海浪破碎对海洋上混合层中湍能量收支的影响

海浪破碎产生一向下输入的湍动能通量,在近海表处形成一湍流生成明显增加的次层,加强了海洋上混合层中的湍流垂向混合。为了研究海浪破碎对混合层中湍能量收支的影响,文中分析了海浪破碎对海洋上混合层中湍流生成的影响机制,采用垂向一维湍封闭混合模式,通过改变湍动能方程的上边界条件,引入了海浪破碎产生的湍动能通量,并分别对不同风速下海浪破碎的影响进行了数值研究,分析了混合层中湍能量收支的变化。当考虑海浪破碎影响时,近海表次层中的垂直扩散项和耗散项都有显著的增加,该次层中被耗散的湍动能占整个混合层中耗散的总的湍能量的92.0%,比无海浪破碎影响的结果增加了近1倍;由于平均流场切变减小,混合层中的湍流剪切生成减小了3.5%,形成一种存在于湍动能的耗散和垂直扩散之间的局部平衡关系。在该次层以下,局部平衡关系与壁层定律的结论一致,即湍动能的剪切生成与耗散相平衡。研究结果表明,海浪破碎在海表产生的湍动能通量影响了海洋上混合层中的各项湍能量收支间的局部平衡关系。     

Modeling of the Turbulence in the Water Column under Breaking Wind Waves

Past studies have shown that there is a wave-enhanced, near-surface mixed-layer in which the dissipation rate is greater than that derived from the “law of the wall”. In this study, turbulence in water columns under wind breaking waves is investigated numerically and analytically. Improved estimations of dissipation rate are parameterized as surface source of turbulent kinetic energy (TKE) for a more accurate modelling of vertical profile of velocity and TKE in the water column. The simulation results have been compared with the experimental results obtained by Cheung and Street (1988) and Kitaigorodskii et al. (1983), with good agreement. The results show that the numerical full model can well simulate the near-surface wave-enhanced layer and suggest that the vertical diffusive coefficients are highly empirical and related to the TKE diffusion, the shear production and the dissipation. Analytical solutions of TKE are also derived for near surface layer and in deep water respectively. Near the surface layer, the dissipation rate is assumed to be balanced by the TKE diffusion to obtain the analytical solution; however, the balance between the dissipation and the shear production is applied at the deep layer. The analytical results in various layers are compared with that of the full numerical model, which confirms that the wave-enhanced layer near the surface is a diffusion-dominated region. The influence of the wave energy factor is also examined, which increases the surface TKE flux with the wave development. Under this region, the water behavior transits to satisfy the classic law of the wall. Below the transition depth, the shear production dominantly balances the dissipation. This revised version was published online in August 2006 with corrections to the Cover Date.     

初始倾斜跃层所致内波的数值研究

The pycnocline in a closed domain is tilted by external wind forcing and tends to restore to a level posi- tion when the wind falls. An internal seiche oscillation exhibits if the forcing is weak, otherwise internal surge and internal solitary waves emerge, which serve as a link to cascade energy to small-scale processes. A two-dimensional non-hydrostatic code with a turbulence closure model is constructed to extend previous laboratory studies. The model could reproduce all the key phenomena observed in the corresponding labo- ratory experiments. The model results further serve as a comprehensive and reliable data set for an in-depth understanding of the related dynamical process. The comparative analyses indicate that nonlinear term favors the generation of internal surge and subsequent internal solitary waves, and the linear model predicts the general trend reasonably well. The vertical boundary can approximately reflect all the incoming waves, while the slope boundary serves as an area for small-scale internal wave breaking and energy dissipation. The temporal evolutions of domain integrated kinetic and potential energy are also analyzed, and the results indicate that about 20% of the initial available potential energy is lost during the first internal wave breaking process. Some numerical tactics such as grid topology and model initialization are also briefly discussed.     

