风浪和涌浪分离方法的比较（英文）

海浪通常以风浪和涌浪混合的形式存在,如何进行分离风浪和涌浪一直是海浪理论研究和海洋工程应用中的重要问题。本文利用模型试验和实测资料,对目前提出的一种二维谱风涌浪分离方法（2D法）和三种一维谱风涌浪分离方法（PM法、WH法、JP法）进行了检验,分析发现：2D法给出的结果整体而言最为可靠,与2D法相比,PM法明显高估了风浪成分,WH法低风速时高估了风浪,高风速时跟2D法比较接近,而JP法在整体上高估了风浪成分。通过调整分割频率的比例系数,改进了PM法,改进后的PM法给出的分离结果与2D法最为一致。     

Modelling of the spectral characteristics of the wind wave envelope

A method applied for the determination of the statistical characteristics of the wind wave envelope is considered. It is shown that the correlation function envelope for a normal random process defines the basic properties of the process envelope and it can be expressed through the spectrum width. No limitations are imposed on the form or the width of the spectrum. The model is effective for a developing and steady sea disturbance when the attenuation of the temporal correlation function can be approximated by an exponent. Numerical computations and experimental results for typical cases of sea disturbance are compared.Translated by Mikhail M. Trufanov.     

不同TVD 格式对内孤立波数值模拟结果影响研究

为了研究不同TVD格式对内孤立波模拟结果的影响,利用改进后的SUNTANS三维非静压海洋模型,通过理想算例和南海东北部海域内孤立波的模拟,比较分析了求解温盐方程TVD格式的4种经典通量限制函数(superbee, minmod, van Leer和MUSCL)对计算结果的影响。综合理想算例和南海东北部海域模拟结果,在所讨论的4种通量限制函数中,利用MUSCL限制函数所得模拟结果最优,建议在南海东北部海域内孤立波模拟中采用MUSCL限制函数。     

潮波方程数值格式与摩阻系数选取

基于一维阻尼潮波传播方程解析解,从求解数值格式及Heuristic稳定性分析方面,讨论了数值解的精度、计算耗时和摩阻系数选取等问题。研究结果表明:1)Courant数小于1时,潮波方程显格式解的精度略高于隐格式解,计算耗时少于隐格式解;2)为减少计算耗时,潮波方程的隐格式解允许较大的时间步长,但解的精度有所降低,须通过减小底床摩阻系数以保证计算精度;3)隐格式解摩阻系数的选取与Courant数有关,Courant数越大,摩阻系数的选取值比实际值越小,通过理论分析结合数值试验得到了相应的关系式。这些研究结论对实际海域的潮波传播的数值模拟具有重要的应用价值。     

Padé coefficients for the solution of the wave dispersion equation under ice

The equations governing the propagation of linear gravity waves in ice-covered waters of finite depth is delineated for the linear elastic deformation of the ice plates that are modeled as elastically supported. The possible limiting condition for the validity of the assumptions involved in the formulation of the problem is discussed. A solution procedure for the solution of the wave dispersion equation under ice is discussed and a set of coefficients synthesized using the properties of infinite series and Padé approximants. Direct application of these coefficients for the calculation of wave characteristics in ice-covered sea will eliminate the need for iterative procedure, and hence will reduce the computational time. The derived coefficients were used for the computation of the wave characteristics of laboratory simulated waves and compared with the values obtained through iteration and the error was found to be less than 2%.     

寒潮影响下江苏沿海风浪场数值模拟研究

基于第三代浅水波浪数值预报模型SWAN,建立自西北太平洋嵌套至东中国海、江苏沿海的三重嵌套模型,对2010年12月12日至15日江苏沿海寒潮大风引起的风浪过程进行了数值模拟研究。利用西北太平洋和江苏沿海实测数据对模型进行了验证,结果表明SWAN嵌套模型能较好地模拟江苏沿海寒潮风浪场的时空分布。通过响水站实测数据对江苏沿海底摩擦系数进行了率定,研究表明选取Collins拖曳理论中摩擦因数C_f=0.001时,有效波高模拟误差相对较小。寒潮风浪场的特征分析表明,有效波高分布与风场分布基本一致,寒潮风浪在江苏沿海北部影响较为显著,辐射沙洲附近由于其特殊地形影响相对较小。     

A hybrid model for numerical wave forecasting and its implementation——Ⅰ. The wind wave model

