A two layer model for wave dissipation in sea ice

Sea ice is highly complex due to the inhomogeneity of the physical properties (e.g. temperature and salinity) as well as the permeability and mixture of water and a matrix of sea ice and/or sea ice crystals. Such complexity has proven itself to be difficult to parameterize in operational wave models. Instead, we assume that there exists a self-similarity scaling law which captures the first order properties. Using dimensional analysis, an equation for the kinematic viscosity is derived, which is proportional to the wave frequency and the ice thickness squared. In addition, the model allows for a two-layer structure where the oscillating pressure gradient due to wave propagation only exists in a fraction of the total ice thickness. These two assumptions lead to a spatial dissipation rate that is a function of ice thickness and wavenumber. The derived dissipation rate compares favourably with available field and laboratory observations.     

Analysis and simulation of wave records through fast Hartley transform

The Hartley transform, a real-valued alternative to the complex Fourier transform, is presented as an efficient tool for the analysis and synthesis of ocean surface wave records. Basic theoretical properties of this real-valued transform are briefly reviewed. Similarities and differences between Fourier and Hartley integral transforms, as well as computational benefits and disadvantages between numerical algorithms used to evaluate their discrete versions, are presented. The fast Hartley transform algorithm is used to simulate stationary Gaussian time series of the sea surface elevation and to estimate the spectral density function, the Hilbert transform and the envelope function of wave records.     

Numerical study for vegetation effects on coastal wave propagation by using nonlinear Boussinesq model

The vegetation has important impacts on coastal wave propagation. In the paper, the sensitivities of coastal wave attenuation due to vegetation to incident wave height, wave period and water depth, as well as vegetation configurations are numerically studied by using the fully nonlinear Boussinesq model. The model is based on the implementation of drag resistances due to vegetation in the fully nonlinear Boussinesq equation where the drag resistance is provided by the Morison’s formulation for rigid structure induced drag stresses. The model is firstly validated by comparing with the experimental results for wave propagation in vegetation zones. Subsequently, the model is used to simulate waves with different height, period propagating on vegetation zones with different water depth and vegetation configurations. The sensitivities of wave attenuation to incident wave height, wave period, water depth, as well as vegetation configurations are investigated based on the numerical results. The numerical results indicate that wave height attenuation due to vegetation is sensitive to incident wave height, wave period, water depth, as well as vegetation configurations, and attenuation ratio of wave height is increased monotonically with increases of incident wave height and decreases of water depth, while it is complex for wave period. Moreover, more vegetation segments can strengthen the interaction of vegetation and wave in a certain range.     

Wavelet analysis for processing of ocean surface wave records

Wavelet analysis is a relatively new technique and in the recent years enormous interest in application of wavelets has been observed. This modern technique is particularly suitable for non-stationary processes as in contrast to the Fourier transform, (FT), the wavelet transform (WT) allows exceptional localization, both in time and frequency domains. The wavelet transform has been successfully implemented in signal and image processing, ordinary and partial differential equation theory, numerical analysis, communication theory and other fields. On the other hand, the application of the WT to ocean engineering and oceanography is rare. In this paper the WTs capability to give a full time–frequency representation of the wave signals is demonstrated. The processing of the time series of the non-stationary deep water waves, waves breaking at the tropical coral reefs and mechanically generated waves in the wave flume demonstrates the ability of the wavelet transform technique to detect a complex variability of these signals in the time–frequency domain. Various spectral representations resulting from the wavelet transform are discussed and their application for wave signals is shown.     