非线性流函数在实验风浪场计算中的应用

风作用于水面产生风浪, 其中由于波流紊动产生的动量和能量的交换机制是一个很复杂的过程。风应力一般用来描述这种能量交换, 可以分为3个部分: 水面的剪切力、波生应力以及紊动应力。采用一种有效的非线性波流分离方法——NSFM(Nonlinear Stream Function Method)对波流运动的动量和能量输移进行定性描述。构造能够有效表达非线性波浪的解析流函数, 摄动求解使其满足拉普拉斯方程、动力边界条件和运动边界条件, 结合实验室风浪数据, 分离出波生速度场。通过交叉谱分析, 得到波生雷诺应力在不同风速下对风应力的贡献。结果表明: NSFM对不同工况条件下的风浪的处理具有较高的精度, 模型适应性良好; 且风速越大, 波生应力沿着水深衰减得越快, 且自由面波生应力在动量输移中的比重会逐渐减弱。     

Effect of Stokes drift on upper ocean mixing

Stokes drift is the main source of vertical vorticity in the ocean mixed layer. In the ways of Coriolis - Stokes forcing and Langmuir circulations, Stokes drift can substantially affect the whole mixed layer. A modified Mellor-Yamada 2. 5 level turbulence closure model is used to parameterize its effect on upper ocean mixing conventionally. Results show that comparing surface heating with wave breaking, Stokes drift plays the most important role in the entire ocean mixed layer, especially in the subsurface layer. As expected, Stokes drift elevates both the dissipation rate and the turbulence energy in the upper ocean mixing. Also, ilffluence of the surface heating, wave breaking and wind speed on Stokes drift is investigated respectively. Research shows that it is significant and important to assessing the Stokes drift into ocean mixed layer studying. The laboratory observations are supporting numerical experiments quantitatively.     

破碎波群间隔统计分布

基于一系列实验室风浪破碎实验,讨论破碎波群间隔的统计分布。实验时风速分别设定在6～9 m/s间几个不同的风速水平,破碎波群间隔定义为两个相继发生破碎的波群中破碎首发时刻之间的时间间隔,破碎依据波面信号和实验者同步记录的破碎标记信号判别,分布拟合检验采用Kolmogorov-Smirnov检验。数据分析结果表明:1)所有实验信号的破碎波群间隔都服从Gamma分布;2)低风速情形的破碎波群间隔大多服从指数分布——Gamma分布的一种特殊情形;3)相同实验条件下的破碎波群间隔具有相同的分布。这意味着破碎波群的发生可以视为一种更新过程。     

Modeling of the eddy viscosity by breaking waves

Breaking wave induced nearsurface turbulence has important consequences for many physical and biochemical processes including water column and nutrients mixing,heat and gases exchange across air-sea interface.The energy loss from wave breaking and the bubble plume penetration depth are estimated.As a consequence,the vertical distribution of the turbulent kinetic energy(TKE),the TKE dissipation rate and the eddy viscosity induced by wave breaking are also provided.It is indicated that model results are found to be consistent with the observational evidence that most TKE generated by wave breaking is lost within a depth of a few meters near the sea surface.High turbulence level with intensities of eddy viscosity induced by breaking is nearly four orders larger than υwl(=κuwz),the value predicted for the wall layer scaling close to the surface,where uw is the friction velocity in water,κ with 0.4 is the von Kármán constant,and z is the water depth,and the strength of the eddy viscosity depends both on wind speed and sea state,and decays rapidly through the depth.This leads to the conclusion that the breaking wave induced vertical mixing is mainly limited to the near surface layer,well above the classical values expected from the similarity theory.Deeper down,however,the effects of wave breaking on the vertical mixing become less important.     