The authors make an endeavor to explain why a new hybrid wave model is here proposed when several such models have already been in operation and the so- called third generation wave modej is proving attractive. This part of the paper is devoted to the wind wave model. Both deep and shallow water models have been developed, the former being actually a special case of the latter when water depth is great. The deep water model is exceptionally simple in form. Significant wave height is the only prognostic variable. In comparison with the usual methods to compute the energy input and dissipations empirically or by "tuning", the proposed model has the merit that the effects of all source terms are combined into one term which is computed through empirical growth relations for significant waves, these relations being, relatively speaking, easier and more reliable to obtain than those for the source terms in the spectral energy balance equation. The discrete part of the model and the implementation of the mode     

An algorithm for the quality checking of wind speeds measured at sea against measured wave spectral energy

The purpose of this study is to provide a quality-checking tool for the evaluation of wind-wave data from buoys deployed by the National Data Buoy Center (NDBC). In particular, an algorithm is sought that will compare measured wind speed with spectral data in a chosen range. In the past, anemometers have been known to fail without failing completely, returning data that are bad, but not obviously bad. The aim here is to provide an automated test that will flag such data, as well as detecting certain malfunctions of the wave-measuring system. Towards this end, large quantities of data are studied and several approaches to the problem are described before an algorithm is finally recommended. The algorithm takes account of physical properties of the ocean (as observed from this data set) as well as the statistical relationships determined between wind speed and wave energy. The implementation and testing of the algorithm are described.     

Water-temperature effect on the spectral density of wind gravity waves and on sea-surface roughness

The results of hourly measurements of sea roughness and hydrometeorological parameters, which were automatically taken from special buoys over a long period of time, were used. These buoys were located in the open regions of both the Atlantic and Pacific oceans in different climatic zones; the mean water-surface temperature around the buoys varies from 1–3°C to 26–28°C. In addition to measurement results, the tables contain data on the spectral density of sea roughness for a wide range of frequencies. An analysis of these data, which was made for a short-wave region of the wind-wave spectrum, for the first time revealed a noticeable watertemperature dependence of the spectral density of wind waves within the frequency range 0.30–0.40 Hz, which corresponds to wave lengths of 9-4 m. The presence of such dependence is explained by a rapid temperature change in kinematic sea-water viscosity. Earlier, we indicated the temperature dependence of only very short spectral components that relate to a centimetric wavelength range. The statistical significance of the watertemperature effect on the spectral density of waves of the indicated frequency is supported by the results of a variance analysis. Temperature variations in the parameter of sea-surface roughness, which is determined, first of all, by the energy of the spectral shortwave region, are estimated. Altimetry is the basic method which is used in remotely determining the velocity of near-water wind. This method allows one to obtain records of deviations of the sea surface from the geoid surface and to calculate (on the basis of these records) the spectral density of wave components of almost any frequency. It is known that the wave-spectrum components in the region of low frequencies are almost always affected by ripple. Consequently, the energy of these components is determined not only by wind forcing, and only the components in the range of frequencies exceeding approximately 0.3 Hz are purely windy. Therefore, using the results of sea-surface altimetry in order to determine the velocity of near-water wind, one should use the spectral densities of wave components in this frequency region. The water-temperature dependence of the spectral density of short wind waves is manifested only in a certain frequency interval, which supports this recommendation.     

An analytic solution to the wave bottom boundary layer governing equation under arbitrary wave forcing

Existing models of the wave bottom boundary layer have focused on the vertical and temporal dynamics associated with monochromatic forcing. While these models have made significant advances, they do not address the more complicated dynamics of random wave forcing, commonly found in natural environments such as the surf zone. In the closed form solution presented here, the eddy viscosity is assumed to vary temporally with the bed shear velocity and linearly with depth, however, the solution technique is valid for any eddy viscosity which is separable in time and space. A transformation of the cross-shore velocity to a distorted spatial domain leads to time-independent boundary conditions, allowing for the derivation of an analytic expression for the temporal and vertical structure of the cross-shore velocity under an arbitrary wave field. The model is compared with two independent laboratory observations. Model calculations of the bed shear velocity are in good agreement with laboratory measurements made by Jonsson and Carlsen (1976, J. Hydraul. Res., 14, 45–60). A variety of monochromatic, skewed, and asymmetric wave forcing conditions, characteristic of those found in the surf zone, are used to evaluate the relative effects on the bed shear. Because the temporal variation of the eddy viscosity is assumed proportional to the bottom shear, a weakly nonlinear interaction is created, and a fraction of the input monochromatic wave energy is transferred to the odd harmonics. For a monochromatic input wave, the ratio of the third harmonic of velocity at the bed to the first is <10%. However, for a skewed and asymmetric input wave, this ratio can be as large as 30% and is shown to increase with increasing root-mean-square input wave acceleration. The work done by the fluid on the bed is shown to be a maximum under purely skewed waves and is directed onshore. Under purely asymmetric waves, the work done is significantly smaller and directed offshore.     

