Burial and scour of short cylinders under combined random waves and currents including effects of second order wave asymmetry

This paper provides an approach by which the burial and scour of short cylinders under combined second order random waves and currents can be derived. Here the formulas for burial and scour for regular waves plus currents presented by Catano-Lopera and Garcia [Catano-Lopera, Y.A. and Garcia, M.H. (2006). Burial of short cylinders induced by scour under combined waves and currents. ASCE J. Waterway, Port, Coastal and Ocean Eng. 132(6), 439–449., Catano-Lopera, Y.A. and Garcia, M.H. (2007). Geometry of scour hole around, and the influence of the angle of attack on the burial of finite cylinders under combined flows. Ocean Eng. 34(5, 6), 856–869.] are used together with Stokes second order wave theory by assuming the basic harmonic wave motion to be a stationary Gaussian narrow-band random process. An example of calculation is also presented.     

海气动量通量研究综述

海气界面动量通量也称为风应力,是海流和表面海浪的主要驱动力,是海洋从大气获得动量的重要途径。因此,合理可靠的海洋表面风应力的参数化对于海洋、大气和波浪以及气候模式的准确预报都具有非常重要的科学意义和实用价值。对风应力拖曳系数的参数化是风应力参数化的主要内容。近来的观测发现,风应力拖曳系数随着风速的增加出现了先增后减的趋势,同时还与海面的波浪状态以及海流有关。基于观测或理论分析,目前已经得到了一系列的风应力拖曳系数计算方法或公式,有的考虑了海浪的作用,有的没有,但这些方案大都是适合中低风速,在高风速下的适用性还有待检验。本文回顾了目前在海气动量通量观测和参数化方面的研究进展,并建议应增加高风速下风速、海流以及海浪等的同步观测,以进一步完善风应力参数化方案。     

A new kind of nonlinear mild-slope equation for combined refraction-diffraction of multifrequency waves

This paper presents the numerical solution of a new nonlinear mild-slope equation governing waves with different frequency components propagating in a region of varying water depth. There are two new nonlinear equations. The linear part of the equations is the mild-slope equation, and one of the models has the same non-linearity as the Boussinesq equations. The new equations are directly applicable to the problems of nonlinear wave-wave interactions over variable depth. The equations are first simplified with the parabolic approximation, and then solved numerically with a finite difference method. The Crank-Nicolson method is used to discretize the models. The numerical models are applied to a set of published experimental cases, which are nonlinear combined refraction-diffraction with generation of higher harmonic waves. Comparison of the results shows that the present models generally predict the measurements better than other nonlinear numerical models which have been applied to the data set.     

结合抛物型缓坡方程计算波浪辐射应力

将波浪辐射应力与抛物型缓坡方程中的待求变量联系起来,提出了一种计算辐射应力的新方法,并用有限差分法对控制方程进行了数值求解。数值结果表明这种方法精度高、编程简单、求解快速,可用于实际大区域波浪辐射应力的计算。     

Flow under standing waves: Part 1. Shear stress distribution,energy flux and steady streaming

The conditions for energy flux, momentum flux and the resulting streaming velocity are analysed for standing waves formed in front of a fully reflecting wall. The exchange of energy between the outer wave motion and the near bed oscillatory boundary layer is considered, determining the horizontal energy flux inside and outside the boundary layer. The momentum balance, the mean shear stress and the resulting time averaged streaming velocities are determined. For a laminar bed boundary layer the analysis of the wave drift gives results similar to the original work of Longuet–Higgins from 1953. The work is extended to turbulent bed boundary layers by application of a numerical model. The similarities and differences between laminar and turbulent flow conditions are discussed, and quantitative results for the magnitude of the mean shear stress and drift velocity are presented. Full two-dimensional simulations of standing waves have also been made by application of a general purpose Navier–Stokes solver. The results agree well with those obtained by the boundary layer analysis. Wave reflection from a plane sloping wall is also investigated by using the same numerical model and by physical laboratory experiments. The phase shift of the reflected wave train is compared with theoretical and empirical models.     

