Research has shown considerable variability in whitecap coverage(W)under low to moderate wind conditions.During an expedition to the Northwestern Pacific,oceanographic variables and photographic measurements were coll...Research has shown considerable variability in whitecap coverage(W)under low to moderate wind conditions.During an expedition to the Northwestern Pacific,oceanographic variables and photographic measurements were collected to investigate the influence of wave-induced stress on W within these wind ranges.The friction velocity was recalculated based on turbulent stress,and wind profiles were modified to account for wave-induced stress and swell presence on the sea surface.The study examined W’s relationship with multiple parameters,including friction velocity(u*),breaking wave Reynolds numbers,wavesea Reynolds numbers,and wave age.The analysis utilized both conventional u*and turbulent stress-based friction velocity(u*turb).When utilizing u*turb rather than u*,the estimation model’s fitting results revealed an increase in correlation coefficient(R2)from 0.51 to 0.62,and a decrease in root mean square error(RMSE)from 0.0652 to 0.0574.Additionally,when parameterizing W using the windsea Reynolds number,with u_(*turb) replacing u*and wind wave height substituting mixed wave height,the R^(2) increased from 0.38 to 0.53,and the RMSE decreased from 0.0737 to 0.0668.The results demonstrate that calculating u*using the turbulent stress-based method,along with wind wave height and peak wave speed of mixed waves,yields stronger correlation with W.This correlation improvement stems from the inhibition of wave breaking by swell and wave-induced stress.The integration of turbulent stress and wind wave field measurements enhances the understanding of relationships between W and various parameters.However,swell effects on wind profiles do not substantially affect W estimation using wind speed-related parameters.展开更多
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
The pro and con of whitecap parameterizations and a statistical wave breaking model are discussed. An improved model is derived by combining satellite-based parameterization and the wave breaking model. The appropriat...The pro and con of whitecap parameterizations and a statistical wave breaking model are discussed. An improved model is derived by combining satellite-based parameterization and the wave breaking model. The appropriate constants for the general wave state are obtained by considering the breaking condition of the wave slope and fitting with the satellite-based parameterization. The result is close to the constants based on the whitecap data from Monahan. Comparing with satellite-based data and the original model＇s results, the improved model＇s results are consistent with satellite-based data and previous studies. The global seasonal distributions of the whitecap coverage averaged from 1998 to 2008 are presented. Spatial and seasonal features of the whitecap coverage are analyzed.展开更多
Sea spray droplets are produced by waves breaking on the sea surface, and they vary the transfer of energy between the atmosphere and ocean. The sea spray generation function(SSGF) is generally considered as a functio...Sea spray droplets are produced by waves breaking on the sea surface, and they vary the transfer of energy between the atmosphere and ocean. The sea spray generation function(SSGF) is generally considered as a function of the initial radius of the spray droplets and the wind speed. However, ocean waves always exist at the air-sea interface, so it is not reasonable to consider only the effect of sea surface winds while ignoring the effects of ocean waves. Whitecap coverage is an important characteristic parameter of breaking waves, and researchers believe that this parameter is related to both wave state and wind speed. In this paper, the SSGF is parameterized by the whitecap coverage, and a new SSGF describing different droplet radii is organically integrated based on the whitecap coverage parameter. Then, with the relationship between the whitecap coverage and wave state, the influence of ocean waves on the SSGF for different wave states was analyzed by using observational data in the laboratory. The results show that the new SSGF that considers wave effects can reasonably describe the droplet generation process under different wave state conditions.展开更多
Whitecapping plays an important role in many air-sea exchange and upper ocean processes.Traditionally,whitecap coverage is parameterized as a function of wind speed only.At present,the relative speed of ocean current ...Whitecapping plays an important role in many air-sea exchange and upper ocean processes.Traditionally,whitecap coverage is parameterized as a function of wind speed only.At present,the relative speed of ocean current to wind is considered to be important in the air-sea exchange parameterization which is the function of wind speed only.In this paper,the effects of ocean surface velocity (current velocity and wave induced velocity) and the wave parameters on whitecap coverage through relative speeds are investigated,by applying a 2-parameter whitecap coverage model to the Atlantic Ocean.It is found that the impacts of both current and wave on whitecap coverage are considerable in the most part of the Atlantic Ocean.It is interesting that the effect of wave is more significant than that of current.展开更多
