Analytic solution of long wave propagation over a submerged hump

A new analytical solution of the long wave refraction by a submerged circular hump is presented. The geometry of the hump is assumed to be axisymmetric and be described by a power function in the radial direction with arbitrary values of both the exponent and the scaling factor. The submergence of the hump is also variable. The water surface elevation governed by the long wave version of the mild slope wave equation is solved by separation of variables, and a series solution of the Frobenius type is obtained. The solution is shown to be valid when the hump is sufficiently submerged or is of a relatively small height. Matching method is employed to illustrate the refraction of long waves under given conditions of incidence. Effects of the shape, the scale, and the submergence of the hump on wave refraction are discussed.     

孤立波在岸礁地形上传播与爬坡数值模拟研究

为准确模拟孤立波在岸礁地形上的传播和爬坡,采用基于完全非线性Boussinesq方程开发的Funwave-TVD模型,探究模型的可行性,并利用验证后的模型进一步研究岸礁各地形因素对孤立波爬高的影响。研究结果表明:模型能准确模拟孤立波在岸礁陡变地形上的传播及变形,摩擦系数对礁前陡坡及礁坪上的波浪传播模拟影响不大,但对爬坡预测的敏感性较强;模型空间步长可适当增大,提高计算效率;随着礁坪宽度的增大以及礁后斜坡的变缓,孤立波爬坡高度下降明显,而礁前陡坡坡度变化对孤立波爬坡高度影响不大。     

有限长正弦地形上的波浪传播问题研究

应用基于势流理论的频域边界元方法,研究了波浪在有限长正弦周期地形上的传播问题.开展了网格收敛性分析,并与物理模型试验结果做了对比,验证了数值方法的准确性.研究了正弦地形长度和幅度对水波反射率的影响,以及波浪在周期性地形上传播时的沿程波幅变化.研究发现,波浪反射系数随波数的变化及波浪幅值沿程的变化均呈包络状;当频率处于布拉格共振区域边缘且反射率为零时,周期地形上会出现极大的波幅;随海床波幅增大,第一布拉格共振带变宽且向低频移动.     

礁坪上波浪传播的数值模拟

本文基于具备间断捕捉能力的二阶全非线性Boussinesq数值模型,对规则波和随机波在礁坪地形上的传播变形进行了数值模拟。该模型采用高阶有限体积法和有限差分方法求解守恒格式的控制方程,将波浪破碎视为间断,同时采用静态重构技术处理了海岸动边界问题。重点针对礁坪上波浪传播过程中的波高空间分布和沿程衰减,礁坪上的平均水位变化,以及波浪能量频谱的移动和空间差异等典型水动力现象开展数值计算。将数值结果与实验结果对比,两者吻合情况良好,验证了模型具有良好的稳定性,具备模拟破碎波浪和海-岸动边界的能力,能较为准确地模拟波浪在礁坪地形上的传播过程中发生的各种水动力现象。     

Bottom friction and its effects on periodic long wave propagation

A new set of Boussinesq-type equations describing the free surface evolution and the corresponding depth-integrated horizontal velocity is derived with the bottom boundary layer effects included. Inside the boundary layer the eddy viscosity gradient model is employed to characterize Reynolds stresses and the eddy viscosity is further approximated as a linear function of the distance measured from the seafloor. Boundary-layer velocities are coupled with the irrotational velocity in the core region through boundary conditions. The leading order boundary layer effects on wave propagation appear in the depth-integrated continuity equation to account for the velocity deficit inside the boundary layer. This formulation is different from the conventional approach in which a bottom stress term is inserted in the momentum equation. An iterative scheme is developed to solve the new model equations for the free surface elevation, depth-integrated velocity, the bottom stress, the boundary layer thickness and the magnitude of the turbulent eddy viscosity. A numerical example for the evolution of periodic waves propagating in one-dimensional channel is discussed to illustrate the numerical procedure and physics involved. The differences between the conventional approach and the present formulation are discussed in terms of the bottom frictional stress and the free surface profiles.     