Alternative forms of the higher-order Boussinesq equations: Derivations and validations

An alternative form of the Boussinesq equations is developed, creating a model which is fully nonlinear up to O(μ⁴) (μ is the ratio of water depth to wavelength) and has dispersion accurate to the Padé [4,4] approximation. No limitation is imposed on the bottom slope; the variable distance between free surface and sea bottom is accounted for by a σ-transformation. Two reduced forms of the model are also presented, which simplify O(μ⁴) terms using the assumption ε = O(μ^2/3) (ε is the ratio of wave height to water depth). These can be seen as extensions of Serre's equations, with dispersions given by the Padé [2,2] and Padé [4,4] approximations. The third-order nonlinear characteristics of these three models are discussed using Fourier analysis, and compared to other high-order formulations of the Boussinesq equations. The models are validated against experimental measurements of wave propagation over a submerged breakwater. Finally, the nonlinear evolution of wave groups along a horizontal flume is simulated and compared to experimental data in order to investigate the effects of the amplitude dispersion and the four-wave resonant interaction.     

Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications

Regional Ocean Modeling System (ROMS v 3.0), a three-dimensional numerical ocean model, was previously enhanced for shallow water applications by including wave-induced radiation stress forcing provided through coupling to wave propagation models (SWAN, REF/DIF). This enhancement made it suitable for surf zone applications as demonstrated using examples of obliquely incident waves on a planar beach and rip current formation in longshore bar trough morphology (Haas and Warner, 2009). In this contribution, we present an update to the coupled model which implements a wave roller model and also a modified method of the radiation stress term based on Mellor (2008, 2011a,b,in press) that includes a vertical distribution which better simulates non-conservative (i.e., wave breaking) processes and appears to be more appropriate for sigma coordinates in very shallow waters where wave breaking conditions dominate. The improvements of the modified model are shown through simulations of several cases that include: (a) obliquely incident spectral waves on a planar beach; (b) obliquely incident spectral waves on a natural barred beach (DUCK'94 experiment); (c) alongshore variable offshore wave forcing on a planar beach; (d) alongshore varying bathymetry with constant offshore wave forcing; and (e) nearshore barred morphology with rip-channels. Quantitative and qualitative comparisons to previous analytical, numerical, laboratory studies and field measurements show that the modified model replicates surf zone recirculation patterns (onshore drift at the surface and undertow at the bottom) more accurately than previous formulations based on radiation stress (Haas and Warner, 2009). The results of the model and test cases are further explored for identifying the forces operating in rip current development and the potential implication for sediment transport and rip channel development. Also, model analysis showed that rip current strength is higher when waves approach at angles of 5° to 10° in comparison to normally incident waves.     

A coupled-mode system with application to nonlinear water waves propagating in finite water depth and in variable bathymetry regions

A non-linear coupled-mode system of horizontal equations is presented, modelling the evolution of nonlinear water waves in finite depth over a general bottom topography. The vertical structure of the wave field is represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional terms, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The present coupled-mode system fully accounts for the effects of non-linearity and dispersion, and the local-mode series exhibits fast convergence. Thus, a small number of modes (up to 5–6) are usually enough for precise numerical solution. In the present work, the coupled-mode system is applied to the numerical investigation of families of steady travelling wave solutions in constant depth, corresponding to a wide range of water depths, ranging from intermediate depth to shallow-water wave conditions, and its results are compared vs. Stokes and cnoidal wave theories, as well as with fully nonlinear Fourier methods. Furthermore, numerical results are presented for waves propagating over variable bathymetry regions and compared with nonlinear methods based on boundary integral formulation and experimental data, showing good agreement.     

Impacts of a wind stress and a buoyancy flux on the seasonal variation of mixing layer depth in the South China Sea

The seasonal variation of mixing layer depth(MLD) in the ocean is determined by a wind stress and a buoyance flux.A South China Sea(SCS) ocean data assimilation system is used to analyze the seasonal cycle of its MLD.It is found that the variability of MLD in the SCS is shallow in summer and deep in winter,as is the case in general.Owing to local atmosphere forcing and ocean dynamics,the seasonal variability shows a regional characteristic in the SCS.In the northern SCS,the MLD is shallow in summer and deep in winter,affected coherently by the wind stress and the buoyance flux.The variation of MLD in the west is close to that in the central SCS,influenced by the advection of strong western boundary currents.The eastern SCS presents an annual cycle,which is deep in summer and shallow in winter,primarily impacted by a heat flux on the air-sea interface.So regional characteristic needs to be cared in the analysis about the MLD of SCS.     

