Calculation of Interannual Variations of Sea Level in the Subtropical North Pacific

The interannual variations of sea level at Chichi-jima and five other islands in the subtropical North Pacific are calculated for 1961–95 with a model of Rossby waves excited by wind. The Rossby-wave forcing is significant east of 140°E. Strong forcing of upwelling (downwelling) Rossby wave occurs during El Niño (La Niña) and warm (cold) water anomaly in the eastern equatorial Pacific. The first and second baroclinic modes of Rossby wave are more strongly generated than the barotropic mode in the study area. A higher vertical mode of Rossby wave propagates more slowly and is more decayed by eddy dissipation. The best coefficient of vertical eddy dissipation is determined by comparing the calculated sea level with observation. The variation in sea level at Chichi-jima is successfully calculated, in particular for the long-term change of the mean level between before and after 1986 with a rise in 1986 as well as the variations with periods of two to four years after 1980. It is concluded that variations of sea level at Chichi-jima are produced by wind-forced Rossby waves, the first baroclinic wave primarily and the barotropic wave secondly. The calculation for other islands is less successful. Degree of the success in calculation almost corresponds to a spatial difference in quantity of wind data, and seems to be determined by quality of wind data.     

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.     

On a theoretical model of rough turbulent wave boundary layers

An analytical theory which describes the motion in a turbulent wave boundary layer near a rough sea bottom by using a two-layer time invariant eddy viscosity model is presented. The eddy viscosity in the inner layer increases quadratically with the height above the sea bottom. In the outer layer the eddy viscosity is taken as a constant. The mean velocity and shear stress profiles, the bottom shear stress and the bottom friction coefficient are presented, and comparisons are made with experimental results.     

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.     

Energy balance of wind waves as a function of the bottom friction formulation

Four different expressions for wave energy dissipation by bottom friction are intercompared. For this purpose, the SWAN wave model and the wave data set of Lake George (Australia) are used. Three formulations are already present in SWAN (ver. 40.01): the JONSWAP expression, the drag law friction model of Collins and the eddy–viscosity model of Madsen. The eddy–viscosity model of Weber was incorporated into the SWAN code. Using Collins' and Weber's expressions, the depth- and fetch-limited wave growth laws obtained in the nearly idealized situation of Lake George can be reproduced. The wave model has shown the best performance using the formulation of Weber. This formula has some advantages over the other formulations. The expression is based on theoretical and physical principles. The wave height and the peak frequency obtained from the SWAN runs using Weber's bottom friction expression are more consistent with the measurements. The formula of Weber should therefore be preferred when modelling waves in very shallow water.     

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.     

高频表面波对定常Ekman流解的影响

基于Jenkins(1989)建立的包含Stokes漂流、风输入和波耗散影响的修正Ekman模型,采用Paskyabi等(2012)使用的推广的Donelan等(1987)中的谱和波耗散函数,并利用Paskyabi等(2012)中修正方法给出的包含高频波的风输入函数,在粘性不依赖于水深及粘性随深度线性变化的条件下,研究了包含高频毛细重力波的随机表面波对Stokes漂流和Song(2009)导出的波浪修正定常Ekman流解的影响。结果表明高频表面波使Stokes漂流在海表面剪切加强,对定常Ekamn流解的影响通常不能忽略,但对Ekman流场的角度偏转影响很小。最后,将考虑高频表面波尾谱影响所估算的定常Ekman流解与已有观测结果以及经典Ekman解进行了比对分析。     

Eddy viscosities and velocities in combined wave-current flows

The eddy viscosities for the steady and the periodic components of combined wave-current flows have been studied quantitatively from the presently available experimental data. It has been found that inside the boundary interaction layer [z < δ] the eddy viscosity ε_c for the steady flow is increased in the presence of waves while outside the boundary interaction layer [z >δ] it is affected little by the wave motion, and that the eddy viscosity ε_w for the wave motion in the boundary layer is independent of the current strength U^*. On the other hand, a new eddy viscosity model is presented to give a good prediction of the velocity distributions of the waves and currents in comparison with experimental data.     

