Energy dissipation through wind-generated breaking waves

Wave breaking is an important process that controls turbulence properties and fluxes of heat and mass in the upper oceanic layer.A model is described for energy dissipation per unit area at the ocean surface attributed to wind-generated breaking waves,in terms of ratio of energy dissipation to energy input,windgenerated wave spectrum,and wave growth rate.Also advanced is a vertical distribution model of turbulent kinetic energy,based on an exponential distribution method.The result shows that energy dissipation rate depends heavily on wind speed and sea state.Our results agree well with predictions of previous works.     

A VOF-based numerical model for breaking waves in surf zone

This paper introduces a numerical model for studying the evolution of a periodic wave train, shoaling, and breaking in surf zone. The model can solve the Reynolds averaged Navier-Stokes (RANS) equations for a mean flow, and (he k-s equations for turbulence kinetic energy k and turbulence dissipation rate e. To track a free surface, the volume of fluid (VOF) function, satisfying the advection equation was introduced. In the numerical treatment, third-order upwind difference scheme was applied to the convection terms of the RANS equations in order to reduce the effect of numerical viscosity. The shoaling and breaking processes of a periodic wave train on gently sloping beaches were modeled. The computed wave heights of a sloping beach and the distribution of breaking wave pressure on a vertical wall were compared with laboratory data.     

Wave breaking on turbulent energy budget in the ocean surface mixed layer

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）.     

Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model’s capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model’s breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.     

A mechanism of the effect of non-uniform current on the spectrum of short wind waves

A mechanism is suggested in this paper concerning the effect of non-uniform current on the spectrum of short wind waves. According to this mechanism, a non-uniform current brings changes to the breaking criteria of short wind waves through modulating the surface drift, and hence enhances or weakens wave breaking. Some modification is proposed to the source term, which represents the spectral rate of wave energy dissipation due to wave breaking so that the source term can incorporate this mechanism. In order to illustrate whether this mechanism is significant, a real case is studied, in which the wind waves propagate on a tidal current flowing over the sea bottom covered with sand waves. Finally, the effect of the new mechanism on the equilibrium spectrum of small scale gravity waves is discussed. Numerical estimates suggest that, for water depths less than 50 m and wavelengths less than 1 m, this current field may result in distinct spatial variations of the wave breaking criteria, the spectral rate of wave energy dissipation and the equilibrium spectrum of short gravity waves.     

Hydrodynamic conditions in front of a vertical wall with an overhanging horizontal cantilever slab

Transforming wave heights from offshore to the shoreline is the first step of any coastal engineering work. Wave breaking is analyzed to understand hydrodynamic conditions. For vertical breakwaters and sea walls, wave reflection is an important process that affects the determination of the wave height. Many of the design formulas presented in the literature depend on empirical studies based on the structures tested. In this study, the hydrodynamic conditions in front of a vertical wall with an overhanging horizontal cantilever slab with a foreshore slope of 1/20 are determined experimentally under regular wave conditions to assess the applicability of the formulas of Goda (2000) for predicting the nearshore wave height and breaker index equation (Goda, 2010). The selection of wave measurements used to determine the design wave height, the reflection coefficients, and wave breaking is also analyzed, and the reflection equations are derived from the dataset covering different breaker types. Small-scale tests show that the incident wave height is a good representative of the design wave height and that the values predicted by Goda are in good agreement with actual measurements. However, the predicted H_max values are overestimated. In addition, the inception of the wave breaking point is postponed because of the reflection and/or turbulence left over from preceding waves, which is an effect of the vertical wall. At higher water levels, the effect of the vertical wall on the inception point becomes more significant.     

Calculation of significant wave height using the linear mean square estimation method

Significant wave height is an important criterion in designing coastal and offshore structures. Based on the orthogonality principle, the linear mean square estimation method is applied to calculate significant wave height in this paper. Twenty-eight-year time series of wave data collected from three ocean buoys near San Francisco along the California coast are analyzed. It is proved theoretically that the computation error will be reduced by using as many measured data as possible for the calculation of significant wave height. Measured significant wave height at one buoy location is compared with the calculated value based on the data from two other adjacent buoys. The results indicate that the linear mean square estimation method can be well applied to the calculation and prediction of significant wave height in coastal regions.     

Numerical Study of the Secondary Circulations in Rip Current Systems

To investigate the mechanism of secondary circulations in rip current systems, and to explore the relationship between wave conditions and secondary circulation intensity, a series of numerical experiments is performed using coupled nearshore wave model and circulation model. In these experiments, the rip currents and secondary circulations generated above barred beaches with rip channels are simulated. A comparison experiment is conducted to investigate the formation and hydrodynamics of the secondary circulations. Model results indicate that the secondary circulations consist of alongshore flows driven by wave set-up near the shoreline, part of the feeder currents driven by the wave set-up over the bars, and onshore flows at the end of the rip channel driven by wave breaking and convection. The existence of the secondary circulation barely affects the rip current, but narrows and intensifies the feeder currents. Three groups of experiments of varying incident wave conditions are performed to investigate the relationship between wave conditions and secondary circulation intensity. The velocity of the alongshore flow of the secondary circulation is sensitive to the variation of the incident wave height and water depth. It is also found that the alongshore flow intensity is in direct proportion to the alongshore variation of the wave height gradient between the bars and the shoreline.     