近岸波浪在刚性植被区域传播的数值模型

基于扩展型Boussinesq水波方程,建立了波浪在刚性植被覆盖的近岸海域传播的数值模型。通过在动量方程源项中引入拖曳阻力项考虑植被对波浪的衰减作用。控制方程采用有限差分和有限体积混合格式求解,模型稳定性强,具备间断捕捉能力,能有效模拟近岸区域波浪的传播变形、破碎和处理海岸动边界问题。利用所建立模型对典型物理模型实验进行模拟,计算结果与实验结果吻合良好,表明模型可用于波浪在刚性植被覆盖海域的数值计算。     

A numerical model of wave overtopping on seadikes

This paper describes the development of a numerical model for wave overtopping on seadikes. The model is based on the flux-conservative form of the nonlinear shallow water equations (NLSW) solved with a high order total variation diminishing (TVD), Roe-type scheme. The goal is to reliably predict the hydrodynamics of wave overtopping on the dike crest and along the inner slope, necessary for the breach modelling of seadikes. Besides the mean overtopping rate, the capability of simulating individual overtopping events is also required. It is shown theoretically that the effect of wave breaking through the drastic motion of surface rollers in the surfzone is not sufficiently described by the conventional nonlinear shallow water equations, neglecting wave setup from the mean water level and thus markedly reducing the model predictive capacity for wave overtopping. This is significantly improved by including an additional source term associated with the roller energy dissipation in the depth-averaged momentum equation. The developed model has been validated against four existing laboratory datasets of wave overtopping on dikes. The first two sets are to validate the roller term performance in improving the model prediction of wave overtopping of breaking waves. The last two sets are to test the model performance under more complex but realistic hydraulic and slope geometric conditions. The results confirm the merit of the supplemented roller term and also demonstrate that the model is robust and reliable for the prediction of wave overtopping on seadikes.     

Applications of sediment sudden deposition model based on the third-generation numerical model for shallow water wave

The existing numerical models for nearshore waves are briefly introduced, and the third-generation numerical model for shallow water wave, which makes use of the most advanced productions of wave research and has been adapted well to be used in the environment of seacoast, lake and estuary area, is particularly discussed. The applied model realizes the significant wave height distribution at different wind directions. To integrate the model into the coastal area sediment, sudden deposition mechanism, the distribution of average silt content and the change of sediment sudden deposition thickness over time in the nearshore area are simulated. The academic productions can give some theoretical guidance to the applications of sediment sudden deposition mechanism for stormy waves in the coastal area. And the advancing directions of sediment sudden deposition model are prospected.     

基于四阶完全非线性Boussinesq水波方程二维波浪传播数值模型

建立基于四阶完全非线性Boussinesq水波方程的二维波浪传播数值模型。采用Kennedy等提出的涡粘方法模拟波浪破碎。在矩形网格上对控制方程进行离散,采用高精度的数值格式对离散方程进行数值求解。对规则波在具有三维特征地形上的传播过程进行了数值模拟,通过数值模拟结果与实验结果的对比,对所建立的波浪传播模型进行了验证。同时,为了考察非线性对波浪传播的影响,给出和上述模型具有同阶色散性、变浅作用性能但仅具有二阶完全非线性特征的波浪模型的数值结果。通过对比两个模型的数值结果以及实验数据,讨论非线性在波浪传播过程中的作用。研究结果表明,所建立的Boussinesq水波方程在深水范围内不但具有较精确的色散性和变浅作用性能,而且具有四阶完全非线性特征,适合模拟波浪在近岸水域的非线性运动。     

Wavelet transform based coherence analysis of freak wave and its impact

The present paper presents the results of a wavelet transform-based coherence analysis of freak wave and its impact. Wavelet transform has been used as a tool in analyzing signals in the time domain as well as in the frequency domain. The analysis was applied to laboratory-generated freak waves. The wavelet transform of the time history of the freak wave and its impact force revealed that a wide range of frequency components were contained in them. The coherence analysis was conducted on the wave and its impact force time histories. The coherence analysis revealed that some high-frequency components were highly correlated with the impact forces. The present study demonstrates that the wavelet transform can be an alternative tool in the analysis of strongly nonlinear freak wave and its impact.     

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。     

An efficient method for the numerical calculation of viscous effects on transient long waves

Previous studies have shown that the Boussinesq equations can be used to calculate the instantaneous bottom shear stress induced by transient or periodic waves. The bottom friction term occurs as a convolution integral in time in the continuity equation. The exact numerical integration of a convolution integral demands large computational resources, which makes the method less useful for large scale computations. In this paper we explore how the value of the convolution integral can be estimated if we only use the values of the variables in a limited number of time steps, and discuss the accuracy and computational cost of this method.     