The shipboard measurements of whitecap coverage(W)and the meteorological and oceanographic information from two cruises in the South China Sea and Western Pacific are explored for estimating W.This study aims at evalu...The shipboard measurements of whitecap coverage(W)and the meteorological and oceanographic information from two cruises in the South China Sea and Western Pacific are explored for estimating W.This study aims at evaluating how to im-prove the parameterizations of W while considering the effects of currents and swells on wave breaking.Currents indeed affect W in a way that winds with following currents can decrease W,whereas winds with opposing currents can increase W.Then,10-m wind speed over sea surface(U_(10))is calibrated by subtracting the current velocity from U_(10) when the propagating directions of winds and currents are aligned.By contrast,when the direction is opposite,U_(10) is calibrated by adding the parallel velocity com-ponent of the opposing current to U_(10).The power fits of W dependence on the U_(10)-related parameters of U_(10),friction velocity,wind sea Reynolds number in terms of this calibrated-U_(10) obtain better results than those directly fitted to U_(10).Different from the effect of currents on W,wind blowing along the crest line of swells may contribute to the increase in W.The conclusions suggest that U_(10) should be calibrated first before parameterizing W in areas with a strong current or some swell-dominant areas.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
Joint probability function of local surfaces-particle and phase velocities is derived for a stationary Gaussianwave field with narrow-band spectrum. From the function a model of whitecap coverage is further derived by...Joint probability function of local surfaces-particle and phase velocities is derived for a stationary Gaussianwave field with narrow-band spectrum. From the function a model of whitecap coverage is further derived by using thekinematic condition (including the effect of drift current) for wave breaking. The drift current velocity in the model isthen replaced by the friction velocity through an existing empirical formula. A coefficient in the model for relating temporal and spatial scales of wave breaking is determined by using an existing empirical formula of oceanic whitecap coverage and the well-known Pierson-Moskowitz spectrum. The main features of the model agree well with our generalknowledge and observational evidence on wave breaking in deep waters.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
基金supported by the National Natural Science Foundation of China(Grant No.42276001)2024 Qinhuangdao Social Science Development Research Project(Grant No.2024LX206)Hebei Agricultural University Research Project for Talented scholars(Grant No.YJ201835).
文摘Research has shown considerable variability in whitecap coverage(W)under low to moderate wind conditions.During an expedition to the Northwestern Pacific,oceanographic variables and photographic measurements were collected to investigate the influence of wave-induced stress on W within these wind ranges.The friction velocity was recalculated based on turbulent stress,and wind profiles were modified to account for wave-induced stress and swell presence on the sea surface.The study examined W’s relationship with multiple parameters,including friction velocity(u*),breaking wave Reynolds numbers,wavesea Reynolds numbers,and wave age.The analysis utilized both conventional u*and turbulent stress-based friction velocity(u*turb).When utilizing u*turb rather than u*,the estimation model’s fitting results revealed an increase in correlation coefficient(R2)from 0.51 to 0.62,and a decrease in root mean square error(RMSE)from 0.0652 to 0.0574.Additionally,when parameterizing W using the windsea Reynolds number,with u_(*turb) replacing u*and wind wave height substituting mixed wave height,the R^(2) increased from 0.38 to 0.53,and the RMSE decreased from 0.0737 to 0.0668.The results demonstrate that calculating u*using the turbulent stress-based method,along with wind wave height and peak wave speed of mixed waves,yields stronger correlation with W.This correlation improvement stems from the inhibition of wave breaking by swell and wave-induced stress.The integration of turbulent stress and wind wave field measurements enhances the understanding of relationships between W and various parameters.However,swell effects on wind profiles do not substantially affect W estimation using wind speed-related parameters.
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The National Key Basic Research Program(973 Program)of China under contract No.2010CB950404the National High Technology Research and Development Program(863 Program)of China under contract No.2013AA09A506+1 种基金the Basic Scientific Fund for National Public Research Institutes of China under contract No.GY0214G01the Ocean Renewable Energy Special Fund Project of the State Oceanic Administration of China under contract No.GHME2011ZC07
文摘The pro and con of whitecap parameterizations and a statistical wave breaking model are discussed. An improved model is derived by combining satellite-based parameterization and the wave breaking model. The appropriate constants for the general wave state are obtained by considering the breaking condition of the wave slope and fitting with the satellite-based parameterization. The result is close to the constants based on the whitecap data from Monahan. Comparing with satellite-based data and the original model＇s results, the improved model＇s results are consistent with satellite-based data and previous studies. The global seasonal distributions of the whitecap coverage averaged from 1998 to 2008 are presented. Spatial and seasonal features of the whitecap coverage are analyzed.