Effects of wind waves of the Pacific westerly on the eastern Pacific wave transport

There exists a tongueshaped swelldominance pool known as Swell Pool (SP) in the Eastern Pacific region. The monthlymean wave transports (WT) for each month of 2000 is computed using the wave products of ECMWF reanalysis data. By comparing the 2000 monthlymean WT and monthlymean wind field from QUICKSCAT, large differences are found between the wave transport direction and the wind direction over the Eastern Pacific. This may serve as an evidence for the existence of the SP in this region. The work done in this study indicates that the sources of swell in the Tropical Eastern Pacific (TEP) are in the westerly regions of the Southern and Northern Pacific.     

适于模拟不规则水域波浪的缓坡方程两种数值模型比较

本文分析比较了适于不规则水域波浪模拟的椭圆型缓坡方程两种数值模型。两种数值模型均采用有限体积法离散,分别基于四叉树网格和非结构化三角形网格建立。首先结合近岸缓坡地形上波浪传播的经典物理模型实验对两种数值模型分别进行了验证,并结合计算结果对比分析了两种模型的计算精度和效率。计算结果表明,两种数值模型均可有效地模拟近岸波浪的传播变形;相对非结构化三角形网格下的模型,基于四叉树网格建立的数值模型在数值离散和求解过程中无需引入形函数、不产生复杂的交叉项,离散简单,易于程序实现,且节约计算存储空间,计算效率高。     

Baroclinic pressure gradient difference schemes of subtracting the local averaged density stratification in sigma coordinates models

Much has been written of the error in computing the baroclinic pressure gradient (BPG) with sigma coordinates in ocean or atmos- pheric numerical models. The usual way to reduce the error is to subtract area-averaged density stratification of the whole computa- tion region. But if there is great difference between the area-averaged and the local averaged density stratification, the error will be obvious. An example is given to show that the error from this method may be larger than that from no correction sometimes. The definition of local area is put forward. Then, four improved BPG difference schemes of subtracting the local averaged density strat- ification are designed to reduce the error. Two of them are for diagnostic calculation (density field is fixed), and the others are for prognostic calculation (density field is not fixed). The results show that the errors from these schemes all significantly decrease.     

波高非线性概率分布高阶谱数值模型研究

由于波浪的调制不稳定以及非线性波-波相互作用等因素的存在,波浪的分布会偏离线性假设下瑞利分布的结果。通过使用高阶谱模型对不同初始条件下波浪数值模拟。对统计得到的波高与线性理论下的瑞利分布和考虑非线性下改进的埃奇沃思-瑞利（MER）分布和依据Gram-Charlier展开的分布（GC分布）进行对比。结果表明,深水条件下波浪传播过程中偏度值变化较小,而峰度值出现增长。在较小有效波高值的波况下波高分布符合瑞利分布,但随着有效波高值的增加,波浪的非线性增强,波高分布与考虑非线性影响下的GC和MER分布结果相符。宽谱下的波高分布偏离瑞利分布的程度小于窄谱的情况,波高分布更接近瑞利分布的结果。     

A finite difference method for effective treatment of mild-slope wave equation subject to non-reflecting boundary conditions

A numerical model for coastal water wave motion that includes an effective method for treatment of non-reflecting boundaries is presented. The second-order one-way wave equation to approximate the non-reflecting boundary condition is found to be excellent and it ensures a very low level of reflection for waves approaching the boundary at a fairly wide range of the incidence angle. If the Newman approximation is adopted, the resulting boundary condition has a unique property to allow the free propagation of wave components along the boundary. The study is also based on a newly derived mild-slope wave equation system that can be easily made compatible to the one-way wave equation. The equation system is theoretically more accurate than the previous equations in terms of the mild-slope assumption. The finite difference method defined on a staggered grid is employed to solve the basic equations and to implement the non-reflecting boundary condition. For verification, the numerical model is then applied to three coastal water wave problems including the classical problem of plane wave diffraction by a vertical circular cylinder, the problem of combined wave diffraction and refraction over a submerged hump in the open sea, and the wave deformation around a detached breakwater. In all cases, the numerical results are demonstrated to agree very well with the relevant analytical solutions or with experimental data. It is thus concluded that the numerical model proposed in this study is effective and advantageous.     