Comparative study on the accuracy of solitary wave generations in an ISPH-based numerical wave flume

In the present study, six solitary wave generations by different mathematical approximations are investigated using a piston type wave maker at dimensionless amplitudes ranging from 0.1 to 0.6 and two water depths. Incompressible smoothed particle hydrodynamics is used to simulate solitary wave propagation along the fixed depth channel. The present numerical results are compared with analytical results and experimental data in terms of free surface displacements, fluid particle velocity, phase speed, paddle motion, etc. The present mesh-free numerical results of wave profile variations over time proved that “Rayleigh” has the lowest relative wave height variation. However, its solitary wave has notable phase lead, while “Third order” and “Ninth order” have the least wave lags. Furthermore, the record of present numerical free surface elevation at different distances and the loss of amplitude of the main pulse showed that regarding both of them, “Ninth order” has supremacy over five others. Considering the numerical velocity components of generated solitary wave, “Third order” and “Ninth order” trace analytical results more accurately than other four ones, whereas “Rayleigh” is the most accurate one in predicting the maximum runup. Finally, the paddle motion, its velocity, and displacement, as well as phase speed and outskirts decay coefficient are also compared and discussed intensely.     

Evaluation of methods to remove inertial force from measured model wave impact force signals

The subject of wave impact on offshore structures and their components is important to vessel designers and operators for many reasons. They are often required to quantify these impact loads. Standard methods for wave load prediction will underestimate the forces on these structures due to intermittent loading. This necessitates the use of physical model tests to establish wave impact loads. The model measurement systems are designed to have high stiffness. This ensures that the natural frequency of the structure is above the wave frequency. However, it is widely believed that impacting waves contain high-frequency energy components that cause the structure to vibrate at its modal frequencies. This impact-induced vibration is recorded by the measuring system as a force (inertial force), and corrupts the actual applied force measurement. Before scaling can occur, the inertial force must be removed from the measured signal.A number of techniques for removing inertial force from measured signals are described in the published literature. Three methods are discussed, implemented and compared in this paper. The algorithms and procedures are presented. Each technique contains inherent and unique problems, while some are common to all methods.Neither of the techniques produced results that are fully satisfactory. The main problem is unwanted high-frequency content after the application of the methods. While neither method offers the perfect solution, the use of digital filtering techniques is recommended based on their relative performance and ease of implementation.     

An active wave generating–absorbing boundary condition for VOF type numerical model

The objective of the present work is to discuss the implementation of an active wave generating–absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces. First an overview of the development of VOF type models with special emphasis in the field of coastal engineering is given. A new type of numerical boundary condition for combined wave generation and absorption in the numerical model VOFbreak² is presented. The numerical boundary condition is based on an active wave absorption system that was first developed in the context of physical wave flume experiments, using a wave paddle. The method applies to regular and irregular waves. Velocities are measured at one location inside the computational domain. The reflected wave train is separated from the incident wave field in front of a structure by means of digital filtering and subsequent superposition of the measured velocity signals. The incident wave signal is corrected, so that the reflected wave is effectively absorbed at the boundary. The digital filters are derived theoretically and their practical design is discussed. The practical use of this numerical boundary condition is compared to the use of the absorption system in a physical wave flume. The effectiveness of the active wave generating–absorbing boundary condition finally is proved using analytical tests and numerical simulations with VOFbreak².     

Bragg resonant reflection of carrier waves composing wave groups

Numerical analyses for the Bragg resonant reflection of carrier waves associated long waves due to sinusoidally varying seabeds are performed by using a set of coupled ordinary differential equations derived from the Boussinesq equations. The Boussinesq equations are firstly approximated with the Fourier decomposition. The coupled governing equations are then derived and used to simulate evolution of both short and long wave components. It is also found that wave groups are generated by two carrier waves with slightly different frequencies. The wave energy of the initial wave components is transferred to other harmonic components during propagation over a long distance. Evolution and reflection of both short and long waves were largely affected by nonlinearity.     

