Simulation of the ocean surface mixed layer under the wave breaking

A one-dimensional mixed-layer model, including a Mellor-Yamada level 2.5 turbulence closure scheme, was implemented to investigate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic energy 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 corresponding 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 temperature gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.     

Effect of surface wave breaking on the surface boundary layer of temperature in the Yellow Sea in summer

Near-surface enhancement of turbulent mixing and vertical mixing coefficient for temperature owing to the effect of surface wave breaking is investigated using a two-dimensional (2-D) ocean circulation model with a tidal boundary condition in an idealized shelf sea. On the basis of the 2-D simulation, the effect of surface wave breaking on surface boundary layer deepening in the Yellow Sea in summer is studied utilizing a 3-D ocean circulation model. A well-mixed temperature surface layer in the Yellow Sea can be successfully reconstructed when the effect of surface wave breaking is considered. The diagnostic analysis of the turbulent kinetic energy equation shows that turbulent mixing is enhanced greatly in the Yellow Sea in summer by surface wave breaking. In addition, the diagnostic analysis of momentum budget and temperature budget also show that surface wave breaking has an evident contribution to the turbulent mixing in the surface boundary layer. We therefore conclude that surface wave breaking is an important factor in determining the depth of the surface boundary layer of temperature in the Yellow Sea in summer.     

The effect of wave disturbances of the near-surface layer on the structure of the air-sea boundary layers

A method is suggested to consider energy transfer to surface waves via introducing wave stresses into the numerical model for the interaction of air-sea boundary layers. In numerical simulations, the wave stresses are shown to influence the air-sea interaction parameters and the profiles of the major quantities.Translated by V. Puchkin.     

海洋内波破碎问题的研究

从理论、观测、数值实验和实验室实验四个方面对国内外近20年来关于海洋内波破碎问题的研究成果进行了分析总结.数值实验和实验室实验表明:中高频内波破碎时,初始的不稳定是二维的,当最终有横向对流卷团形成时,能量开始大量耗散,这时不稳定发展成为三维的;从初始的二维不稳定到对流卷团的产生这一过程,到底是一个剪切不稳定过程,还是一个对流不稳定过程,或者是对流不稳定和剪切不稳定共同存在的一个过程,取决于海水的层化、地形、背景剪切流和内波的自身性质.现场曾观测到内孤立波破碎时存在的剪切不稳定过程,数值研究模拟出了内孤立波破碎时存在的对流不稳定过程.现有的海洋内波破碎判据主要是关于中高频海洋内波的.理论分析侧重于确定线性或弱非线性内波的破碎机制和破碎条件.     

Imagery of the inhomogeneities of currents on the ocean surface state

The influence of inhomogeneities of surface currents on the intensity of breaking wind waves is considered and a model for the relation between whitecap contrasts and the tensor of current gradients is developed. The imagery of typical patterns of ocean currents is discussed. The results of field observations supporting this model are given.Translated by Mikhail M. Trufanov.     

Wind wave breaking under the conditions of inhomogeneous currents and of the atmospheric boundary layer

As known fromin situ observations, inhomogeneities of flows and of the atmospheric boundary layer produce variations of the intensity of wind wave breaking. A relevant phenomenological model is suggested here, describingin situ data on the breaking of waves in the presence of internal waves. The response of the wave breaking to the flow's inhomogeneity enhances with the growth of its spatial or temporal scale. For the mesoscale (10–100 km) inhomogeneities, the model is essentially simplified—wave breakings depict the local energy inputs to wind waves. The model allows us to compute currents of various type in the wave breaking intensity field. The results may have practical implications, in terms of remote sensing of the ocean. Translated by Vladimir A. Puchkin.     

Large eddy simulation of turbulence in ocean surface boundary layer at Zhangzi Island offshore

This study uses a large eddy simulation （LES） model to investigate the turbulence processes in the ocean surface boundary layer at Zhangzi Island offshore. Field measurements at Zhangzi Island （39°N, 122°E） during July 2009 are used to drive the LES model. The LES results capture a clear diurnal cycle in the oceanic turbulence boundary layer. The process of the heat penetration and heat distribution characteristics are analyzed through the heat flux results from the LES and their differences between two diurnal cycles are discussed as well. Energy balance and other dynamics are investigated which show that the tide-induced shear production is the main source of the turbulence energy that balanced dissipation. Momentum flux near the surface shows better agreement with atmospheric data computed by the eddy correlation method than those computed by bulk formula.     

Dynamics of air-sea planetary boundary layer under the geostrophic momentum approximation condition

In this paper, the air-sea planetary boundary is divided into three layers. With the aid of geostrophic momentum approximation, wind and current profiles, surface wind, surface wind stress and Ekman pumpinii in the atmosphere as well as in the ocean affected by the atmospheric baroclini-city, stratification and nonlinear effects are investigated systematically for an ocean of infinite depth. Meanwhile, the characteristics of the air-sea interaction is analyzed.     