Quasi-linear model of interaction of surface waves with strong and hurricane winds

A quasi-linear model for determining the aerodynamic drag coefficient of the sea surface and the growth rate of surface waves under a hurricane wind is proposed. The model explains the reduction (stabilization) in the drag coefficient during hurricane winds. This model is based on the solution of the Reynolds equations in curvilinear coordinates with the use of the approximation of the eddy viscosity, which takes into account the presence of the viscous sublayer. The profile of the mean wind velocity is found with consideration for nonlinear wave stresses (wave momentum flux), whereas wave disturbances induced in air by waves on the water surface are determined in the context of linear equations. The model is verified by comparing the calculation results with experimental data for a wide range of wind velocities. The growth rate and drag coefficient for hurricane winds are calculated both with and without consideration for the shortwave portion of the windwave spectrum. On the basis of calculations with the quasi-linear model, a simple parametrization is proposed for the drag coefficient and the growth rate of surface waves during hurricane winds. This model is convenient for use in models of forecasting winds and waves.     

基于选定风浪方向谱的海浪模拟方法(英文)

简要回顾当前第三代海浪模式中的困难。为避开这些困难,作者提出一种新的海浪模拟方法,其中特定定义的风浪组成波依常风下随时间成长的方向谱计算,而涌浪组成波藉考虑涡动黏性和底摩擦加以计算。并进行了常风场和变风场下系统的数值试验。在常风速情形中,模拟结果能精确地化为建立模拟所根据的谱和风浪成长关系。计算显示出台风中心附近浪场的极端复杂的谱结构。当风速骤然降低时,模拟的波高减小与观测符合。在风向逐渐或骤然改变情形下,计算的时间响应尺度与海上观测符合,而且演化中的二维谱结构得到良好刻画。对于涌浪在无风下的传播,模拟结果合理,包括波参量及谱结构的变化。后报得到的波高、周期和海上资料符合。与第三代模式相比,文中提出的方法较易改进,需用的计算机时间显著减少。最后讨论采用一个已知谱来建立谱形式的海浪预报模型的合理性以及有关的问题。     

Numerical modeling of multi-directional irregular waves incorporating 2-D numerical wave absorber and subgrid turbulence

In this paper, a finite difference scheme with an efficient 2-D numerical wave absorber for solving the extended Boussinesq equations as derived by Nwogu (Nwogu, O., 1993. Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterway, Port, Coastal and Ocean Engineering, ASCE 119, 618–638) is proposed. The alternate direction iterative method combined with an efficient predictor-corrector scheme are adopted for the numerical solution of the governing differential equations. To parameterize the contribution of unresolved small-scale motions, the philosophy of the large eddy simulation is applied on the horizontal plane. The proposed method is verified by two test cases where experimental data are available for comparison. The first case is wave diffraction around a semi-infinite breakwater studied by Briggs et al. (Briggs, M.J., Thompson, E.F., Vincent, C.L., 1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE 121, 23–35). The other case is wave concentration by a navigation channel as reported by Yu et al. (Yu, Y.-X., Liu, S.-X., Li, Y.S., Wai, O.W.H., 2000. Refraction and diffraction of random waves through breakwater. Ocean Engineering 27, 489–509). Numerical results agree very well with the corresponding experimental data in both cases.     

Contributions to dynamics of the Antarctic Circumpolar Current (A.C.C.) (I. Zonal transport)

