More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact render...More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact renders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabilistic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks if the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4. Then the JONSWAP spectrum is used to represent the fetch limited sea waves in deep water, so as to relate the probability of wave breaking and the whitecap coverage with wind parameters. To this end, the time averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.展开更多
A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and ...A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point. The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direc- tion. The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress. An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy. The wave driver model is a phase-averaged wave model based on the wave action balance equation. Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach am used to evaluate the model＇s performance. The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.展开更多
As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer (OSML). When breaking waves occur at the ocean surface, turbulent kineti...As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer (OSML). When breaking waves occur at the ocean surface, turbulent kinetic energy (TKE) is input downwards, and a sublayer is formed near the surface and turbulence vertical mixing is intensively enhanced. A one-dimensional ocean model including the Mellor-Yamada level 2.5 turbulence closure equations was employed in our research on variations in turbulent energy budget within OSML. The influence of wave breaking could be introduced into the model by modifying an existing surface boundary condition of the TKE equation and specifying its input. The vertical diffusion and dissipation of TKE were effectively enhanced in the sublayer when wave breaking was considered. Turbulent energy dissipated in the sublayer was about 92.0% of the total depth-integrated dissipated TKE, which is twice higher than that of non-wave breaking. The shear production of TKE decreased by 3.5% because the mean flow fields tended to be uniform due to wave-enhanced turbulent mixing. As a result, a new local equilibrium between diffusion and dissipation of TKE was reached in the wave-enhanced layer. Below the sublayer, the local equilibrium between shear production and dissipation of TKE agreed with the conclusion drawn from the classical law-of-the-wall (Craig and Banner, 1994).展开更多
In this paper, the solitary wave deformation along a gentle slope and the impact pressure, on the wall are investigated experimentally and the results are compared with numerical results obtained based on the volume o...In this paper, the solitary wave deformation along a gentle slope and the impact pressure, on the wall are investigated experimentally and the results are compared with numerical results obtained based on the volume of fluid (VOF) method. The topography used in the experiment consists of three segments. The left segment is a 1:4 slope, the middle segment 1 :SO slope and the right segment a horizontal bed. Both the wave heights and breaking points obtained from numerical simulation and experiments are in good agreement. Numerical results give reasonable pressure distributions of breaking waves on the wall.展开更多
Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally's analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution...Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally's analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.展开更多
The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index, AI = Hm...The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index, AI = Hmas/Hs, being used to characterize the freak waves, and the changes of the coefficient due to wave breaking. The results show that the occurrence probability of freak wave events in non-breaking waves is much larger than that in bleaking waves and such occurrence in deep water is larger than that in shallow water.展开更多
This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine...This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine the eddy viscosity in the Boussinesq equations. To calculate the turbulence production term in the equation, a new formula is derived based on the concept of surface roller. By use of this formula, the turbulence production in the one-equation turbulence scheme is directly related to the difference between the water particle velocity and the wave celerity. The model is verified by Hansen and Svendsen's experimental data (1979) in terms of wave height and setup and setdown. The comparison between the model and experimental results of wave height and setup and setdown shows satisfactory agreement. The modeled turbulence energy decreases as waves attenuate in the surf zone. The modeled production term peaks at the breaking point and decreases as waves propagate shoreward. It is also suggested that both convection and diffusion play their important roles in the transport of turbulence energy immediately after wave breaking. When waves approach to the shoreline, the production and dissipation of turbulence energy are almost balanced. By use of the slot technique for the simulation of the movable shoreline boundary, wave runup in the swash zone is well simulated by the present model.展开更多