近岸流对波浪传播影响的数值分析

使用近岸波浪模型SWAN计算存在沿岸流和离岸流时的近岸波浪传播。先设离岸流u=0m/s,模拟均匀、非均匀沿岸流的流速和梯度对波高传播的影响;再设沿岸流v=0.5m/s,模拟均匀、非均匀离岸流的流速和梯度对波能高传播的影响。从模拟中得到,近岸波浪传播受沿岸流、离岸流的流速和梯度影响时,波高的变化规律。     

A two-point method for estimating wave reflection over a sloping beach

This work presents a frequency-domain method for estimating incident and reflected waves when normally incident waves’ propagating over a sloping beach in a wave flume is considered. Linear wave shoaling is applied to determine changes of the wave amplitude and phase due to variations of the bathymetry. The wave reflection coefficient is estimated using wave heights measured at two fixed wave gauges with a distance. The present model demonstrates a high capacity of estimating reflection and shoaling coefficients from synthetic wave-amplitude data. Sensitivity tests for the present model due to measurement errors of wave amplitudes and distance of two probes can more accurately predict the reflection coefficients. The measurement error of wave amplitude affects more significantly than measurement error of distance of two probes on calculating reflection coefficient of waves over a sloping bed.     

Numerical simulation of solitary wave propagation based on MPS method

The concept of candidate particle set is introduced in the MPS gridless numerical method to generate neighboring particle set matrix, which can reduce the CPU time to 1/11 of that before introduction. The Bi-CGSTAB (bi-conjugate gradient stabilized) algorithm is applied to solving the Poisson pressure equation, by which the solving speed is significantly accelerated. The process of solitary waves propagating over a numerical flume and interacting with a vertical wall is simulated. The simulated results of water surface elevation are in good agreement with the analytical solution as well as the measured data. The predicted maximum values of the run-up of solitary waves with various relative incident wave heights agree well with the measured results.     

Modeling of nonlinear wave propagation over fringing reefs

The applicability of existing nonlinear (triad) spectral models for steep slopes (0.1–0.2) characteristic of reef environments was investigated, using both deterministic (phase-resolving) and stochastic (phased-averaged) formulations. Model performance was tested using laboratory observations of unidirectional wave transformation over steep and smooth bathymetry profiles. The models, developed for mild slopes, were implemented with minimal modifications (the inclusion of breaking parametrizations and linear steep-slope corrections) required by laboratory data. The deterministic model produced typically more accurate predictions than the stochastic one, but the phase averaged formulation proved fast enough to allow for an inverse modeling search for the optimal breaking parametrization. The effects of the additional assumptions of the stochastic approach resulted in a slower than observed evolution of the infragravity band. Despite the challenge posed by the fast wave evolution and energetic breaking characteristic to the steep reef slopes, both formulations performed overall well, and should be considered as good provisional candidates for use in numerical investigation of wave–current interaction processes on steep reefs.     

基于MPS无网格方法的孤立波传播的数值模拟

在MPS无网格方法中,引进预定候选粒子集概念用以生成邻接粒子集矩阵,使该部分的机时耗费缩短为引进前的1/11;采用Bi-CGSTAB方法求解压力泊松方程,显著地提高了求解速度.模拟了孤立波在数值波浪水槽中的传播及其与直墙作用时的爬升、回落过程,结果表明模拟波面结果与解析值及实测结果基本相符,针对不同波高的孤立波计算得到的墙前最大爬升值与实测结果也是一致的.     

斜坡平台波浪破碎数值模拟

波浪在斜坡地形上破碎,破波后稳定波高多采用物理模型试验方法进行研究,利用近岸波浪传播变形的抛物型缓坡方程和波能流平衡方程,导出了适用于斜坡上波浪破碎的数值模拟方法。首先根据波能流平衡方程和缓坡方程基本型式分析波浪在破波带内的波能变化和衰减率,推导了波浪传播模型中波能衰减因子和破波能量流衰减因子之间的关系;其次,利用陡坡地形上的高阶抛物型缓坡方程建立了波浪传播和波浪破碎数学模型;最后,根据物理模型试验实测数据对数值模拟的效果进行验证。数值计算与试验资料比较表明,该模型可以较好地模拟斜坡地形的波浪传播波高变化。     

Numerical study of enhanced energy dissipation near a seamount

Using a two-dimensional primitive equation model, we examine nonlinear responses of a semidiurnal tidal flow impinging on a seamount with a background Garrett-Munk-like (GM-like) internal wavefield. It is found that horizontally elongated pancake-like structures of high vertical wavenumber near-inertial current shear are created both in the near-field (the region over the slope of the seamount) and far-field (the region over the flat bottom of the ocean). An important distinction is that the high vertical wavenumber near-inertial current shear is amplified only at mid-latitudes in the far-field (owing to a parametric subharmonic instability (PSI)), whereas it is amplified both at mid-and high-latitudes (above the latitude where PSI can occur) in the near-field. In order to clarify the generating mechanism for the strong shear in the near-field, additional numerical experiments are carried out with the GM-like background internal waves removed. The experiments show that the strong shear is also created, indicating that it is not caused by the interaction between the background GM-like internal waves and the semidiurnal internal tides. One possible explanation is proposed for the amplification of high vertical wavenumber near-inertial current shear in the near-field where tide residual flow resulting from tide-topography interaction plays an important role in transferring energy from high-mode internal tides to near-inertial internal waves.     