Improvement and application of a saturation based wave dissipation function in SWAN model

Wave dissipation characteristics in SWAN (Simulating Waves Nearshore) model are investigated through numerical experiments. It is found that neither the fully developed integral parameters of wind waves (significant wave height and peak frequency) nor the high frequency spectral tail can be well reproduced by the default wave dissipation source terms. A new spectral dissipation source term is proposed, which comprises saturation based dissipation above two times of peak frequency and improved whitecapping dissipation at lower frequency spectrum. The reciprocal wave age (u /c p ) is involved into the whitecapping model to adjust dissipation rate at different wind speed. The Phillips higher frequency saturation parameter in the saturation-based dissipation is no longer taken as a constant, but varies with wave age. Numerical validations demonstrate that both the wind wave generation process and higher frequency spectrum of wind waves can be well simulated by the new wave dissipation term.     

A note on the direct injection of turbulence by breaking waves

We investigate the turbulence induced by wave-breaking at the ocean surface. Two recent models use a mechanism of direct depth injection of turbulent kinetic energy (TKE) by breaking waves. Those models aim to reproduce the near-surface mean and turbulent properties, in particular the TKE dissipation rates. Of critical importance are the injection depth of each breaking wave and the size distribution of those breaking waves. The models by Sullivan et al. (2007) and by Kudryavtsev et al. (2008) have very different parameterizations, and those differences are reviewed here and compared to available observations. Using realistic parameterizations in these models leads to TKE injections too shallow to compare to observations, in particular for developed seas. The near-surface turbulence is thus still not well understood to the zeroth order. For instance, whether developed seas produce deeper or shallower mixing than young seas is neither well understood nor well modelled. Additional dedicated measurements as well as investigations of breaking non-breaking wave interactions are needed.     

Dissipation Rate of Turbulence in a Water Layer under Wind Waves Based on Data of a Laboratory Experiment

Izvestiya, Atmospheric and Oceanic Physics - The aim of this work is to obtain estimates and parameterization of the dissipation rate of the turbulence kinetic energy (TKE dissipation), ε,...     

Microstructure measurements and finescale parameterization assessment of turbulent mixing in the northern South China Sea

Both microscale and finescale measurements were conducted along 20°N and 21°N in the northern South China Sea (SCS) during July 2007. Spatial variability of turbulent kinetic energy (TKE) dissipation rate was examined, and two finescale parameterizations were assessed and compared. TKE dissipation rates along the 21°N section were found to be much higher than those along 20°N; in particular, remarkably high TKE dissipation rates existed near the Luzon Strait and around the Dongsha Plateau, which were likely caused by internal tides and internal solitary waves, respectively. The Gregg–Henyey scaling does not work well in the northern SCS, while the MacKinnon–Gregg scaling with a modified parameter matches the observations in both magnitude and variability. One explanation is that the large-scale/low-mode shear mainly comes from low-frequency internal waves such as internal tides, which are not described well by the Garrett–Munk spectrum.     

基于白冠覆盖率的飞沫生成函数参数化

海浪破碎使得海面产生飞沫水滴,由于飞沫水滴的存在改变着大气和海洋之间的能量传输。飞沫生产函数一般认为是水滴初始半径和风速的函数,但海浪时刻存在于海-气界面,仅仅考虑海面风的作用,而忽略海浪的影响是不够完善的。白冠覆盖率是海浪破碎的重要特征参数,有研究者发现白冠覆盖率与海面风速和海浪均存在相关性。本文尝试从白冠覆盖率出发,构建飞沫水滴的生成函数参数化方案,将描述不同飞沫水滴半径的飞沫生成函数基于白冠覆盖率参数有机整合,然后结合白冠覆盖率和海浪状态的关系,利用实验室观测数据,分析不同海浪状态条件下海浪对飞沫生成函数的影响。研究结果表明,新的考虑波浪效应的飞沫生成函数可以合理地描述不同海浪状态条件下飞沫水滴的生成过程。     

An approximate solution of wave-modified Ekman current for gradually varying eddy viscosity

An approximate steady solution of the wave-modified Ekman current is presented for gradually varying eddy viscosity by using the WKB method with the variation of parameters technique. The parameters involved in the solution can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water. The solution reduces to the exact solution when the eddy viscosity is taken as a constant. As illustrative examples, for a fully developed wind-generated sea with different wind speeds and a few proposed gradually varying eddy viscosities, the current profiles calculated from the approximate solutions are compared with those of the exact solutions or numerical ones by using the Donelan and Pierson wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. It is shown that the approximate solution presented has an elegant form and yet would be valid for any given gradually varying eddy viscosity. The applicability of the solution method to the real ocean is discussed following the comparisons with published observational data and with the results from a large eddy simulation of the Ekman layer.     