Temporal and spatial variability of sea level and volume flux in the Murderkill Estuary

The instantaneous sea level determined at two sites in the Murderkill Estuary, a tributary of Delaware Bay, results from the superposition of temporal variability operating over different time and spatial scales. Over the relatively short tidal time scales, the semidiurnal tides that represent the dominant tidal constituents in lower Delaware Bay show a modest increase in tidal amplitudes from the bay mouth (Lewes, Delaware), up to Bowers Beach (the mouth of the Murderkill Estuary). However, as the tides propagate into the Murderkill Estuary, the semidiurnal constituents undergo heavy attenuation, resulting in a 48% reduction in tidal amplitude from Bowers to Frederica (approximately the extent of saline intrusion). The diurnal tide, on the other hand, experiences only a 25% reduction in amplitude. The limited tidal asymmetry that is observed may be a result of interaction between flows in the tidal channel and the adjacent salt marsh. At longer time scales, the subtidal sea level experiences no attenuation. The Murderkill Estuary thus behaves like a low pass filter to preferentially damp out high frequency sea level forcing from lower Delaware Bay. The subtidal volume flux in the Murderkill is highly coherent with the time rate of change of sea level, indicating that the Murderkill basically co-oscillates with Delaware Bay in a standing wave fashion over the subtidal time scale. This remote coupling controls more than 90% of the variance in subtidal sea level in the estuary. The surface slopes in the lower bay and the Murderkill Estuary are closely correlated with winds along the orientation of the two waterways, consistent with the effect of local wind on subtidal sea level.     

近岸海域水沙界面通量与水流挟沙力研究

近岸海域的波浪、潮流及海流等动力因素具有周期性和时间、空间尺度差异大的特点,在综合考虑各动力因子的联合作用时具有较大的难度。本文根据平动动能叠加原理给出了一种近岸动力因子的表达形式,并提出了海洋波动有效速度的概念,结合水沙界面处泥沙通量的切应力与挟沙力关系,得到了水流挟沙力的新的计算公式。指出了水流挟沙力与水流临界速度有关,并且该水流临界速度随水深的增大及相对糙率的减小而增大。采用近岸实测数据和模拟结果,对本文的近岸水流挟沙力公式进行了验证,结果表明该公式的计算值与实测值吻合较好,可以适用于近岸海域。     

Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone

In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.     

A 3-D model based on Navier–Stokes equations for regular and irregular water wave propagation

A spatial fixed σ-coordinate is used to transform the Navier–Stokes equations from the sea bed to the still water level. In the fixed σ-coordinate system only a very small number of vertical grid points are required for the numerical model. The time step for using the spatial fixed σ-coordinate is efficiently larger than that of using a time dependent σ-coordinate, as there is substantial truncation error involved in the time dependent σ-coordinate transformation. There is no need to carry out the σ-coordinate transformation at each time step, which can reduce computational times. It is important that wave breaking can be potentially modeled in the fixed σ-coordinate system, but in a time-dependent σ-coordinate system the wave breaking cannot be modeled. A projection method is used to separate advection and diffusion terms from the pressure terms in Navier–Stokes equations. The pressure variable is further separated into hydrostatic and hydrodynamic pressures so that the computer rounding errors can be largely avoided. In order to reduce computational time of solving the hydrodynamic pressure equation, at every time step the initial pressure is extrapolated in time domain using computed pressures from previous time steps, and then corrected in spatial domain using a multigrid method. For each time step, only a few of iterations (typically six iterations) are required for solving the pressure equation. The model is tested against available experimental data for regular and irregular waves and good agreement between calculation results and the measured data has been achieved.     

Exact solution and approximate solution of irregular wave radiation stress for non-breaking wave

Wave radiation stress is the main driving force of wave-induced near-shore currents. It is directly related to the hydrodynamic characteristics of near-shore current whether the calculation of wave radiation stress is accurate or not. Irregular waves are more capable of reacting wave motion in the ocean compared to regular waves.Therefore, the calculation of the radiation stress under irregular waves will be more able to reflect the wave driving force in the actual near-shore current. Exact solution and approximate solution of the irregular wave radiation stress are derived in this paper and the two kinds of calculation methods are compared. On the basis of this, the experimental results are used to further verify the calculation of wave energy in the approximate calculation method. The results show that the approximate calculation method of irregular wave radiation stress has a good accuracy under the condition of narrow-band spectrum, which can save a lot of computing time, and thus improve the efficiency of calculation. However, the exact calculation method can more accurately reflect the fluctuation of radiation stress at each moment and each location.     