Laboratory Experiments on an Internal Solitary Wave over a Triangular Barrier

Laboratory experiments were conducted to investigate the evolution of interfacial internal solitary waves(ISWs) incident on a triangular barrier. ISWs with different amplitudes were generated by gravitational collapse. The ISW energy dissipation and turbulence processes were calculated as waves passed over the triangular barrier. Experimental results showed that ISWs were reflecting back off the triangular barrier, and shoaling ISWs led to wave breaking and mixing when waves propagated over the obstacle. Wave instability created the dissipation of energy as it was transmitted from waves to turbulence. The rate of ISW energy dissipation, the maximum turbulent dissipation, and the buoyancy diffusivity linearly increased with the increase in the incident wave energy.     

A THIRD GENERATION SHALLOW WATER WAVE NUMERICAL MODEL-YE-WAM

This paper pnesents a third gneration shallow Whter disode spedtal wave nbotal medeIYE-WAM based on the spedtal action balance equation. The mode accounts for all edevan effectsof currents on waves, incuding tmpotally and spatialy varying depth and current inded refraction,sttalning and fequency shift and also explidtly takeS into aanunt all source terms, speclally adePth-limited breaking dheipation. In addition, an energy forcing scheme is propond and applied to themode's open boundaries to areUn for the propagution of sedIs into the study spstem The upwinddiffeIenng scheme and a standard hybrid diffdrencing scheme for the propagaion terrn and a simpleEuler method for the source teme are employed.     

Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations.The model is first tested by the additional experimental data,and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated.Then,the model's breaking index is replaced and tested.The new breaking index,which is optimized from the several breaking i...     

Numerical simulation and preliminary analysis of typhoon waves during three typhoons in the Yellow Sea and East China Sea

In this study, typhoon waves generated during three typhoons(Damrey(1210), Fung-wong(1416), and Chan-hom(1509)) in the Yellow Sea and East China Sea were simulated in a simulating waves nearshore(SWAN) model, and the wind forcing was constructed by combining reanalyzed wind data with a Holland typhoon wind model. Various parameters, such as the Holland fitting parameter(B) and the maximum wind radius(R), were investigated in sensitivity experiments in the Holland model that affect the wind field construction. Six different formulations were considered and the parameters determined by comparing the simulated wind results with in-situ wind measurements. The key factors affecting wave growth and dissipation processes from deep to shallow waters were studied, including wind input, whitecapping, and bottom friction. Comparison with in-situ wave measurements suggested that the KOMEN scheme(wind input exponential growth and whitecapping energy dissipation) and the JONSWAP scheme(dissipation of bottom friction) resulted in good reproduction of the significant wave height of typhoon waves. A preliminary analysis of the wave characteristics in terms of wind-sea and swell wave revealed that swell waves dominated with the distance of R to the eye of the typhoon, while wind-sea prevailed in the outer region up to six to eight times the R values despite a clear misalignment between wind and waves. The results support the hypothesis that nonlinear wave-wave interactions may play a key role in the formation of wave characteristics.     

Numerical Study of Storm Surge Inundation in the Southwestern Hangzhou Bay Region During Typhoon Chan-Hom in 2015

Storm surge inundation is a major concern in marine hazard risk assessment during extreme weather conditions.In this study,a high-resolution coupled model(the ADVanced CIRCulation model+the Simulating WAves Nearshore model)was used to investigate the storm surge inundation in the southwestern Hangzhou Bay region during Typhoon Chan-hom in 2015.The simulated hydrodynamic processes(sea surface wave and storm tide)were validated with measured data from wave buoys and tide gauges,indicating that the overall performance of the model was satisfactory.The storm surge inundation in the coastal area was simulated for several idealized control experiments,including different wave effects(wave-enhanced wind stress,wave-enhanced bottom stress,and wave radiation stress).Dike overflowing cases with different dike heights and dike breaking cases with different dike breach lengths were considered in the simulation.The results highlight the necessity of incorporating wave effects in the accurate simulation of storm surge inundation.Dike height significantly influences the magnitude and phase of the maximum inundation area in the dike overflowing cases,and dike breach length is an important factor impacting the magnitude of the maximum inundation area in the dike breaking cases.This study may serve as a useful reference for accurate coastal inundation simulation and risk assessment.     