Turbulence and energy dissipations of surf-zone spilling breakers

A laboratory study on the turbulence and wave energy dissipations of spilling breakers in a surf zone is presented. Instantaneous velocity fields of propagating breaking waves on a 1/20 slope were measured using Particle Image Velocimetry (PIV). Due to the large region of the evolving wave breaking generated turbulent flow, seven PIV fields of view (FOVs) were mosaicked to form a continuous flow field in the surf zone. Mean and turbulence quantities were extracted by ensemble averaging 25 repeated instantaneous measurements at each FOV. New results for distribution and evolution of turbulent kinetic energy, mean flow energy, and total energy across the surf zone were obtained from analyzing the data. The turbulence dissipation rate was estimated based on several different approaches. It was found that the vertical distribution of the turbulence dissipation rate decays exponentially from the crest level to the bottom. The resulting energy budget and energy flux were also calculated. The calculated total energy dissipation rate was compared to that based on a bore approximation. It was found that the ratio of turbulence dissipation rate to total energy dissipation rate was about 0.01 in the outer surf zone and increased to about 0.1 after the breaking waves transformed into developed turbulent bores in the inner surf zone.     

大洋细结构的一种可能的机制Ⅲ.对混合过程动能耗散的估计

继第部分之后研究了惯性内波和近惯性内波由f～的作用所致的剪切不稳定引起的破碎机制。物理上,该机制很象存在由风应力所致薄表面涡旋漂流层时表面波的破碎与饱和过程。惯性内波和近惯性内波的破碎产物与小尺度湍流一起形成了混合块,它与Gregg等人(1986)的持久混合观测结果一致。依据Thorpe(1973)实验的结果作者提出了一个估计湍流动能耗散率和消衰时间的方法。结果表明,在剪切不稳定中近惯性内波在湍动耗散中起了关键作用,而惯性内波引起非常弱的湍动耗散。使用内波能量谱的标准总能量密度估计出的近惯性内波的耗散率和消衰时间与PATCHEX测量结果非常一致。文中还讨论了几个与此破碎机制有关的问题。     

Parameterization of rain induced surface roughness and its validation study using a third generation wave model

The effect of raindrops striking water surface and their role in modifying the prevailing sea-surface roughness is investigated. The work presents a new theoretical formulation developed to study rain-induced stress on sea-surface based on dimensional analysis. Rain parameters include drop size, rain intensity and rain duration. The influences of these rain parameters on young and mature waves were studied separately under varying wind speeds, rain intensity and rain duration. Contrary to popular belief that rain only attenuates surface waves, this study also points out rain duration under certain condition can contribute to wave growth at high wind speeds. Strong winds in conjunction with high rain intensity enhance the horizontal stress component on the sea-surface, leading to wave growth. Previous studies based on laboratory experiments and dimensional analysis do not account for rain duration when attempting to parameterize sea-surface roughness. This study signifies the importance of rain duration as an important parameter modifying sea-surface roughness. Qualitative as well quantitative support for the developed formulation is established through critical validation with reports of several researchers and satellite measurements for an extreme cyclonic event in the Indian Ocean. Based on skill assessment, it is suggested that the present formulation is superior to prior studies. Numerical experiments and validation performed by incorporating in state-of-art WAM wave model show the importance of treating rain-induced surface roughness as an essential pre-requisite for ocean wave modeling studies.     