Numerical experiments on estimating the accuracy of four-dimensional analysis of hydrophysical fields using a quasi-geostrophic model of currents

The relationship between the results of four-dimensional (4-D) analysis and the approximations employed in the assimilation scheme, as well as the initial fields, is studied. The contribution made by a procedure of correcting the horizontal velocities by theT, S data to the increase of the quality of the data obtained is estimated. Numerical experiments were carried out on the data of measurements made in the observation site located in the Newfoundland energy-active zone in August 1985.Translated by Mikhail M. Trufanov.     

Numerical experiments on estimating the accuracy of the methods of solution of the Kalman smoothing problems

The model numerical experiments on estimating the accuracy of two methods for solving the problem of Kalman smoothing, both iteration and precise, are described on the basis of a simple equation for the passive admixture transport. Some quantitative estimations are given.Translated by Mikhail M. Trufanov.     

Non-linear propagation of unidirectional wave fields over varying topography

The present study aims at investigating the non-linear triad interaction process affecting shoaling surface gravity wave fields. The triad interaction phenomenon being enhanced towards the shore, the domain of study is extended up to the surf zone. Three 1D non-linear wave models (one phase-resolving and two phase-averaged spectral models) have been implemented and compared to laboratory experiments performed in a wave flume. This set of models includes two existing models and a new one which has been developed in the frame of this work. The models include a breaking dissipation term based on the parametrical model of Battjes and Janssen [Battjes, J.A., Janssen, P.A.E.M., 1978. Energy loss and set-up due to breaking of random waves. Proc. 16th Int. Conf. Coastal Eng. (ASCE), Vol. 1, pp. 569–587.]. The investigations concern the evolution of variance spectra, spectral significant wave height and mean period over a barred bathymetric profile. In addition, the performances of the different models are analysed by computing the spectral source term for triad interactions. We found that all models are able to reproduce the main features of non-linear mechanisms affecting a wave field in the near-shore zone. The phase-resolving model gives the most accurate results for non-breaking situations. It correctly reproduces the non-linear coupling effect in decreasing water depths due to wave–wave interactions, as well as the harmonic release after a bar. However, the model is computationally time-consuming. The CPU time is considerably reduced using phase-averaged models. They give satisfactorily results on harmonic generation. However, they do not reproduce the release of harmonics as water depth increases. In breaking conditions, the variance spectra undergo significant changes under the combined effects of non-linear energy transfers and dissipation. The depth-induced wave breaking model included in the equations provides a good estimate of the energy decay in the surf zone.     

一般曲线坐标系下波浪传播的数值模拟

在曲线坐标系下,建立了缓变水深水域波浪传播的数值模拟模型.模型适宜于复杂变化的边界形状,克服了各种代数坐标变换的局限性.在建立模型时,将原始的椭圆型缓坡方程的近似型式——依赖时间变化的抛物型方程,作为控制方程,既克服了一般抛物近似方法的缺点,又便利了方程的求解;从开边界条件、不同反射特性的固壁边界条件相统一的表达式出发,对边界条件进行处理;用ADI法数值求解控制方程.对模型的验证表明,数值解与物模实验值吻合良好,模型对于具有复杂边界的工程实际有较强的适应性.     

网衣对波浪传播影响的三维数值模拟

为研究网衣对波浪传播的影响,采用多孔介质模型模拟网衣,建立了模拟网衣与波浪相互作用的三维数值波浪水槽模型。基于该数值模型研究了波浪经过网衣作用后波高衰减的变化规律,并与物理模型试验结果进行比较。通过对比数值模拟和物理模型试验的结果,证明了该三维数值模型模拟网衣对波浪传播影响的可行性。     

基于改进缓坡方程的波浪传播数值模拟

用变分原理导出考虑底坡一阶导数平方项和二阶曲率项影响的缓坡方程,对传统缓坡方程作了改进,提高波浪在海底地形变化剧烈、水深较浅时数值模拟精度。数值计算与已有实验室试验资料比较表明,该模型可以较好地模拟有剧烈变化的海底地形的波浪传播,比传统缓坡方程模型计算结果在精度上有明显提高。