A numerical wave tank is used to investigate the onset and strength of unforced wave breaking, and the waves have three types of initial spectra： constant amplitude spectrum, constant steepness spectrum and Pierson-M...A numerical wave tank is used to investigate the onset and strength of unforced wave breaking, and the waves have three types of initial spectra： constant amplitude spectrum, constant steepness spectrum and Pierson-Moscowitz spectrum. Numerical tests are performed to validate the model results. Then, the onset of wave breaking is discussed with geometric, kinematic, and dynamic breaking criteria. The strength of wave breaking, which is always characterized by the fractional energy loss and breaking strength coefficient, is studied for different spectra. The results show how the energy growth rate is better than the initial wave steepness on estimating the fractional energy losses as well as breaking strength coefficient.展开更多
The features of large-scale circulation, storm tracks and the dynamical relationship between them were examined by investigating Rossby wave breaking （RWB） processes associated with Eastern Pacific （EP） and Centra...The features of large-scale circulation, storm tracks and the dynamical relationship between them were examined by investigating Rossby wave breaking （RWB） processes associated with Eastern Pacific （EP） and Central Pacific （CP） E1-Nifio. During EP E1-Nino, the geopotential height anomaly at 500 hPa （Z500） exhibits a Pacific-North America （PNA） pattern. During CP EI-Nifio, the Z500 anomaly shows a north positive-south negative pattern over the North Pacific. The anomalous distributions of baroclinicity and storm track are consistent with those of upper-level zonal wind for both EP and CP EI-Nino, suggesting impacts of mean flow on storm track variability. Anticyclonic wave breaking （AWB） oczurs less frequently in EP EI-Nino years, while cyclonic wave breaking （CWB） occurs more frequently in CP EI-Nino years over the North Pacific sector. Outside the North Pacific, more CWB events occur over North America during EP Ei-NiNo. When AWB events occur less frequently over the North Pacific during EP EI-Nino, Z500 decreases locally and the zonal wind is strengthened （weakened） to the south （north）. This is because AWB events reflect a monopoie high anomaly at the centroid of breaking events. When CWB events occur more frequently over the North Pacific under CP EI-Nino conditions, and over North America under EP EI-Nino condition, Z500 increases （decreases） to the northeast （southwest）, since CWB events are related to a northeast-southwest dipole Z500 anomaly. The anomalous RWB events act to invigorate and reinforce the circulation anomalies over the North Pacific-North America region linked with the two types of EI-Nino.展开更多
Regular wave deformation and breaking on very gentle slopes is calculated by Mixed-Eulerian-Lagrangian procedure. The velocity potentials and their normal derivatives on the boundary are calculated through the mixed 0...Regular wave deformation and breaking on very gentle slopes is calculated by Mixed-Eulerian-Lagrangian procedure. The velocity potentials and their normal derivatives on the boundary are calculated through the mixed 0-1 boundary element method. The wave elevation and the potentials of Lime-stepping integration are determined by the 2nd-order Taylor expansion at the nodes of free surface boundary elements. During calculation the x-coordinates of the free surface element nodes are supposed to remain unchanged, i.e. the partial derivatives of wave elevation and potentials with respect to x are considered as zero. The numerical results of asymmetric parameters of breaking waves are verified by experimental study. It is shown that when the wave asymmetry is weak, the maximum horizontal velocity of water particales occurs at the wave peak and, the average ratio of this maximum velocity to wave celerity is 0.96. However, when the wave asymmetry is strong, the maximum horizontal velocity of water particles occurs just before the wave crest, and the average ratio of the maximum velocity to wave celerity is about 0.98. The numerical results also show that the asymmetry of wave profiles affects the value of the wave breaking index (H/d) (b), that is, when the asymmetric characteristics are weak, the value of wave breaking index coincides with that given by Goda; on the contrary, when the asymmetry of wave profiles is notable, the value of wave breaking index is close to Nelson's result. The experimental study gives the same conclusions.展开更多
The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions （MTF） of radar was investigated based on Bragg resonance theory and parametric method. The...The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions （MTF） of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic （e.m.） wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.展开更多