Scaling of the equations of motion of the Antarctic Circumpolar Current indicates that the Rossby number and the Ekman number are 10⁻⁴ to 10⁻⁵ but the vertical Ekman number may reach unity in the bottom boundary layer. The equations of motion are integrated vertically from the surface to the bottom and averaged over a latitude circle. The resulting equation in the meridional direction is predominantly geostrophic, whereas the main terms of the equation in the zonal direction are the wind stress and the bottom stress. When the vertical eddy viscosity near the bottom is of the order of 10²cm²/sec, the total zonal transport through the Drake Passage computed from the balance of the wind stress and the bottom stress equals 260×10⁶m³/sec, the amount determined byReid andNowlin (1970) from observations. The northward transport reduces the eastward transport corresponding to the wind stress of the westerlies in the A. C. C. through the Coriolis' term in the vertically integrated equation of motion of the zonal direction. South of the Drake Passage, such reduction reaches about ten percent of the wind-driven transport mainly due to the peripheral water discharge. North of the Drake Passage, the northward transport may be generated by the effect of the South American coast which prevents free eastward movement of the A. C. C., causing a wake to the east. This transport may contribute to a part of the northward transport of the bottom water postulated byMunk (1966). The effect of the horizontal eddy viscosity in the zonal transport equation is negligible except near the Antarctic coast, if the eddy viscosity is less than 10⁹cm²/sec.     

Three dimensional modal model of wind induced flow in a sea region

The solution of the linear three dimensional hydrodynamic equations describing wind induced flow in a sea region is developed using the Galerkin method through the vertical. A basis set of B-splines is shown to have some computational advantages over a set of eigenfunctions (vertical modes). However, a basis set of modes leads to a system of essentially uncoupled equations and current profiles can be interpreted in terms of vertical modes.The influence of wind induced surface turbulence and turbulence at depth due to tidal motion upon current profiles in both deep (260 m) and shallow (35 m) sea regions is examined. The variation in the angle between surface current and surface wind for different viscosity profiles, and the effect of bottom friction upon it is considered.The magnitude and direction of the surface current is significantly influenced by surface eddy viscosity. However, viscosity at depth due to tidal motion also has an important effect upon the surface current.The time evolution of current structure following the sudden onset of a wind is examined using the modal model. Calculations show that the rate of damping of the internal modes is inversely proportional to the square of the depth. Consequently wind induced current structure takes longer to reach a steady state in a deep sea region than a shallow area.The influence of sea surface elevation gradients in determining the direction of surface current is also considered.     

苏门答腊岛西北海域中尺度涡源区特征与形成机制

孟加拉湾内和湾口附近有丰富的中尺度现象,本文利用2.0版可分辨低纬地区中尺度涡的Chelton数据集,通过溯源的方法得到中尺度涡的源地分布。苏门答腊岛西北海域(以5°N,94°E为核心的区域)是中尺度涡重要源区之一。通过拉格朗日方法的涡旋追踪表明,1993—2017年该海域(3°N—6°N、92°E—95°E),分别有57个气旋式和40个反气旋式中尺度涡。频谱分析显示海表面高度异常存在180 d和360 d两个显著周期。地形和风场的共同作用是该海域产生中尺度涡的动力机制：沿5°N西传的罗斯贝波在海岭地形的作用下触发了中尺度涡的生成;赤道风场是源区重要的能量来源,局地风场能诱发中尺度涡的极性。本研究也揭示了以往文献虽刻画了苏门答腊岛西北部海域为高涡动能区,却没有识别出较多中尺度涡的原因。     

Interannual Variations of Sea Level at the Nansei Islands and Volume Transport of the Kuroshio Due to Wind Changes

Interannual variations of sea level at the Nansei Islands and volume transport of the Kuroshio during 1967–95 are calculated by integrating variations carried by windforced Rossby waves. Effects of eddy dissipation and ocean ridges are considered. Ridge effect is inferred by comparing between the calculated and observed sea levels. The calculation is satisfactory to sea levels and Kuroshio transport for the whole period. They are mostly caused by Rossby waves forced by wind and modified by the ridges, and are due to barotropic wave primarily and the first baroclinic wave secondly. The calculated Kuroshio transport well represents variations of several-year scales with maximums in respective duration of the large meander (LM) of the Kuroshio, as well as bi-decadal variation that transport was small during the non-LM period of 1967–75 and large during the LM-dominant period of 1975–91. Mean volume transport of the subtropical gyre is estimated at 57 Sv (1 Sv = 10⁶ m³s^–1) and divided by the Nansei Shoto Ridge into those of the Kuroshio in the East China Sea (25.5 Sv) and a subsurface current east of this ridge (31.5 Sv). The Subtropical Countercurrent and a southward deep current east of the Izu-Ogasawara Ridge are estimated at 16 Sv and 7 Sv, respectively. The calculated transports of the Kuroshio and other subtropical currents reach maximums at every El Niño event due to strong excitement of upwelling barotropic Rossby wave.     