Evolution and breaking of a propagating internal wave in stratified ocean

The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.     

A quasi-isopycnic model of the eastern boundary layer in the ocean

This paper considers the response of the eastern boundary layer and restructuring of the upwelling and downwelling regimes due to the periodic changing of the alongshore wind direction using the data from a numerical experiment conducted in the frame of a multi-layer non-linear model of the ocean, based on hydrothermodynamic primitive equations.Translated by Vladimir A. Puchkin.     

Boundary layer approach in the modeling of breaking solitary wave runup

The boundary layer is very important in the relation between wave motion and bed stress, such as sediment transport. It is a known fact that bed stress behavior is highly influenced by the boundary layer beneath the waves. Specifically, the boundary layer underneath wave runup is difficult to assess and thus, it has not yet been widely discussed, although its importance is significant. In this study, the shallow water equation (SWE) prediction of wave motion is improved by being coupled with the k–ω model, as opposed to the conventional empirical method, to approximate bed stress. Subsequently, the First Order Center Scheme and Monotonic Upstream Scheme of Conservation Laws (FORCE MUSCL), which is a finite volume shock-capturing scheme, is applied to extend the SWE range for breaking wave simulation. The proposed simultaneous coupling method (SCM) assumes the depth-averaged velocity from the SWE is equivalent to free stream velocity. In turn, free stream velocity is used to calculate a pressure gradient, which is then used by the k–ω model to approximate bed stress. Finally, this approximation is applied to the momentum equation in the SWE. Two experimental cases will be used to verify the SCM by comparing runup height, surface fluctuation, bed stress, and turbulent intensity values. The SCM shows good comparison to experimental data for all before-mentioned parameters. Further analysis shows that the wave Reynolds number increases as the wave propagates and that the turbulence behavior in the boundary layer gradually changes, such as the increase of turbulent intensity.     

On one model of the upper boundary layer of the ocean

A steady model of the ocean's upper boundary layer is considered. It uses the dependence on the velocity gradient, suggested in ref. 1, which is analogous to formulae of the Prandtl type for the coefficient of turbulence. The analytical solution of the problem is provided. A numerical estimate of the model's parameters points to satisfactory concordance with the field data for various characteristics.Translated by Mikhail M. Trufanov.     

Local balance in the air-sea boundary processes

In the course of the new treatment of the growth process of wind waves presented in part I of the present series of the articles, there was a point where the wave energy and wave momentum were not related correctly. This point has been revised with critical argument, and at the same time, the form of the ratior, between the wind stress that directly enter the wind waves and the total wind stress, has been derived analytically. The growth equation, under the condition that the wind stress is constant, is still the same with that derived in part I, with the exception that the ratior is given analytically.A comparison between the ratior obtained analytically and that estimated empirically in part I, raises a problem to be studied about the wave current of the actual wind waves.     

Local balance in the air-sea boundary processes

A new growth equation for wind waves of simple spectrum is presented upon three basic concepts. The period and the wave height of significant waves in dimensionless forms, which are considered to correspond to the peak frequency and the energy level, respectively, are used as representative quantities of wind waves. One of the three basic concepts is the concept of local balance, and the other two concern the acquisition of wave energy and the dissipation of wave energy, respectively. It is shown from some actual data that the equation, together with two universal constants concerning the acquisition and the dissipation of wave energy (B=6.2×10^?2 andK=2.16×10^?5, respectively), is applied universally to wide ranges of wind waves from those in a wind-wave tunnel to fully developed sea in the open ocean. “The three-second power law for wind waves of simple spectrum”, and a few relations as the lemmas, are derived, such that the mean surface transport due to the orbital motion of wind waves is always proportional to the friction velocity in wind, and that the steepness is inversely proportional to the root of the wave age. It is also derived that the portion of wind stress which directly enters the wind waves decreases exponentially with increasing wave age and is 7.5 % of the total wind stress for very young waves. Also, equations are presented as to the increase of momentum of drift current, and as to the supply of turbulent energy by wind waves into the upper ocean.     

The role of surface waves in the ocean mixed layer

Previously, most ocean circulation models have overlooked the role of the surface waves. As a result, these models have produced insufficient vertical mixing, with an under - prediction of the ,nixing layer （ML） depth and an over - prediction of the sea surface temperature （SST）, particularly during the summer season. As the ocean surface layer determines the lower boundary conditions of the atmosphere, this deficiency has severely limited the performance of the coupled ocean - atmospheric models and hence the climate studies. To overcome this shortcoming, a new parameterization for the wave effects in the ML model that will correct this systematic error of insufficient mixing. The new scheme has enabled the mixing layer to deepen, the surface excessive heating to be corrected, and an excellent agreement with observed global climatologic data. The study indicates that the surface waves are essential for ML formation, and that they are the primer drivers of the upper ocean dynamics; therefore, they are critical for climate studies.     