The role of wave breaking(WB) in the ocean dynamics in the Bohai Sea,China under typhoon condition is systematically investigated utilizing a coupled wave-current model.The influences of WB on ocean dynamics and proce...The role of wave breaking(WB) in the ocean dynamics in the Bohai Sea,China under typhoon condition is systematically investigated utilizing a coupled wave-current model.The influences of WB on ocean dynamics and processes(mixing coefficient,temperature,mixed layer depth,and current) during the entire typhoon period(including the pre-typhoon,during-typhoon and after-typhoon stages) are comprehensively detected and discussed.Experimental results show that WB greatly enhances the turbulent mixing at about top 10 m depth under typhoon condition,the increase can be up to 10 times that of the normal weather.At the same time,WB generally strengthens the sea surface cooling by ~1.2°C at the during-typhoon stage,about 3 times that in normal weather.The mixed layer depth,is rapidly increased by ~1.6–3.6 m during typhoon due to WB,particularly,the deepening is stronger in the region from 120.5°E to 121.0°E on account of close to the typhoon eye.In addition,WB renders the current speed more uniformly within the entire depth in the Bohai Sea,the change in speed is ~0.2 m/s,whereas the alternation in current vector is generally opposite to the wind direction except for the typhoon eye region,reflecting that WB has an inhibitory effect on the typhoon-forced current change.The effects of WB on vertical mixing coefficient response to the typhoon rapidly,while the impacts of WB on temperature,and mixed layer depth present hysteretic responses to typhoon.Finally,the mechanisms and distribution characteristics of WB-induced mixing and tidal mixing are compared under typhoon condition.展开更多
The model for whitecap coverage and wave breaking probability are parameterized by the dimensionless wind fetch X^-. This paper aims at replacing X^- with other parameters such as the average wave period T^-, wind spe...The model for whitecap coverage and wave breaking probability are parameterized by the dimensionless wind fetch X^-. This paper aims at replacing X^- with other parameters such as the average wave period T^-, wind speed U10 or wave age ξ in order to improve the suitability and convenience of the model for application. First, W and B are expressed in terms of T^- and U10, which are relatively easy to measure in the field. Further, U10 is replaced with the friction velocity U. by use of the empirical relationship. As wave age has been widely used to parameterize spectral models of ocean waves and air-sea fluxes, W and B are then expressed as a simple function of wave age, respectively. The new forms of the model obtained are W= 1 - Ф（3.02ξ0＂76） and B = exp（ - 4.54ξ^1.52） . The two forms are mere applicable in pracrice, since ξ is relatively easy to measure or determine from wave and wind records. Comparisons between these expressions and data collected from published literature are made and agreement is fairly good.展开更多
The influence of wave breaking on wave statistics for finite-depth random wave trains is investigated experimentally. This paper is to investigate the influence of wave breaking and water depth on the wave statistics ...The influence of wave breaking on wave statistics for finite-depth random wave trains is investigated experimentally. This paper is to investigate the influence of wave breaking and water depth on the wave statistics for random waves on water of finite depth. Greater attention is paid to changes in wave statistics due to wave breaking in random wave trains. The results show skewness of surface elevations is independent of wave breaking and kurtosis is suppressed by wave breaking. Finally, the exceedance probabilities for wave heights are also investigated.展开更多
Using the limit surface slope as a criterion of wave breaking, a simple model for estimating the spatial fraction of breaking surface of sea at an instant, which is regarded as the whitecap coverge in this paper, is a...Using the limit surface slope as a criterion of wave breaking, a simple model for estimating the spatial fraction of breaking surface of sea at an instant, which is regarded as the whitecap coverge in this paper, is analytically derived from the probability density of surface slope based on Gaussian statistics. The resulting fraction is found depending on the fourth moment of wave spectum, m(4), as well as the critical threshold of surface slope. By expressing the fourth moment in terms of the Neumann spectrum, a formula linking the fraction and wind speed for fully developed sea states is obtianed. Another formula relating the fraction to both wind speed and fetch (or duration) is achieved by expressing m, in terms of the Krylov spectrum and applying the empirical relationships used in the SMB ocean wave predicting technique. A comparison between these results and the field data of whitecap coverage collected by Monahan and O'Muircheartuigh shows an encouraging agreement.展开更多
Wavelet transform is a particularly useful tool to characterize transient phenomena such as wave breaking. In this paper, we apply wavelet transform to the detection and quantification of the breaking waves, We use a ...Wavelet transform is a particularly useful tool to characterize transient phenomena such as wave breaking. In this paper, we apply wavelet transform to the detection and quantification of the breaking waves, We use a new method that uses the local properties of wavelet transform to detect and quantify the breaking waves and give some new breaking criteria. By comparing this method with the classic method, we find that wavelet transform is very effective in the detection of breaking waves. With wavelet transform, a set of measured wind wave data is investigated. The results have revealed some previously unknown phenomena about wave breaking.展开更多
