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.     

The effect of wave breaking on surface wave imaging by Synthetic Aperture Radar

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.     

The efifect of wave breaking on surface wave imaging by Synthetic Aperture Radar

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.     

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）.     

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.     

Study of long-wave breaking

This paper reports study on the mechanism of long-wave breaking in a one-dimensional open chan-nel,without bottom friction,or with linear bottom friction.In general,the wave breaking phenomenon is related to the notion of"blow-up of solution"and can be studied by using the blow-up theory of par-tial differential equations(PDE).A pair of Riemann invariants are introduced to transform the governingequations into ordinary differential equations(ODE)along the characteristic directions of the governingequations.From the properties of the solutions of the ODE,the time and location of wave breakingare estimated and the criterion of long-wave breaking for the case with linear bottom friction is obtained.     

A COMBINED REFRACTION-DIFFRACTION-DISSIPATION MODEL OF WAVE PROPAGATION

A numerical model based on the mild-slope equation of water wave propagation over complicated bathymetry,taking into account the combined effects of refraction,diffraction and dissipation due to wavebreaking is presented.Wave breaking is simulated by modifying the wave height probability density func-tion and the wave energy dissipation mechanism is parameterized according to that of the hydraulic jumpformulation.Solutions of the wave height,phase function,and the wave direction at every grid point areobtained by finite difference approximation of the governing equations,using Gauss-Seidel Iterative Method(GSIM)row by row.Its computational convenience allows it to be applied to large coast regions tostudy the wave transformation problem.Several case studies have been made and the results compare verywell with the experiment data and other model solutions.The capability and utility of the model forreal coast areas are illustrated by application to a shallow bay of northeast Australia.     

On Long-waves breaking II. in a half infinite channel with bottom slope

The propagation of long-waves, such as tidal waves from the coastal ocean into shallow estuarine waters, often produces asymmetries of velocity and water level in time series resulting in long-wave breaking. Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth, consideringnth power bottom friction. This study is for the case of a half infinite channel with bottom slope, taking linear bottom friction into account. The wave breaking time and wave breaking location are estimated and the criteria for long-wave breaking in this particular case are obtained. The results obtained can also be easily applied to the case considering wind stress.     

Distribution of the nonlinear random ocean wave period

Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (ν=0.3−0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional statistical wave theory.     

STATISTICAL PROPERTIES OF WAVE GROUPS DESCRIBED BY GROUP-INDUCED LONG WAVES

A new method using group-induced second-order long waves (GSLW) to describe wave groups is presented in this paper on the basis of the GSLW theory by Longuet- Higgins and Steward (1964) . In the method , the parabolic relationship between GSLW and the wave envelope is first deduced , and then the distribution function of GSLW amplitude is derived . Thus, the formulae in terms of the moments of GSLW and short wave spectra for the average time duration and the mean length of runs of wave heights exceeding a certain level can be derived . A new groupiness factor equivalent to half the mean wave number in wave groups is defined by taking into account the widths of spectra of GSLW and short waves . Compared with theoretical results of others , ours are closer to measured wave data .     

Statistical distribution of nonlinear random water wave surface elevation

This study deals with the development of statistical modeling for water wave surface elevation by using a method that combines a dynamic solution with random process statistics. Ocean wave data taken from four NOAA (National Oceanic and Atmospheric Administration) buoys moored in the northeast Pacific were used to validate the model. The results indicated that the nonlinear probability density distribution of ocean wave surface elevation derived from the model described the measurements much better than Gaussian distribution and Longuet-Higgins distribution.     

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...     

On long-wave breaking I. Consideringnth power bottom friction

Longwave breaking is the agent for many important upper ocean layer processes including the transfer of horizontal momentum. In a previous study on the process of longwave breaking, only linear bottom friction was considered. In this paper, we discuss the longwave breaking phenomena in the more general case ofnth power bottom friction. Using the theory of blowup of solution, the criterion for the time and location of the longwave breaking can be obtained. Contribution No. 2559 from the Institute of Oceanology, Chinese Academy of Sciences. This project was supported by NSFC (No. 49376254).     

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.     

Crest-height distribution of nonlinear random waves

The wave crest is an important factor for the design of both fixed and floating marine structures. Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage. Many empirical and theoretical distribution functions for wave crest heights have been proposed, but there is a lack of agreement between them. It is of significance to develop a better new nonlinear wave crest height distribution model. The progress in the research of wave crest heights is reviewed in this paper. Based on Stokes’ wave theory, an approximate nonlinear wave crest-height distribution formula with simple parameters is derived. Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail. The new crest-height distribution model agrees well with observations. Also, the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.     

基于R/S分析的碎波带波面标度不变性研究

波浪经破碎、折射、绕射等过程后进入到碎波带,波面已经不再满足经典波浪理论的正态分布假设.利用R/S分析方法对碎波带波面的进行分析,揭示碎波带波面具有标度不变性特征,波面序列具有“记忆性”和持久性,其Hurst指数为0.76,这对建立和解释碎波带波面及波高概率分布有指示意义.进一步分析后指出Hurst指数H和谱尖度参量Qp 及波群参数Ka 呈显著的负相关,Hurst指数有可能作为反映碎波带状态的一个参数.     

A new probability distribution function of wave steepness

Wave steepness is an important characteristic describing the severity of sea state in ocean engineering. In the existing theoretical and experimental studies, wave steepness is often substituted by some related quantities. In this paper, a new probability density function (pdf) of steepness, which is a pdf of the steepness in its original definition, is obtained for narrowband Gaussian processes. The drawback inherent in the previous theoretical pdfs of steepness, that is, the probability density at zero steepness is nonzero, has been eliminated. Laboratory experiments were conducted in a wind-wave flume to measure the wave steepness distribu- tion. Comparisons among laboratory measurements and some theoretical pdfs of steepness show that the new pdf generally fits the data better than the one proposed by Zheng et al. (1999).     

Numerical simulation of 3-D wave crests

1　Introduction　Anefficientwaytostudywaveforceonoffshorestructuresisthroughphysicalandnumericalwavesim ulation .Althoughmanysimulationsof 2 Dregularorirregularwaveshavesuccessfullybeencarriedoutinlaboratorythroughwindandwavegenerator ,itisstillratherdifficulttosimulate 3 Drandomwavesinlabo ratory .Therefore ,numericalsimulationiswidelyusedinsuchstudies (Baietal.,2 0 0 0 ;Zhuetal.,1999) .Tobuildlargeoffshorestructureslikemarineairports ,itisofinteresttostudytheeffectof 3 Dwaves .Goda(1994 …     

A wave modulation model of ripples over long surface waves

A study is presented on the modulation of ripples induced by a long surface wave (LW) and a new theoretical modulation model is proposed. In this model, the wind surface stress modulation is related to the modulation of ripple spectrum. The model results show that in the case of LW propagating in the wind direction with the wave age parameter of LW increasing, the area with enhanced shear stress shifts from the region near the LW crest on the upwind slope to the LW trough. With a smaller wave age parameter of LW, the ripple modulation has the maximum on the upwind slope in the vicinity of LW crest, while with a larger parameter the enhancement of ripple spectrum does not occur in that region. At low winds the amplitude of ripple modulation transfer function (MTF) is larger in the gravity wave range, while at moderate or high winds it changes little in the range from short gravity waves to capillary waves.