基于Korteweg-de Vries方程解析解的海洋内波模拟研究

主要是利用非线性发展方程丰富的解析解,基于含有散射项和微扰项的Korteweg-de Vries方程对台湾东北部东海海域内波的传播特性进行研究,并着重分析海洋内波在SAR图像上的信号特征,进而讨论耗散项和微扰项对海洋内波所引起的表层流速变化的影响.     

基于双层Boussinesq方程的三维波浪数值模型及其验证

Liu等给出的最高导数为2的双层Boussinesq水波方程具有较好的色散性和非线性,基于该方程建立了有限差分法的三维波浪数值模型。在矩形网格上对方程进行了空间离散,采用高阶导数近似方程中的时、空项,时间积分采用混合4阶Adams-Bashforth-Moulton的预报—校正格式。模拟了深水条件下的规则波传播过程,计算波面与解析结果吻合较好,反映出数值模型能很好地刻画波面过程及波面处的速度变化;在kh=2π条件下可较为准确获得沿水深分布的水平和垂向速度,这与理论分析结果一致。最后,利用数值模型计算了规则波在三维特征地形上的传播变形,数值结果和试验数据吻合较好;高阶非线性项会对波浪数值结果产生一定的影响,当波浪非线性增强,水深减少将产生更多的高次谐波。建立的双层Boussinesq模型对强非线性波浪的演化具有较好的模拟精度。     

南麂站定常波风浪波高与风速的经验关系

本文以南麂海洋站１９８３～１９９０年风、浪的实测资料为依据，建立了南麂海城春、夏、秋、冬季定常波风浪波高与风速的经验关系式。检验结果表明，曲线回归显著，计算值与实测值吻合良好。文中还对偏ＮＮＥ向和偏ＳＳＷ向计算波高随风速增大的快慢，同一方向在同一风速作用下计算波高的季节变化及其机理作了初浅的讨论。     

Three-dimensional linear solution for wave propagation with slopingbottom

This paper presents a three-dimensional analytic linear wave solution for surface gravity wave propagation over a sloping bottom that is valid for small, but realistic, slopes. The sloping-bottom linear model is compared to published laboratory data and to predictions of two-dimensional, constant-bottom nonlinear theories. The model is shown to describe the measured wave-height growth in the wave transformation region up to a limiting local Ursell number U_r of 0.35-1.0, depending on the wave type, although, as a linear model, it does not predict the harmonics observed in that range. For U_r<0.35, the harmonics can generally be neglected and the sloping-bottom linear theory agrees closely with both the published wave-height data and third-order Stokes nonlinear theory. As a three-dimensional linear model, superposition can be invoked to synthesize and relate wave structure in the transformation region to complex incident ocean spectra with both wind wave and swell components that arrive with a range of incidence angles. As such, the sloping-bottom linear model presented here should be a convenient useful tool for ocean modeling through a significant portion of the wave transformation region     

Evaluation of two spectral wave models for wave hindcasting in the Mackenzie Delta

Climate change, reduced sea ice and increased ice-free waters over extended areas for longer summer periods potentially lead to increased wave energy in the Beaufort Sea (Wang et al., 2015; Khon et al., 2014) [1], [2], which is a major concern for coastal and offshore engineering activities. We compare two spectral wave models SWAN (Simulating WAves Nearshore) and MIKE 21 SW (hereafter MIKE21) in simulations of storm-generated waves in the Mackenzie Delta region of the southern Beaufort Sea. SWAN model simulations are performed using two nested grids system, whereas MIKE21 uses an unstructured grid system. Forcing fields are defined by hourly hindcast winds. Moving ice edge boundaries are incorporated during storm simulations. Modelled wave spectra from four storms are shown to compare well with field observations. Two established whitecapping formulations in SWAN are investigated: one dependent on mean spectral wave steepness, and the other on local spectral steepness. For the Beaufort Sea study area, we suggest that SWAN wave simulations using the latter local spectral steepness formulation are better than those using the former mean spectral steepness formulation. MIKE21 simulations also tend to agree with SWAN results using the latter whitecapping formulation.