A one-dimensional mixed-layer model, including a Mellor- Yamada level 2.5 turbulence closure scheme, was implemented to investi- gate the dynamical and thermal structures of the ocean surface mixed layer in the northe...A one-dimensional mixed-layer model, including a Mellor- Yamada level 2.5 turbulence closure scheme, was implemented to investi- gate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic ener- gy released through wave breaking was incorporated into the model as a source of energy at the ocean surface, and the influence of the breaking waves on the mixed layer was studied. The numerical simulations show that the simulated SST is overestimated in summer without the breaking waves. However, the cooler SST is simulated when the effect of the breaking waves is considered, the corre- sponding discrepancy with the observed data decreases up to 20% and the MLD calculated averagely deepens 3.8 m. Owing to the wave-enhanced turbulence mixing in the summertime, the stratification at the bottom of the mixed layer was modified and the tempera- ture gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.展开更多
Bow wave breaking is a common phenomenon during ship navigation,especially at a high speed,involving complex physical mechanism such as interface mixing,air entrainment,and jet splashing.This study uses the delayed de...Bow wave breaking is a common phenomenon during ship navigation,especially at a high speed,involving complex physical mechanism such as interface mixing,air entrainment,and jet splashing.This study uses the delayed detached eddy simulation(DDES)turbulence model on the OpenFOAM platform to simulate flow around a KRISO Container Ship(KCS)model for a Froude number of 0.35,examining trim angles of 0°,0.5°,1°.This paper analyzes the statistical and power spectral density(PSD)characteristics of bow wave heights.The analysis shows root mean square(rms)and mean difference between top and bottom views indicate wave breaking.As the trim angle increases,peaks of rms in the bottom view become much higher than that in the top view,reaching 38%at 1°.PSD analysis reveals that resistance and wave height periods differ by no more than 5%,with small-scale structures like jetting and splashing causing non-dominant periodic and high-frequency wave height variations.展开更多
Ship bow wave breaking is a common phenomenon during navigation,involving complex multi-scale flow interactions.However,the understanding of this intense free surface flow issue is not sufficiently deep,especially reg...Ship bow wave breaking is a common phenomenon during navigation,involving complex multi-scale flow interactions.However,the understanding of this intense free surface flow issue is not sufficiently deep,especially regarding the lack of research on the impact of scale effects on bow wave breaking.This paper focuses on the benchmark ship model KCS and conducts numerical simulations and comparative analyses of bow wave breaking for three model scales under the condition of Fr=0.35.The numerical calculations were performed using the in-house computational fluid dynamics(CFD)solver naoe-FOAM-SJTU,which is developed on the open source platform OpenFOAM.Delayed detached eddy simulation(DDES)method is utilized to calculate the viscous flow field around the ship hull.The present method was validated through measurement data of wave profiles and wake flows obtained from model tests.Flow field results for three different scales,including bow wave profiles,vorticity at various sections,and wake distribution,were presented and analyzed.The results indicate that there is small difference in the bow wave overturning and breaking for the first two occurrences across different scales.However,considerable effects of scale are observed on the temporal and spatial variations of the free surface breaking pattern after the second overturning.The findings of this study can serve as valuable data references for the analysis of scale effects in ship bow wave breaking phenomena.展开更多
An internal solitary wave of elevation in a two-layer density stratified system of an incompressible, viscous and homogeneous fluid was studied. The run-up of a wave of elevation encountering different slopes was inve...An internal solitary wave of elevation in a two-layer density stratified system of an incompressible, viscous and homogeneous fluid was studied. The run-up of a wave of elevation encountering different slopes was investigated numerically based on solving the continuity, Navier-Stokes and convective-diffusion equations within the Boussinesq approximation. The commercial software COMSOL Multiphysics was used to conduct the numerical simulations. For gradual shoals, a bolus formed that transported dense fluid up the shoal. The bolus disappeared when it reached its maximum height on the slope due to the draining of the dense fluid. Various shoal angles were simulated to detect the critical angle above which a bolus does not form. An angle of 30 or less resulted in the formation of a bolus. In addition, the simulations demonstrated that the size of the bolus induced by shallower slopes was larger and that the vertical height traveled by the bolus was insensitive to the slope of the shoal.展开更多
文摘More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact renders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabilistic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks if the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4. Then the JONSWAP spectrum is used to represent the fetch limited sea waves in deep water, so as to relate the probability of wave breaking and the whitecap coverage with wind parameters. To this end, the time averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.