A coupled numerical model for simulation of wave breaking and hydraulic performances of a composite seawall

A numerical model is developed by combining a porous flow model and a two-phase flow model to simulate wave transformation in porous structure and hydraulic performances of a composite type low-crest seawall. The structure consists of a wide submerged reef, a porous terrace at the top and an impermeable rear wall. The porous flow model is based on the extended Navier-Stokes equations for wave motion in porous media and k−ε turbulence equations. The two-phase flow model combines the water domain with the air zone of finite thickness above water surface. A unique solution domain is established by satisfying kinematic boundary condition at the interface of air and water. The free surface advection of water wave is modeled by the volume of fluid method with newly developed fluid advection algorithm. Comparison of computed and measured wave properties shows reasonably good agreement. The influence of terrace width and structure porosity is investigated based on numerical results. It is concluded that there exist optimum value of terrace width and porosity that can maximize hydraulic performances. The velocity distributions inside and in front of the structure are also investigated.     

Application of a Boussinesq model for the computation of breaking waves: Part 2: Wave-induced setdown and setup on a submerged coral reef

Based on a set of Boussinesq-type equations with improved linear frequency dispersion characteristics in deeper water, the present paper incorporates the simplified effect of spilling wave breaking into the equations. The analysis is restricted to a single horizontal dimension but the method can be extended to include the second horizontal dimension. Inside the surf zone the vertical variation of the horizontal velocity profile is assumed to be composed of an (initially unknown) organised velocity component below the roller and a surface roller travelling with the wave celerity. This leads to a new set of equations which is capable of simulating the transformation of waves before, during and after wave breaking. The model is calibrated and verified by comparison with several wave flume measurements. The results show that the model produces sound physical results.     

Determination of internal wave properties from X-Band radar observations

The application of nautical X-Band radars to measure internal wave (IW) properties is investigated. A methodology based on the use of Radon transform (RT) techniques to detect internal wave related features from backscatter image sequences is introduced to compute properties such as direction of propagation, non-linear velocity (c₀), distance between solitons (L_cc) and number of solitons per packet. The proposed methodology was applied to several events recorded by a ship-mounted X-Band radar system (WaMoS) during the NLIWI experiment in 2006. Results from the comparisons to simultaneous measurements taken at neighboring oceanographic moorings indicated that c₀ can be estimated with a RMS error of 0.06 m s⁻¹, which corresponds to a mean relative error of −1.4%. Similarly, L_cc can be estimated with a RMS error of 98 m, which is associated with a mean relative error of 14.6%. This latter error estimate however is likely to be overestimated, because it reflects strongly the separation between sampling stations as L_cc was shown to be highly dependent on propagation distance. The accuracy of the results shows that X-Band systems are well suited to measure internal wave properties offering some advantages over SAR and other in situ devices.     

一个改进的二阶Boussinesq方程模型在线性波浪反射问题中的适用性研究

基于改进型的二阶Boussinesq方程,在交错网络下建立数值模型.利用模型模拟波浪在常水深情况下的传播,波浪反射系数均低于2％.利用该模型模拟波浪在平斜坡前的反射,并将数值结果与解析解进行对比.结果表明,对于相对水深较大情况,坡度较陡时模拟结果明显偏大;对 于相对水深较小情况,坡度超过1:1时,数值结果仍与解析解有....     

Comparison of wind and wave measurements and models in the Western Mediterranean Sea

We have hindcast the wind and wave conditions in the Mediterranean Sea for two one month periods. Four different meteorological models and three different wave models have been used. The results have been compared with satellite and buoy wind and wave observations.Several conclusions concerning both the instruments and the models have been derived. The quality of both wind and wave results has been assessed. Close to the coasts high resolution, nested wave models are required for sufficient reliability.A wave threshold analysis suggests a sufficient reliability only off the coast, with a substantial decrease for low wave heights.