. In the eddy viscosity curve, there is a turn-point obviously, dividing water depth into two parts, in the upper part, the eddy viscosity becomes very large near the wave breaking position.
基金This research is supported by the National Science Council of Taiwan under the grant of NSC 86-2611-E-006-019.
文摘The purpose of this paper is to extend the validity of Li's parabolic model (1994) by incorporating a combined energy factor in the mild-slope equation and by improving the traditional radiation boundary conditions. With wave breaking and energy dissipation expressed in a direct form in the equation, the proposed model could provide an efficient numerical scheme and accurate predictions of wave transformation across the surf zone. The radiation boundary conditions are iterated in the model without use of approximations. The numerical predictions for wave height distributions across the surf zone are compared with experimental data over typical beach profiles. In addition, tests of waves scattering around a circular pile show that the proposed model could also provide reasonable improvement on the radiation boundary conditions for large incident angles of waves.
基金Supported by Doctoral Fund of Education Ministry of China ( No. 20010056033) , National Natural Science Foundation of China(No. 10202003, No. 50479015) ,and National Science Fund for Distinguished Young Scholars(No. 03QMH1408).
文摘The wave characteristics affecting coastal sediment transport include wave height, wave period and breaking wave direction. Wave height is a critical factor in determining the amount of sediment transport in the coastal area. The force of sediment transport is much more intense under breaking waves than under non-breaking waves. Breaking waves exhibit various patterns, principal- ly depending on the incident wave steepness and the beach slope. Based on the equations of con- servation of mass, momentum and energy, a theoretical model for wave deformation in and outside the surf zone was obtained, which is used to calculate the wave shoaling, wave set-up and set- down and wave height distributions in and outside the surf zone. The analysis and comparison were made about the breaking point location and the wave height decay caused by the wave breaking and the bottom friction. Flume experiments relating to the spilling wave height distribution across the surf zone were conducted to verify the theoretical model. Advanced wave maker, data sampling de- vices and data processing system were utilized in the flume experiments with a slope covered by sands of different diameters to facilitate the observation and research on the wave transformation and breaking. The agreement between the theoretical and experimental results is good.
文摘The experiments on pollutant movement in surf zone were conducted on the two gentle beaches(with slope of 1:100 and 1:40, respectively), for diverse wave cases. The movement contours and direction of pollutants, under the action of regular and random waves with diverse wave amplitudes, were provided and studied in this paper. It was shown that, due to complicated hydrodynamics in surf zone, the pollutant movement state is quite complicated and different from that in pure current zone.
基金The open foundation of the State Key Laboratory of Hydraulic Engineering Simulation and Safety under contract No.HESS-2006the Shanxi Province Science Foundation under contract No.202103021224116the research project supported by Shanxi Scholarship Council of China under contract No.2023-067.
文摘The effects of surf zone eddy generated by alongshore currents on the deformation and transport of dye are still poorly understood,and related tracer release experiments are lacking.Therefore,a tracer release laboratory experiment was conducted under monochromatic,unidirectional incident waves with a large incident angle(30°)on a plane beach with a 1:100 slope in a large wave basin.A charge-coupled device suspended above the basin recorded the dye patch image.The evolution of eddy dye patch was observed and the transport and diffusion were analyzed based on the collected images.Subsequently,a linear instability numerical model was adopted to calculate the perturbation velocity field at the initial stage.The observation and image processing results show that surf zone eddy patches occurred and were separated from the original dye patches.Our numerical analysis results demonstrate that the structure of the perturbation velocity field is consistent with the experimental observations,and that the ejection of eddy patches shoreward or offshore may be ascribed to the double vortex.
文摘In this paper, the distribution characteristics of the breaking wave current and suspended load transport in the surf zone are discussed in main. Based on the measured data of the waves, the form of breaking wave, the breaking wave current and the sediment concentration of suspended load in the offshore surf zone near Nouakchott, the Islamic Republic of Mauritania, the author has analized the law governing the distribution of longshore current and sediment concentration of suspended load by means of statistical method, and presented a calculation method for the longshore sediment transport in offshore surf zone.