基金supported by the National Natural Science Foundation of China(Grant No.50509007)the Program for New Century Excellent Talents in University of China(Grant No.NCET-07-0255)
文摘A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point. The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direc- tion. The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress. An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy. The wave driver model is a phase-averaged wave model based on the wave action balance equation. Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach am used to evaluate the model＇s performance. The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.
基金Supported by the NSFC (No. 40476008)Knowledge Innovation Programs of the Chinese Academy of Sciences (No. KZCX3-SW-222)the NSFDYS (No. 40425015)
文摘As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer (OSML). When breaking waves occur at the ocean surface, turbulent kinetic energy (TKE) is input downwards, and a sublayer is formed near the surface and turbulence vertical mixing is intensively enhanced. A one-dimensional ocean model including the Mellor-Yamada level 2.5 turbulence closure equations was employed in our research on variations in turbulent energy budget within OSML. The influence of wave breaking could be introduced into the model by modifying an existing surface boundary condition of the TKE equation and specifying its input. The vertical diffusion and dissipation of TKE were effectively enhanced in the sublayer when wave breaking was considered. Turbulent energy dissipated in the sublayer was about 92.0% of the total depth-integrated dissipated TKE, which is twice higher than that of non-wave breaking. The shear production of TKE decreased by 3.5% because the mean flow fields tended to be uniform due to wave-enhanced turbulent mixing. As a result, a new local equilibrium between diffusion and dissipation of TKE was reached in the wave-enhanced layer. Below the sublayer, the local equilibrium between shear production and dissipation of TKE agreed with the conclusion drawn from the classical law-of-the-wall (Craig and Banner, 1994).
文摘In this paper, the solitary wave deformation along a gentle slope and the impact pressure, on the wall are investigated experimentally and the results are compared with numerical results obtained based on the volume of fluid (VOF) method. The topography used in the experiment consists of three segments. The left segment is a 1:4 slope, the middle segment 1 :SO slope and the right segment a horizontal bed. Both the wave heights and breaking points obtained from numerical simulation and experiments are in good agreement. Numerical results give reasonable pressure distributions of breaking waves on the wall.
文摘Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally's analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.
基金supported by the National Natural Science Foundation of China (Grant No.50779004)
文摘The experimental studies of the wave breaking effects on freak wave generation are presented within a finite-depth random wave train in a laboratory wave tank. The main attention is paid to the abnormal index, AI = Hmas/Hs, being used to characterize the freak waves, and the changes of the coefficient due to wave breaking. The results show that the occurrence probability of freak wave events in non-breaking waves is much larger than that in bleaking waves and such occurrence in deep water is larger than that in shallow water.
基金This study was supported by the National Natural Science Foundation of China (Grant No.50479047) and partly by the National Science Fund for Distinguished Young Scholars of China (Estuarine and Coastal Science, Grant No.40225014)
文摘This paper aims to propose an improved numerical model for wave breaking in the nearshore region based on the fully nonlinear form of Boussinesq equations. The model uses the κ equation turbulence scheme to determine the eddy viscosity in the Boussinesq equations. To calculate the turbulence production term in the equation, a new formula is derived based on the concept of surface roller. By use of this formula, the turbulence production in the one-equation turbulence scheme is directly related to the difference between the water particle velocity and the wave celerity. The model is verified by Hansen and Svendsen's experimental data (1979) in terms of wave height and setup and setdown. The comparison between the model and experimental results of wave height and setup and setdown shows satisfactory agreement. The modeled turbulence energy decreases as waves attenuate in the surf zone. The modeled production term peaks at the breaking point and decreases as waves propagate shoreward. It is also suggested that both convection and diffusion play their important roles in the transport of turbulence energy immediately after wave breaking. When waves approach to the shoreline, the production and dissipation of turbulence energy are almost balanced. By use of the slot technique for the simulation of the movable shoreline boundary, wave runup in the swash zone is well simulated by the present model.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.41106019 and 41176016)the Public Science and Technology Research Funds Projects of Ocean(Grant No.201105018)the Scientific Research Fund of the Second Institute of Oceanography,SOA(Grant No.JT1205)
文摘A numerical wave tank is used to investigate the onset and strength of unforced wave breaking, and the waves have three types of initial spectra： constant amplitude spectrum, constant steepness spectrum and Pierson-Moscowitz spectrum. Numerical tests are performed to validate the model results. Then, the onset of wave breaking is discussed with geometric, kinematic, and dynamic breaking criteria. The strength of wave breaking, which is always characterized by the fractional energy loss and breaking strength coefficient, is studied for different spectra. The results show how the energy growth rate is better than the initial wave steepness on estimating the fractional energy losses as well as breaking strength coefficient.