海流流速计算的研究

由于大范围同步连续观测海流流速很困难,这才产生建立一定的理论及方法认真计算海流流速的要求.可是,过去沿用至今的动力计算[1],方法虽简便,但只能计算因密度分布所生的梯度流(或地转流),且存在着既不考虑风力,又不顾及湍流摩擦力,再加无运动面难以确定,即令设法作出浅海订正,其结果又往往与事实不符等根本性缺陷;而如籍Ekman漂流理论计算海流,又仅能计算因风所生的漂流,且还存在着既不考虑海水密度分布,又视海面无倾斜,再加湍流动力粘滞系量难以确定等与实际相差较远的理论依据.近代兴起的一些海流数值计算,又往往都局限于全流或深度平均流速的计算.因此,建立一种既考虑到海洋内部海水分布,又考虑到海面风力外加海面大气压力作用,顾及到海洋中湍流摩擦力,又体现流速随深度变化,而更重要的是应用起来简易的计算海流流速的理论及方法,便成为很需要解决的问题了.     

The effects of random surface waves on the steady Ekman current solutions

The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42, 134–149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313–351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313–351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971–5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift.     

Coastal-Trapped Waves with Several-Day Period Caused by Wind along the Southeast Coast of Honshu, Japan

Generation and propagation of several-day period fluctuations along the southeast coast of Honshu, Japan, were investigated by analyzing sea level data and by using a numerical model. The sea level data obtained at twelve stations from Choshi to Omaezaki in fall in 1991, showed energy peaks at the 3–6 day period at the eastern stations in this coast. Time lags of the 3–6 day period fluctuations between station and station indicate westward propagation along the coast. However, the energy level of the 3–6 day period fluctuations suddenly decreased south of the Izu Peninsula. Numerical experiments using a two-layer model were performed to clarify the generation and propagation mechanism of the several-day period fluctuations by periodical wind in fall. The amplitude distributions of observed sea level were qualitatively explained by a coastal-trapped wave (CTW) in the numerical experiment. From the discussions on propagation of a free wave, CTW with the characteristics of a shelf wave generated by the wind along the northeast of the Boso Peninsula was separated into two types of wave at the southeast of the peninsula. One is an internal Kelvin wave with large interface displacement and the other is the shelf wave propagating over the northern part of the Izu Ridge. The sudden decrease in the surface displacement with the 3–6 day period observed at the western stations is considered to be due to the local effect of the wind and phase relation between the internal Kelvin wave and shelf wave.     

台风暴潮某些特性的分析

台风暴潮的机制和预报,国内已有不少的研究,国外虽然亦进行了许多的研究,但就理论而言,大都局限于全流观点进行分析,从而得出较理想化的结果[1,2]。本文试图直接从线性化了的流体力学运动方程出发,导出适用于浅海中移行风暴所导致的风暴潮的理论模式,以研究其某些特性。     

Wave crest and trough distributions in a broad-banded directional wave field

It is well established that the modulational instability enhances the probability of occurrence for extreme events in long crested wave fields. Recent studies, however, have shown that the coexistence of directional wave components can reduce the effects related to the modulational instability. Here, numerical simulations of the Euler equations are used to investigate whether the modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. The case of a broad-banded directional wave field (i.e. wind sea) is investigated. The analysis is concentrated on the wave crest and trough distribution. For completeness a comparison with a unidirectional wave field is presented also. Results will show that the distributions based on second-order theory provide a good estimate for the simulated crest and trough height also at low probability levels.