Mellor-Yamada模型在波浪边界层中的运用

利用Mellor-Yamada 2.5阶封闭格式建立一维垂线波浪边界层数学模型,利用有限元方法求解,模拟线性波作用下的层流边界层和乔治沙洲南侧海岸一侧点的波浪边界层流速分布,并同理论或其他的计算方法进行比较,结果显示该模型具有较高的精度,能广泛运用于波浪边界层的研究中。     

Local balance in the air-sea boundary processes

A combination of the three-second power law, presented in part I for wind waves of simple spectrum, and the similarity of the spectral form of wind waves, leads to a new concept on the energy spectrum of wind waves. It is well substantiated by data from a wind-wave tunnel experiment.In the gravity wave range, the gross form of the high frequency side of the spectrum is proportional tog u _* ^–4, whereg represents the acceleration of gravity,u _* the friction velocity, the angular frequency, and the factor of proportionality is 2.0×l0^–2. The wind waves grow in such a way that the spectrum slides up, keeping its similar form, along the line of the gross form, on the logarithmic diagram of the spectral density,, versus. Also, the terminal value of, at the peak frequency of the fully developed sea, is along a line of the gradient ofg ^{2 –5}.The fine structure of the spectrum from the wind-wave tunnel experiment shows a characteristic form oscillating around the ^–4-line. The excess of the energy density concentrates around the peak frequency and the second- and the third-order harmonics, and the deficit occurs in the middle of these frequencies. This form of the fine structure is always similar in the gravity wave range, in purely controlled conditions such as in a wind-wave tunnel. Moving averages of these spectra tend very close to the form proportional to ^–5.As the wave number becomes large, the effect of surface tension is incorporated, and the ^–4-line in the gravity wave range gradually continues to a ^–8/3-line in the capillary wave range, in accordance with the wind-wave tunnel data. Likewise, the ^–5-line gradually continues to a ^–7/3-line.Also, through a discussion on these results, is suggested the existence of a kind of general similarity in the structure of wind wave field.     

Mass transport in a two-layer wave boundary layer

The transport of a chemical species under the pure action of surface progressive waves in the benthic boundary layer which is loaded with dense suspended sediments is studied theoretically. The flow structure of the boundary layer is approximated by that of a two-layer Stokes boundary layer with a sharp interface between clear water and a heavy fluid. The simplest model of constant eddy diffusivities is adopted and the exchange of matter with the bed is ignored. For a thin layer of heavy fluid, whose thickness is comparable to the surface wave amplitude and the Stokes boundary layer thickness, effective transport equations are deduced using an averaging technique based on the method of homogenization. The effective advection velocity is found to be equal to the depth-averaged mass transport velocity, while the dispersion coefficient can be shown to be positive definite. Explicit expressions for the transport coefficients are obtained as functions of fluid properties and flow kinematics. Physical discussions on their relations are also presented.     

海浪破碎对北太平洋海表面温度模拟的影响

基于海浪模式WAVEWATCH Ⅲ模拟北太平洋海浪要素,结合NDBC浮标资料进行验证,发现模拟出的有效波高与浮标测量值具有很好的一致性。基于改进型白冠覆盖率耗散模型,利用海浪模式模拟出的有效波高、有效波周期和摩擦速度等海浪要素计算出单位面积水柱内因海浪破碎产生的湍动能通量。通过改变环流模式sbPOM湍动能方程的上边界条件,引入海浪破碎产生的湍动能通量,并探究海浪破碎对北太平洋海表面温度模拟的影响。研究表明,由于海浪破碎的引入,环流模式sbPOM对北太平洋海表面温度模拟的准确程度得到提升,这为大气模式提供一个准确的北太平洋下边界条件具有重要意义。     

不同边界层稳定性下海气湍流热通量日变化的前沿问题探讨

海气湍流热通量(潜热和感热)是研究海气相互作用和大洋环流的关键要素, 认识其变化机理对理解“海洋动力过程及气候效应”有重要意义。然而, 受观测手段和计算能力两方面的限制, 过去对海气湍流热通量日变化研究存在“特征认识较粗、机制理解较疏”的现象。本文探讨了在不同边界层稳定性下海气湍流热通量日变化研究中的问题与难点, 并讨论了“不同边界层稳定性下海气湍流热通量日变化过程和机理”这一关键科学问题。本文提出, 可基于海洋浮标、平台和波浪滑翔机等综合观测数据和高时空分辨率再分析资料, 利用块体算法和脉动分离方法, 揭示全球海气湍流热通量的精细化日变化特征和决定因素, 以及海气湍流热通量日变化强度(日内小时级变化的标准差)与极端天气过程和气候事件的动力关联。同时, 为更精准认识日变化过程, 在技术上可通过耦合高频海表流速和校正边界层物理参数观测高度等方式提升海气湍流热通量估算的精确度。本文提出可将多时空尺度海气湍流热通量变化维度转换到边界层稳定性上, 以便集中认识其日变化特征和机理, 支撑全球海气能量平衡的科学认识。