基金jointly supported by the National Natural Science Foundation of China(Grant No.41275068)the Special Fund for Meteorology Research in the Public Interest(Grant No.GYHY201106017)the 973 Program(Grant No.2010CB428504)
文摘The features of large-scale circulation, storm tracks and the dynamical relationship between them were examined by investigating Rossby wave breaking （RWB） processes associated with Eastern Pacific （EP） and Central Pacific （CP） E1-Nifio. During EP E1-Nino, the geopotential height anomaly at 500 hPa （Z500） exhibits a Pacific-North America （PNA） pattern. During CP EI-Nifio, the Z500 anomaly shows a north positive-south negative pattern over the North Pacific. The anomalous distributions of baroclinicity and storm track are consistent with those of upper-level zonal wind for both EP and CP EI-Nino, suggesting impacts of mean flow on storm track variability. Anticyclonic wave breaking （AWB） oczurs less frequently in EP EI-Nino years, while cyclonic wave breaking （CWB） occurs more frequently in CP EI-Nino years over the North Pacific sector. Outside the North Pacific, more CWB events occur over North America during EP Ei-NiNo. When AWB events occur less frequently over the North Pacific during EP EI-Nino, Z500 decreases locally and the zonal wind is strengthened （weakened） to the south （north）. This is because AWB events reflect a monopoie high anomaly at the centroid of breaking events. When CWB events occur more frequently over the North Pacific under CP EI-Nino conditions, and over North America under EP EI-Nino condition, Z500 increases （decreases） to the northeast （southwest）, since CWB events are related to a northeast-southwest dipole Z500 anomaly. The anomalous RWB events act to invigorate and reinforce the circulation anomalies over the North Pacific-North America region linked with the two types of EI-Nino.
基金This project was supported financially by National Natural Science Foundation of China(Grant No.49876026)
文摘Regular wave deformation and breaking on very gentle slopes is calculated by Mixed-Eulerian-Lagrangian procedure. The velocity potentials and their normal derivatives on the boundary are calculated through the mixed 0-1 boundary element method. The wave elevation and the potentials of Lime-stepping integration are determined by the 2nd-order Taylor expansion at the nodes of free surface boundary elements. During calculation the x-coordinates of the free surface element nodes are supposed to remain unchanged, i.e. the partial derivatives of wave elevation and potentials with respect to x are considered as zero. The numerical results of asymmetric parameters of breaking waves are verified by experimental study. It is shown that when the wave asymmetry is weak, the maximum horizontal velocity of water particales occurs at the wave peak and, the average ratio of this maximum velocity to wave celerity is 0.96. However, when the wave asymmetry is strong, the maximum horizontal velocity of water particles occurs just before the wave crest, and the average ratio of the maximum velocity to wave celerity is about 0.98. The numerical results also show that the asymmetry of wave profiles affects the value of the wave breaking index (H/d) (b), that is, when the asymmetric characteristics are weak, the value of wave breaking index coincides with that given by Goda; on the contrary, when the asymmetry of wave profiles is notable, the value of wave breaking index is close to Nelson's result. The experimental study gives the same conclusions.
基金Supported by the High-Tech Research and Development Program of China (863 Program. Nos. 2001AA633070 and 2003AA604040)the National Basic Research Program of China (973 Program, No. 2005CB422307)
文摘The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions （MTF） of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic （e.m.） wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.
