Accurate determination of internal kinematics from numerical wave model results

The internal kinematics for surface waves propagating over a locally constant depth are expressed as convolution integrals. Given the wave kinematics at the still water level (SWL), this provides explicit and exact potential flow expressions for the internal kinematics as convolutions in space with appropriate impulse response functions. These functions are derived in closed form and they are shown to decay exponentially. This effectively reduces the limits of the convolution integral to a horizontal distance of approximately three water depths from the water column of interest. The SWL kinematics must be provided within this region. The source of SWL kinematics may, e.g. be one of the recently developed highly accurate Boussinesq-type formulations. The method is valid for multidirectional, irregular waves of arbitrary nonlinearity at any constant water depth.     

An energy-controlling boundary condition for partial wave reflections in the mild slope equation

An energy-controlling technique to actively manage the reflective property of waves from solid boundary is presented. As linear waves propagate through an energy-controlling area, a reduction in wave heights occurs due to energy dissipation, which can be placed under direct control through the imaginary part of the wavenumber and phase velocity. Based on this relationship, the present study investigates a new method to control reflected waves with desired heights in the mild slope equation model. The method is validated through numerical tests for various reflection coefficients and the results confirm the promising use of energy-controlling boundary condition for partial wave reflections.     

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.     

Mass transport in a two-layer wave boundary layer

The transport of a chemical species under the pure action of surface progressive waves in the benthic boundary layer which is loaded with dense suspended sediments is studied theoretically. The flow structure of the boundary layer is approximated by that of a two-layer Stokes boundary layer with a sharp interface between clear water and a heavy fluid. The simplest model of constant eddy diffusivities is adopted and the exchange of matter with the bed is ignored. For a thin layer of heavy fluid, whose thickness is comparable to the surface wave amplitude and the Stokes boundary layer thickness, effective transport equations are deduced using an averaging technique based on the method of homogenization. The effective advection velocity is found to be equal to the depth-averaged mass transport velocity, while the dispersion coefficient can be shown to be positive definite. Explicit expressions for the transport coefficients are obtained as functions of fluid properties and flow kinematics. Physical discussions on their relations are also presented.     

Implementation and testing of a lateral boundary scheme as an open boundary condition in a barotropic ocean model

The flow relaxation scheme (FRS) is tested as an open boundary condition (OBC). This scheme was originally designed to relax external solutions (ES) from a large area model towards solutions in a limited area model with a fine mesh. When one uses the FRS as a pure OBC; i.e. the ES are unknown and set equal to zero, the FRS method degenerates to a sponge type OBC. Since a sponge type OBC does not work well in all cases, for instance in the case of an alongshore uniform wind; Chapman (1985) and Røed and Cooper (1987), we introduced local wind induced solutions as a part of the ES.When we also included the tide in the ES, the tests showed that the FRS method handled the tidal input problem very well. Even in the case where noise was added to the tide in the ES, the results were good.The major drawbacks for the FRS method are the required extention of the computer-space and -time.     

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.     

Transparent boundary condition for simulating nonlinear water waves by a particle method

Open boundaries are important when simulating water waves. In this study, a transparent boundary condition at an open boundary was developed for simulating nonlinear water waves propagating to a distant area using the Moving Particle Semi-implicit method. The novelty of this study is that the technique of wave analysis used in the experiment was introduced into the particle simulation to absorb incident waves; the simulation cost was reduced by employing inflow and outflow regions instead of a long dissipation region. Incident waves in front of the boundary were evaluated using Fourier analysis, and the particles on the transparent boundary were forced to move at the velocity of the analytical solution for Stokes waves in order to absorb the incident waves. The analysis was restricted to periodic waves. Wave propagation was simulated for two wave periods using the developed transparent boundary condition. The results showed that this transparent boundary transmitted the incident waves with small reflection and the simulation cost was lower than that for wave damping by a conventional highly viscous region.     