Beach Morphology and Coastline Evolution in the Southern Bohai Strait

The beach studied in this paper spans a length of 51 km and is one of several long sandy beaches in the southern Bohai Strait. Due to the obstruction of islands in the northeast and the influence of the underwater topography, the wave environment in the offshore area is complex; beach types and sediment transport characteristics vary along different coasts. The coastlines extracted from six aerial photographs in different years were compared to demonstrate the evolving features. Seven typical beach profiles were selected to study the lateral beach variation characteristics. Continuous wind and wave observation data from Beihuangcheng ocean station during 2009 were employed for the hindcast of the local wave environment using a regional spectral wave model. Then the results of the wave hindcast were incorporated into the LITDRIFT model to compute the sediment transport rates and directions along the coasts and analyze the longshore sand movement. The results show that the coastline evolution of sand beaches in the southern Bohai Strait has spatial and temporal variations and the coast can be divided into four typical regions. Region(I), the north coast of Qimudao, is a slightly eroded and dissipative beach with a large sediment transport rate; Region(II), the southwest coast of Gangluan Port, is a slightly deposited and dissipative beach with moderate sediment transport rate; Region(III), in the central area, is a beach that is gradually transformed from a slightly eroded dissipative beach to a moderately or slightly strong eroded bar-trough beach from west to east with a relatively moderate sediment transport rate. Region(IV), on the east coast, is a strongly eroded and reflective beach with a weak sediment transport rate. The wave conditions exhibit an increasing trend from west to east in the offshore area. The distribution of the wave-induced current inside the wave breaking region and the littoral sediment transport in the nearshore region exhibit a gradual weakening tendency from west to east, which is opposite to the trend of the wave conditions outside the breaking region. The presence of submerged shoal(Dengzhou Shoal), deep trough(Dengzhou Channel), islands and irregular topography influnces the wave climate, beach types, wave-induced current features, littoral sediment transport trends and coastline evolution patterns in the southern Bohai Strait. Human activities, such as the sand exploitation of Dengzhou Shoal and other coastal engineering projects, also influence the beach morphology and coastline evolution.     

Effects of wind input and wave dissipation formulations on the steady Ekman current solution

The effects of different wind input and wave dissipation formulations on the steady Ekman current solution are described. Two formulations are considered： one from the wave modeling （WAM） program proposed by Hasselmann and Komen and the other provided by Tsagareli and Babanin. The solution adopted for our study was presented by Song for the wave-modified Ekman current model that included the Stokes drift, wind input, and wave dissipation with eddy viscosity increasing linearly with depth. Using the Combi spectrum with tail effects, the solutions are calculated using two formulations for wind input and wave dissipation, and compared. Differences in the results are not negligible. Furthermore, the solution presented by Song and Xu for the eddy viscosity formulated using the K-Profile Parameterization scheme under wind input and wave dissipation given by Tsagareli and Babanin is compared with that obtained for a depth-dependent eddy viscosity. The solutions are further compared with the available well-known observational data. The result indicates that the Tsagareli and Babanin scheme is more suitable for use in the model when capillary waves are included, and the solution calculated using the K-Profile Parameterization scheme agrees best with observations.     

Long-term variation of storm surge-associated waves in the Bohai Sea

When investigating the long-term variation of wave characteristics as associated with storm surges in the Bohai Sea, the Simulating Waves Nearshore(SWAN) model and ADvanced CIRCulation(ADCIRC) model were coupled to simulate 32 storm surges between 1985 and 2014. This simulation was validated by reproducing three actual wave processes, showing that the simulated significant wave height(SWH) and mean wave period agreed well with the actual measurements. In addition, the long-term variations in SWH, patterns in SWH extremes along the Bohai Sea coast, the 100-year return period SWH extreme distribution, and waves conditional probability distribution were calculated and analyzed. We find that the trend of SWH extremes in most of the coastal stations was negative, among which the largest trend was-0.03 m/a in the western part of Liaodong Bay. From the 100-year return period of the SWH distribution calculated in the Gumbel method, we find that the SWH extremes associated with storm surges decreased gradually from the center of the Bohai Sea to the coast. In addition, the joint probability of wave and surge for the entire Bohai Sea in 100-year return period was determined by the Gumbel logistic method. We therefore, assuming a minimum surge of one meter across the entire Bohai Sea, obtained the spatial SWH distribution. The conclusions of this study are significant for offshore and coastal engineering design.     

Investigation of wave characteristics in a semi-enclosed bay based on SWAN model validated with buoys and ADP-observed currents

In this study, the simulating waves nearshore(SWAN) model with a locally refined curvilinear grid system was constructed to simulate waves in Jervis Bay and the neighbouring ocean of Australia, with the aim of examining the wave characteristics in an area with special topography and practical importance.This model was verified by field observations from buoys and acoustic Doppler profilers(ADPs). The model precisions were validated for both wind-generated waves and open-ocean swells. We present an approach with which to convert ADP-observed current data from near the bottom into the significant wave height. Our approach is deduced from the Fourier transform technique and the linear wave theory. The results illustrate that the location of the bay entrance is important because it allows the swells in the dominant direction to propagate into the bay despite the narrowness of the bay entrance. The wave period T p is also strongly related to the wave direction in the semi-enclosed bay. The T p is great enough along the entire propagating direction from the bay entrance to the top of the bay, and the largest T p appears along the north-west coast,which is the end tip of the swells' propagation.