基金The Grant from Guangxi Key Laboratory of Marine Environment Change and Disaster in Beibu Gulf under contract No.2021KF03the National Natural Science Foundation of China under contract Nos 42176020 and 42076007+1 种基金the Foundation from Key Laboratory of Marine Environmental Information Technology,Ministry of Natural Resources of China under contract No.2020GKF-0812the Tianjin Natural Science Foundation under contract No.18JCYBJC84900。
文摘The role of wave breaking(WB) in the ocean dynamics in the Bohai Sea,China under typhoon condition is systematically investigated utilizing a coupled wave-current model.The influences of WB on ocean dynamics and processes(mixing coefficient,temperature,mixed layer depth,and current) during the entire typhoon period(including the pre-typhoon,during-typhoon and after-typhoon stages) are comprehensively detected and discussed.Experimental results show that WB greatly enhances the turbulent mixing at about top 10 m depth under typhoon condition,the increase can be up to 10 times that of the normal weather.At the same time,WB generally strengthens the sea surface cooling by ~1.2°C at the during-typhoon stage,about 3 times that in normal weather.The mixed layer depth,is rapidly increased by ~1.6–3.6 m during typhoon due to WB,particularly,the deepening is stronger in the region from 120.5°E to 121.0°E on account of close to the typhoon eye.In addition,WB renders the current speed more uniformly within the entire depth in the Bohai Sea,the change in speed is ~0.2 m/s,whereas the alternation in current vector is generally opposite to the wind direction except for the typhoon eye region,reflecting that WB has an inhibitory effect on the typhoon-forced current change.The effects of WB on vertical mixing coefficient response to the typhoon rapidly,while the impacts of WB on temperature,and mixed layer depth present hysteretic responses to typhoon.Finally,the mechanisms and distribution characteristics of WB-induced mixing and tidal mixing are compared under typhoon condition.
基金This work was financially supported by the National Natural Science Foundation of China (Grant No.50479028)
文摘The model for whitecap coverage and wave breaking probability are parameterized by the dimensionless wind fetch X^-. This paper aims at replacing X^- with other parameters such as the average wave period T^-, wind speed U10 or wave age ξ in order to improve the suitability and convenience of the model for application. First, W and B are expressed in terms of T^- and U10, which are relatively easy to measure in the field. Further, U10 is replaced with the friction velocity U. by use of the empirical relationship. As wave age has been widely used to parameterize spectral models of ocean waves and air-sea fluxes, W and B are then expressed as a simple function of wave age, respectively. The new forms of the model obtained are W= 1 - Ф（3.02ξ0＂76） and B = exp（ - 4.54ξ^1.52） . The two forms are mere applicable in pracrice, since ξ is relatively easy to measure or determine from wave and wind records. Comparisons between these expressions and data collected from published literature are made and agreement is fairly good.
基金Supported by the National Natural Science Foundation of China under Grant No.50579007the National High Technology Research and Development Program of China (863 Program) under Grant No. 2007AA11Z130
文摘The influence of wave breaking on wave statistics for finite-depth random wave trains is investigated experimentally. This paper is to investigate the influence of wave breaking and water depth on the wave statistics for random waves on water of finite depth. Greater attention is paid to changes in wave statistics due to wave breaking in random wave trains. The results show skewness of surface elevations is independent of wave breaking and kurtosis is suppressed by wave breaking. Finally, the exceedance probabilities for wave heights are also investigated.
基金This work was financially supported by the National Science Foundation of China(No.49476270,49706067)
文摘Using the limit surface slope as a criterion of wave breaking, a simple model for estimating the spatial fraction of breaking surface of sea at an instant, which is regarded as the whitecap coverge in this paper, is analytically derived from the probability density of surface slope based on Gaussian statistics. The resulting fraction is found depending on the fourth moment of wave spectum, m(4), as well as the critical threshold of surface slope. By expressing the fourth moment in terms of the Neumann spectrum, a formula linking the fraction and wind speed for fully developed sea states is obtianed. Another formula relating the fraction to both wind speed and fetch (or duration) is achieved by expressing m, in terms of the Krylov spectrum and applying the empirical relationships used in the SMB ocean wave predicting technique. A comparison between these results and the field data of whitecap coverage collected by Monahan and O'Muircheartuigh shows an encouraging agreement.
基金The project supported by the National Natural Science Foundation of China (49476254,49606070) & the National High Technology Research and Development Program of China (863 Program)
文摘Wavelet transform is a particularly useful tool to characterize transient phenomena such as wave breaking. In this paper, we apply wavelet transform to the detection and quantification of the breaking waves, We use a new method that uses the local properties of wavelet transform to detect and quantify the breaking waves and give some new breaking criteria. By comparing this method with the classic method, we find that wavelet transform is very effective in the detection of breaking waves. With wavelet transform, a set of measured wind wave data is investigated. The results have revealed some previously unknown phenomena about wave breaking.