基金The Open Foundation of the State Key Laboratory of Hydraulic Engineering Simulation and Safety under contract No.HESS-1406the National Science Foundation for Post-doctoral Scientists of China under contract No.2013M541179the Foundation of Taiyuan University of Technology under contract No.2017MS07
文摘This study examines the effects of Stokes drift on pollutant transport within the surf zone on a plane beach both numerically and experimentally. Firstly, the numerical model is described. The wave-induced current is modeled using the concept of the radiation stress. The wave propagation model is based on the wave energy conservation equation. And the advective diffusion model including the Stokes drift is used to describe the pollutant transport in the surf zone. Model validation was achieved in this case versus an analytical solution for an instantaneous point source in a uniform horizontal flow. This study also describes a laboratory experiment on dye release in the surf zone over a plane beach. We examined the final inclination angle required by a continuously released pollutant plume to reach the shoreline under both cases, and transport velocities in the alongshore and cross- shore directions were estimated by linearly fitting the location of a dye-patch front at different time. Results show that this dye patch moved shoreward with an approximate speed of 0.05 m/s (0.017 m/s) between 10 s and 40 s and 0.001 m/s (0.011 m/s) after 40 s for Case 1 (2). This model was then used to simulate pollutant transport in the surf zone on a plane beach as reproduced in the current experiment. Comparisons between our dye transport experiment and numerical results were then also conducted;the data showed that the numerical results including Stokes drift agreed more closely with experimental results than those without it. The data showed that the pollutant was generally transported obviously shoreward in addition to its expected drift along the shore. We also suggest that Stokes drift plays an important role in pollutant movement in the surf zone, especially shoreward.
基金funded by the U.S.Army Engineer Research and Development Center and the Louisiana Sea Grant College Program
文摘Time-averaged suspended sediment concentration profiles across the surf zone were measured in a large-scale three-dimensional movable bed laboratory facility (LSTF:Large-scale Sediment Transport Facility). Sediment suspension under two different types of breaking waves, spilling and plunging breakers, was investigated. The magnitudes and shapes of the concentration profiles varied substantially at different locations across the surf zone, reflecting the different intensities of breaking-induced turbulence. Sediment sus- pension at the energetic plunging breaker-line was much more active, resulting in nearly homogeneous concentration profiles throughout most of the water column, as compared to the reminder of the surf zone and at the spilling breaker-line. Four suspended sediment concentration models were examined based on the LSTF data, including the mixing turbulence length approach, segment eddy viscosity model, breaking-induced wave-energy dissipation approach, and a combined breaking and turbulence length model developed by this study. Neglecting the breaking-induced turbulence and subsequent sediment mixing, suspended sediment concentration models failed to predict the across-shore variations of the sediment suspension, especially at the plunging breaker-line. Wave-energy dissipation rate provided an accurate method for estimating the intensity of turbulence generated by wave breaking. By incorporating the breaking-induced turbulence, the combined breaking and turbulence length model reproduced the across-shore variation of sediment suspension in the surf zone. The combined model reproduced the measured time-averaged suspended sediment concentration profiles reasonably well across the surf zone.
文摘Surf-zone hydrodynamics forced by oblique wave shoaling and breaking on beach slopes were investigated.The results showed that in wave-basin experiments with incident angles in the range of 15°-30°,wave breaking was initiated at a breaker coefficient of around 0.67,which was significantly less than that predicted from empirical relations based on normally incident waves for a given beach slope and deep-water wave steepness.The measurements also showed that subsequent saturated breaking occurred at a breaker coefficient of around 0.47 that was inde-pendent of beach slope in the range of 1∶10 to 1∶100.This result is likely applicable to both oblique and normally incident waves.It is shown that the measured wave heights and longshore velocity profiles in wave-basin studies can be reasonably well predicted by theory with proper ad-justments to the process parameters.Best-match formulations were identified for quantifying bottom friction,eddy viscosity,and energy loss due to surface rollers.
文摘A nonlinear short-wave-averaged (surf beat) model is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the so-called weighted-averaged flux (WAF) method (eg Watson et al., 1992), with time-operator splitting used for the treatment of some of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modelling breaking long waves. The short-wave (or primary-wave) energy equation is solved using a more traditional Lax-Wendroff technique. Results of validation indicate that the model performs satisfactorily in most respects.
基金The National Natural Science Foundation of China under contract Nos 41076048 and 40906044
文摘When waves propagate from deep water to shallow water, wave heights and steepness increase and then waves roll back and break. This phenomenon is called surf. Currently, the present statistical calculation model of surf was derived mainly from the wave energy conservation equation and the linear wave dispersion relation, but it cannot reflect accurately the process which is a rapid increasing in wave height near the broken point. So, the concept of a surf breaking critical zone is presented. And the nearshore is divided as deep water zone, shallow water zone, surf breaking critical zone and after breaking zone. Besides, the calculation formula for the height of the surf breaking critical zone has founded based on flume experiments, thereby a new statistical calculation model on the surf has been established. Using the new model, the calculation error of wave height maximum is reduced from 17.62% to 6.43%.
