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 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.     

The Equilibrium Range of Wind Wave Spectra： an Explanation Based on White Noise

Laboratory experiments and field observations show that the equilibrium range of wind wave spectra presents a – 4 power law when it is scaled properly. This feature has been attributed to energy balance in spectral space by many researchers. In this paper we point out that white noise on an oscillation system can also lead to a similar inverse power law in the corresponding displacement spectrum, implying that the – 4 power law for the equilibrium range of wind wave spectra may probably only reflect the randomicity of the wind waves rather than any other dynamical processes in physical space. This explanation may shed light on the mechanism of other physical processes with spectra also showing an inverse power law, such as isotropic turbulence, internal waves, etc.     

Study on the growth of wind wave frequency spectra generated by cold waves in the northern East China Sea

The growth of frequency spectra and spectral parameters of wind waves generated by cold waves, a kind of severe weather system, in the northern East China Sea is studied in this paper. Based on a third-generation wave action model(the Simulating WAves Nearshore model), simulations were developed to analyze the spatiotemporal characteristics of wind waves and to output spectral data. It is shown that the cold wave-induced spectra can be well described by the modified Joint North Sea Wave Project spectral form. The growth of wave spectra is comprehensively reflected by the evolution of the three characteristic parameters: peak frequency, spectral peak and wave energy. Besides, the approximations of dependences between spectral parameters and the three types of universal induced factors are obtained with the least squares method and compared systematically. Fetch and peak frequency turn out to be suitable parameters to describe the spectral parameters, while the dependences on the inverse wave age vary in different sea areas. In general, the derived relationships improve on results from previous studies for better practical application of the wind wave frequency spectrum in the northern East China Sea.     

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 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.     

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 oceam into shallow estuarine waters,often produces asymmetries of veolcity 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,considering nth power bottom friction. This study is for the case of a half infinite channel with bottomslope, taking linear bottom friction into account. The wave breaking time and wave breaking location areestimated and the criteria for long-wave breaking in this particular case are obtained. The results obtainedcan also be e asily applied to the case considering wind stress.     

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.     

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.     

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.     

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.     

Directional Spectrum of Wind Waves: Part Ⅰ- Model and Derivation

1　Introduction　Numerousinvestigationsondeepwaterwindwavespectrumhavebeen performed (Phillips ,195 8;Bretschneider,195 9;PiersonandMoscowitz ,196 4;Hasselmannetal.,1973;Donelanetal.,1985 ;Ban ner ,1990 ;Wenetal.,1999) .Ondimensionalground ,Phillips (195 8)suggestedthattheequilibriumfre quencyspectrumofwindwavesfordeepwatershouldbe proportionaltoω- 5,andthecorrespondingwavenumberspectrumshouldbe proportionaltok- 4,whereωistheangularfrequencyandkisthewavenumber.Forfully developedwindwaves…     

Directional spectrum of wind waves: Part I—model and derivation

A new model on the directional spectrum of wind waves for deep water is proposed based on the statistics of wind waves. This model contains three parameters: the wave age, the inverse spectral bandwidth and the local spectral-peak angular frequency. The inverse spectral bandwidth is a robust parameter for describing the spectral steepness of wind waves. Using the inverse spectral bandwidth parameter, the proposed model can well describe various observations obtained from the open ocean and laboratory tank.     

WIND WAVES SIMULATION IN THE NORTH AREA OF THE SOUTH CHINA SEA

A third generation wave model was developed to simulate wind waves in the South China Sea near Hong Kong. The model solves the energy conservation equation of the two dimensional wave spectrum by directly computing the nonlinear energy interaction among waves of different frequencies, thus avoiding the imposition of restrictions on the shape of the predicted spectra. The use of an upwind difference scheme in the advective terms produces an artificial diffusion which partly compensates the dispersive effect due to the phase velocity differences among various wave components. The use of a semi-implicit scheme for the source terms together with a special treatment of the high frequency tail of the spectrum allows a large time integration step. Verification of the model was done for wave hindcasting studies under conditions of two typhoons and two cold fronts in the north part of the South China Sea near Hong Kong . The model results agree well with the field measurements except that the presence of a dista     

Interaction of Waves, Surface Currents, and Turbulence： the Application of Surface-Following Coordinate Systems

Surface waves comprise an important aspect of the interaction between the atmosphere and the ocean, so a dynamically consistent framework for modelling atmosphere-ocean interaction must take account of surface waves, either implicitly or explicitly. In order to calculate the effect of wind forcing on waves and currents, and vice versa, it is necessary to employ a consistent formula- tion of the energy and momentum balance within the airflow, wave field, and water column. It is very advantageous to apply sur- face-following coordinate systems, whereby the steep gradients in mean flow properties near the air-water interface in the cross-interface direction may be resolved over distances which are much smaller than the height of the waves themselves. We may account for the waves explicitly by employing a numerical spectral wave model, and applying a suitable theory of wave–mean flow interaction. If the mean flow is small compared with the wave phase speed, perturbation expansions of the hydrodynamic equations in a Lagrangian or generalized Lagrangian mean framework are useful: for stronger flows, such as for wind blowing over waves, the presence of critical levels where the mean flow velocity is equal to the wave phase speed necessitates the application of more general types of surface-following coordinate system. The interaction of the flow of air and water and associated differences in temperature and the concentration of various substances (such as gas species) gives rise to a complex boundary-layer structure at a wide range of vertical scales, from the sub-millimetre scales of gaseous diffusion, to several tens of metres for the turbulent Ekman layer. The bal- ance of momentum, heat, and mass is also affected significantly by breaking waves, which act to increase the effective area of the surface for mass transfer, and increase turbulent diffusive fluxes via the conversion of wave energy to turbulent kinetic energy.     

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.     

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.     

Observation of near-inertial internal waves on the continental slope in the northwestern South China Sea

Based on nearly 3 months of moored acoustic Doppler current profiler records on the continental slope in the northwestern South China Sea(SCS) in 2006,this study examines temporal and vertical characteristics of near-inertial internal waves(NIW).Rotary frequency spectrum indicates that motions in the near-inertial frequency are strongly polarized,with clockwise(CW) energy exceeding counterclockwise(CCW) by about a factor of 10.Wavelet analysis exhibits an energy peak exceeding the 95% confidence level at the frequency of local inertial during the passage of typhoon Xangsane(24 September to 4 October).This elevated near-inertial kinetic energy(NIKE) event possesses about a 4 days delay correlation with the time integral of energy flux induced by typhoon,indicating an energy source of wind.Further analysis shows that the upward phase velocity of this event is 3.8 m h~(-1)approximately,corresponding to a vertical wavelength of about 125 m if not taking the redshift of local inertial frequency into account.Rotary vertical wavenumber spectrum exhibits the dominance of clockwise-with-depth energy,indicating downward energy propagation and implying a surface energy source.Dynamical modes suggest that mode 1 plays a dominant role at the growth stage of NIW,whereas major contribution is from higher modes during the penetration of NIKE into the ocean interior.     

Nonlinear wave-wave interactions and wedge waves

A tetrad mechanism for exciting long waves, for example edge waves, is described based on nonlinear resonant wave-wave interactions. In this mechanism, resonant interactions pass energy to an edge wave,from the three participating gravity waves. The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms, such as triad interactions. Moreover, the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two- to three- orders of magnitude greater than bottom friction.     

Distribution of vertical turbulent mixing parameter caused by internal tidal waves and solitary waves in the South Yellow Sea

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.