基金The National Natural Science Foundation of China under contract No.41676014。
文摘Sea spray droplets are produced by waves breaking on the sea surface, and they vary the transfer of energy between the atmosphere and ocean. The sea spray generation function(SSGF) is generally considered as a function of the initial radius of the spray droplets and the wind speed. However, ocean waves always exist at the air-sea interface, so it is not reasonable to consider only the effect of sea surface winds while ignoring the effects of ocean waves. Whitecap coverage is an important characteristic parameter of breaking waves, and researchers believe that this parameter is related to both wave state and wind speed. In this paper, the SSGF is parameterized by the whitecap coverage, and a new SSGF describing different droplet radii is organically integrated based on the whitecap coverage parameter. Then, with the relationship between the whitecap coverage and wave state, the influence of ocean waves on the SSGF for different wave states was analyzed by using observational data in the laboratory. The results show that the new SSGF that considers wave effects can reasonably describe the droplet generation process under different wave state conditions.
基金Supported by Ministry of Science and Technology of China (Nos.2005CB422307 and 2006BAC03B01)National Natural Science Foundation of China (No.40830959)
文摘Whitecapping plays an important role in many air-sea exchange and upper ocean processes.Traditionally,whitecap coverage is parameterized as a function of wind speed only.At present,the relative speed of ocean current to wind is considered to be important in the air-sea exchange parameterization which is the function of wind speed only.In this paper,the effects of ocean surface velocity (current velocity and wave induced velocity) and the wave parameters on whitecap coverage through relative speeds are investigated,by applying a 2-parameter whitecap coverage model to the Atlantic Ocean.It is found that the impacts of both current and wave on whitecap coverage are considerable in the most part of the Atlantic Ocean.It is interesting that the effect of wave is more significant than that of current.
基金This work was financially supported by the Hebei Ag-ricultural University Research Project for Talented Schol-ars(No.YJ201835)the National Natural Science Foun-dation of China(No.41806028)+1 种基金the China Postdoctoral Science Foundation(No.2019M65206)the Funda-mental Research Funds for the Central Universities(No.N182303031).The efforts of the researchers who obtained and published the data adopted in this study are much appreciated.We thank the crew,scientists,and students in Dongfanghong 2 for the help in the process of collecting observation data.
文摘The shipboard measurements of whitecap coverage(W)and the meteorological and oceanographic information from two cruises in the South China Sea and Western Pacific are explored for estimating W.This study aims at evaluating how to im-prove the parameterizations of W while considering the effects of currents and swells on wave breaking.Currents indeed affect W in a way that winds with following currents can decrease W,whereas winds with opposing currents can increase W.Then,10-m wind speed over sea surface(U_(10))is calibrated by subtracting the current velocity from U_(10) when the propagating directions of winds and currents are aligned.By contrast,when the direction is opposite,U_(10) is calibrated by adding the parallel velocity com-ponent of the opposing current to U_(10).The power fits of W dependence on the U_(10)-related parameters of U_(10),friction velocity,wind sea Reynolds number in terms of this calibrated-U_(10) obtain better results than those directly fitted to U_(10).Different from the effect of currents on W,wind blowing along the crest line of swells may contribute to the increase in W.The conclusions suggest that U_(10) should be calibrated first before parameterizing W in areas with a strong current or some swell-dominant areas.
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.
文摘Joint probability function of local surfaces-particle and phase velocities is derived for a stationary Gaussianwave field with narrow-band spectrum. From the function a model of whitecap coverage is further derived by using thekinematic condition (including the effect of drift current) for wave breaking. The drift current velocity in the model isthen replaced by the friction velocity through an existing empirical formula. A coefficient in the model for relating temporal and spatial scales of wave breaking is determined by using an existing empirical formula of oceanic whitecap coverage and the well-known Pierson-Moskowitz spectrum. The main features of the model agree well with our generalknowledge and observational evidence on wave breaking in deep waters.
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.