2016年夏季北冰洋浮冰站近地层辐射和湍流通量观测

2016年8月7－14日中国第七次北极科学考察期间,在83°N附近设立的长期浮冰站开展了辐射和湍流通量观测研究。结果表明,观测期间反照率变化范围为0.64~0.92,平均反照率为0.78;基于现场观测数据评估了PW79、HIRHAM、ARCSYM和CCSM3 4种不同复杂度的反照率参数化方案在天气尺度的表现,最为复杂的CCSM3结果优于其他参数化方案,但不能体现降雪条件下的反照率快速增长。浮冰区冰雪面平均净辐射为18.10 W/m2,平均感热通量为1.73 W/m2,平均潜热通量为5.55 W/m2,海冰表面消融率为（0.30±0.22） cm/d,表明此时北冰洋浮冰正处于快速消融期。冰面的平均动量通量为0.098（kg·m/s）/（m2·s）,动量通量与风速有很好的对应关系,相关系数达0.80。     

基于全和谐型浅水方程的有限体积海啸数值模型开发与应用

数值模拟作为海啸预报的主要研究方法在海啸预警中起着关键作用。本文采用Godunov格式的有限体积方法,使用MUSCL-Hancock格式,并利用HLLC Riemann近似求解器计算单元界面上的流体通量,建立了球坐标系下二阶精度的海啸数值模型。模型所基于的全和谐型浅水方程保证了数值的稳定性,而地形重构方法实现了干湿边界的精准模拟。本文模拟了2015年9月16日智利M_w8.3级地震海啸,通过与智利近岸14个测站和环太平洋20个DART浮标实测数据比较,验证了模型对实际越洋海啸模拟预报的能力。     

On the radiation and diffraction of water waves by a rectangular structure with a sidewall

A radiation and diffraction boundary value problem is investigated. It arises from the interaction of linear water waves with a freely floating rectangular structure in a semi-infinite fluid domain of finite water depth with the leeward boundary being a vertical wall. Analytical expressions for the radiated potentials and the diffracted potential are obtained by use of the method of separation of variables and the eigenfunction expansion method. The added masses and damping coefficients for the structure heaving, swaying and rolling in calm water are obtained by use of the corresponding radiated potentials and the wave excitation forces are calculated by use of the diffracted potential. To verify the correctness of the method, a boundary element method is used. A comparison of the analytical results with those obtained by the boundary element method is made and good agreement is achieved, which shows that the analytical expressions for the radiated and diffracted potentials are correct. By use of the present analytical solution, the added mass, damping coefficients, wave excitation force, together with the hydrodynamic effects of the draft, width of the structure and the clearance between the structure and the sidewall are also investigated.     

Validation of the three-wave quasi-kinetic approximation for the spectral evolution in shallow water

This paper aims at validating the three-wave quasi-kinetic approximation for the spectral evolution of weakly nonlinear gravity waves in shallow water. The problem is investigated using a one-dimensional numerical wave propagation model, formulated in the spectral representation. This model includes both a nonlinear triad interactions term and a wave breaking dissipation term. Some numerical tests were carried out in order to show the importance of using the triad nonlinear term in wave propagation spectral models, particularly to describe both behavior of the spectral integral parameters and of the spectral shape evolution in shallow water depth. Furthermore; a comparison against different set of experimental observations was carried out. Comparing the numerical results with the experimental observations made it possible to show the modeling efficiency of the three-wave quasi-kinetic approximation.     

潮汐河口断面悬沙通量组分模式及其在长江口的应用

断面泥沙通量估算的误差主要来源于计算方法、测点布局等,通量模式应该建立在通量估算统计误差最小的原则基础之上.在断面网格设计中采用统计误差最小的等面积单元网格,在泥沙通量估算中采用泥沙组分浓度,在流速变量插值上垂向采用对数函数插值,横向采用第一边界三次方样条函数插值.这样建立的潮汐河口悬沙断面通量组分模式较以往的任何模式更完善,断面通量估算的误差最小.将该模式应用于长江河口南港断面悬沙通量估算及其输移机制分析,断面泥沙通量表现为大潮期大进大出、大出大于大进;小潮期小进小出、小出大于小进;主要输移机制是拉格朗日输移和潮泵.