降雨条件下全极化微波辐射计海面风场校正

为提高降雨条件下星载全极化微波辐射计海面风场精度,通过匹配WindSat海面风场和降雨率数据以及美国国家浮标中心浮标观测数据,得到18 996组匹配样本,深入分析了降雨对海面风场反演精度的严重影响,构建了风场校正模型。试验结果表明,降雨导致海面风速被严重高估,风向误差随着降雨率的增大而增大。校正后的风速精度在低风速段提升明显。无论降雨率多大,校正后风速精度均比校正前高。风速均方根误差由原来的2.9 m/s降低到了2.1 m/s,风向均方根误差由原来的26.9°降低到了26.3°。     

Reconstructing the upper ocean thermal profiles using one-dimensional numerical model

The observation data for 5 d at a station in the South China Sea is presented.After brief analysis of the wind speed,air temperature from the ship-borne meteorological instruments and temperature and salinity profiles from the CTD (conductivity,temperature,depth recorder) data,the authors find that the CTD casts are too sparse for us to understand the diurnal evolution of the thermal structure in the upper ocean.A one-dimensional (1D) numerical code based on Mellor-Yamada turbulence closure model is used to reconstruct the upper ocean thermal structure,utilizing the atmospheric forcing data from ship-borne weather station.The simulation results show good agreement with the observational data;the significance of breaking waves is also briefly discussed.The evolution of turbulence kinetic energy (TKE) and the contribution from shear production and buoyancy production are discussed respectively.Finally,several possible factors which might influence the numerical results are briefly analyzed.     

Mixing processes relevant to phytoplankton dynamics in lakes

Active turbulence in lakes is confined to the surface mixed layer, to boundary layers on the lake sides and bottom, and to turbulent patches in the interior. The density stratification present in most lakes fundamentally alters the pathways connecting external mechanical energy inputs, for example by wind, with its ultimate fate as dissipation to heat; the density stratification supports internal waves and intrusions that distribute the input energy throughout the lake. Intrusions may be viewed as internal waves with zero horizontal wavenumber and are formed each time localised mixing occurs in a stratified fluid. Intrusions are also formed in the epilimnion by differential heating or cooling and by differential deepening. The fraction of lake volume below the diurnal mixed layer that is subject to active turbulence is very small, probably of the order of 1% or less in small to medium‐sized lakes. By contrast, in the surface mixed layer, turbulence is less intermittent and maintains phytoplankton in suspension and controls their exposure to the underwater solar flux. Nutrient transport to individual cells depends not only on the cell Reynolds number but also on the Peclet number, which, if large, implies enhanced mass transfer above purely diffusive values.     

Internal wave band kinetic energy production: flat vs. sloping bottom

Velocity and temperature measurements obtained with acoustic Doppler current profilers and thermistor strings are used to evaluate the production of internal wave band kinetic energy mainly in the frequency band σ>15 cpd. Results from a flat 19 m deep, vigorous tidal environment in a shelf sea are compared with energy production in a bottom boundary layer above a continental slope. In the tidal environment, maximum production occurs in the near-bottom and near-surface layers. A distinct mid-depth maximum in KE production occurs during a period when wind speeds exceed 10 m s⁻¹ and significant wave height ∼2 m. At the same time, no significant changes in the along-shore current speed take place but the cross-shore current, generated by strong stratification, is weakened. This suggests a direct energy input from the wind via surface waves into the water column turbulence. Maximum kinetic energy production in the frequency band σ>1.9 cpd, thus including the semidiurnal tide, occurs at mid-depth when strong stratification is present. The overall magnitude of internal wave band kinetic energy production agrees well with independent dissipation estimates obtained from microstructure profilers. Above the sloping bottom, KE production is somewhat larger than observed in the shallow tidal environment, despite rms currents being ∼50% smaller and wind effects being small. Above the sloping bottom KE shear production was comparable to buoyancy production. The latter was negligible at the shelf sea site.