基金supported by the cooperative project of the Chinese Academy of Sciencesthe China National Offshore Oil Corporation+1 种基金the National Natural Science Foundation of China under contract Nos 40376008 and 40476008Open Projects of the Key Laboratory of Physical Oceanography of Ministry of Education of China under contract No.200310.
文摘A one-dimensional mixed-layer model, including a Mellor- Yamada level 2.5 turbulence closure scheme, was implemented to investi- gate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic ener- gy released through wave breaking was incorporated into the model as a source of energy at the ocean surface, and the influence of the breaking waves on the mixed layer was studied. The numerical simulations show that the simulated SST is overestimated in summer without the breaking waves. However, the cooler SST is simulated when the effect of the breaking waves is considered, the corre- sponding discrepancy with the observed data decreases up to 20% and the MLD calculated averagely deepens 3.8 m. Owing to the wave-enhanced turbulence mixing in the summertime, the stratification at the bottom of the mixed layer was modified and the tempera- ture gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.
基金Project supported by the National Natural Science Foundation of China(Grant No.52131102)supported by the Research and Application Demonstration Project of Key Technologies for Safeguarding of Container vessels in Ningbo Zhoushan Port Based on Intelligent Navigation(Grant No.ZJHG-FW-2024-27).
文摘Bow wave breaking is a common phenomenon during ship navigation,especially at a high speed,involving complex physical mechanism such as interface mixing,air entrainment,and jet splashing.This study uses the delayed detached eddy simulation(DDES)turbulence model on the OpenFOAM platform to simulate flow around a KRISO Container Ship(KCS)model for a Froude number of 0.35,examining trim angles of 0°,0.5°,1°.This paper analyzes the statistical and power spectral density(PSD)characteristics of bow wave heights.The analysis shows root mean square(rms)and mean difference between top and bottom views indicate wave breaking.As the trim angle increases,peaks of rms in the bottom view become much higher than that in the top view,reaching 38%at 1°.PSD analysis reveals that resistance and wave height periods differ by no more than 5%,with small-scale structures like jetting and splashing causing non-dominant periodic and high-frequency wave height variations.
基金Project supported by the National Natural Science Foundation of China(Grant No.52131102).
文摘Ship bow wave breaking is a common phenomenon during navigation,involving complex multi-scale flow interactions.However,the understanding of this intense free surface flow issue is not sufficiently deep,especially regarding the lack of research on the impact of scale effects on bow wave breaking.This paper focuses on the benchmark ship model KCS and conducts numerical simulations and comparative analyses of bow wave breaking for three model scales under the condition of Fr=0.35.The numerical calculations were performed using the in-house computational fluid dynamics(CFD)solver naoe-FOAM-SJTU,which is developed on the open source platform OpenFOAM.Delayed detached eddy simulation(DDES)method is utilized to calculate the viscous flow field around the ship hull.The present method was validated through measurement data of wave profiles and wake flows obtained from model tests.Flow field results for three different scales,including bow wave profiles,vorticity at various sections,and wake distribution,were presented and analyzed.The results indicate that there is small difference in the bow wave overturning and breaking for the first two occurrences across different scales.However,considerable effects of scale are observed on the temporal and spatial variations of the free surface breaking pattern after the second overturning.The findings of this study can serve as valuable data references for the analysis of scale effects in ship bow wave breaking phenomena.
文摘An internal solitary wave of elevation in a two-layer density stratified system of an incompressible, viscous and homogeneous fluid was studied. The run-up of a wave of elevation encountering different slopes was investigated numerically based on solving the continuity, Navier-Stokes and convective-diffusion equations within the Boussinesq approximation. The commercial software COMSOL Multiphysics was used to conduct the numerical simulations. For gradual shoals, a bolus formed that transported dense fluid up the shoal. The bolus disappeared when it reached its maximum height on the slope due to the draining of the dense fluid. Various shoal angles were simulated to detect the critical angle above which a bolus does not form. An angle of 30 or less resulted in the formation of a bolus. In addition, the simulations demonstrated that the size of the bolus induced by shallower slopes was larger and that the vertical height traveled by the bolus was insensitive to the slope of the shoal.