Wave kinematics of partial reflection from a vertical wall

A third-order perturbation approximation for the partial reflection from a vertical wall is presented in this paper. The wave parameters are expressed in terms of the amplitude of incident waves. The reflection coefficient is defined as the ratio of the height of reflected waves to incident waves. The numerical results demonstrate the significant influences of reflected coefficient on the wave profile and wave frequency bifurcation. For example, the critical angle of wave frequency bifurcation with partial reflection is about 7.5 degrees, not 21 degrees as reported previously for fully reflection.     

Time-domain simulation of wave–structure interaction based on multi-transmitting formula coupled with damping zone method for radiation boundary condition

Based on the Rankine source, this paper proposed a time-domain method for analyzing the three-dimensional wave–structure interaction problem in irregular wave. A stable integral form of the free-surface boundary condition (IFBC) is employed to update the velocity potential on the free surface. A multi-transmitting formula, with an artificial wave speed, is used to eliminate the wave reflection for radiation condition on the artificial boundary. An effective multi-transmitting formula, coupled with damping zone method, is further used to analyze the irregular wave diffraction at the artificial boundary. We investigate hydrodynamic forces on floating structure and compare our solution to the frequency-domain solution. It is shown that long time simulation can be done with high stability and the numerical results agree well with the solution obtained under the frequency domain. The efficiency of the proposed multi-transmitting formula and the coupled methods for radiation boundary make them promising candidates in studying the irregular water wave problem in time domain.     

Regular wave pressures and forces on submerged pipelines near a sloping boundary

The hydrodynamic pressures induced by regular waves around the circumference of a pipeline normal to the wave direction and near a rigid bed of slope 1:10 have been investigated in a wave flume. The pressures were integrated to obtain the force time history, from which the peak horizontal and vertical forces are evaluated. The maximum and root mean square horizontal and transverse force coefficients are correlated with the Keulegan–Carpenter (KC) number. The effect of the distance between the sloping bed and the pipeline on the force coefficients is discussed. The force coefficients are found to decrease with an increase in KC number and with the decrease in the relative clearance of the pipeline from the boundary. In addition, the reflection characteristics of the sloping bed in the presence of the pipeline as a function of surf similarity parameter and their comparison with the results from existing literature are also reported. The details of the model setup, experimental procedure, results and discussion are presented in this paper.     

Characteristics of the boundary layer at the bottom of a solitary wave

The results of direct numerical simulations of the boundary layer generated at the bottom of a solitary wave are described. The numerical results, which agree with the laboratory measurements of Sumer et al. (2010) show that the flow regime in the boundary layer can be laminar, laminar with coherent vortices and turbulent. The average velocity and bottom shear stress are computed and the results obtained show that the logarithmic law can approximate the velocity profile only in a restricted range of the parameters and at particular phases of the wave cycle. Moreover, the maximum value of the bottom shear stress is found to depend on the dimensionless wave height only, while the minimum (negative) value depends also on the dimensionless boundary layer thickness. Diagrams and simple formulae are proposed to evaluate the minimum and maximum bottom shear stresses and their phase shift with respect to the wave crest.     

Optimal control of salinity boundary condition in a tidal model using a variational inverse method

A variational inverse data assimilation scheme is developed to estimate the salinity boundary conditions in a three-dimensional tidal hydrodynamic and salinity transport model. In this paper, the maximum incoming salinity value and the recovery time from the outflow salinity to the maximum incoming salinity at model open boundaries are treated as poorly known model control variables, and estimated using a variational inverse data assimilation scheme. The variational inverse model is tested in an idealized estuary using identical twin experiments, in which observed data are generated from the same model. Model tests with different initial guesses of the model control variables are conducted to evaluate the capability of the inverse model. A penalty technique is used to eliminate oscillations in the solution during the minimization process. The effects of preconditioning and penalty terms on the convergence rate are investigated. Model results demonstrate that the variational inverse model can be used to efficiently determine the optimal salinity open boundary conditions and improve the model state when there are no observed data available to specify the proper salinity open boundary conditions in a tidal model.     

降雨条件下的导航X波段雷达海浪参数反演算法研究

X波段的电磁波受降雨影响容易产生衰减,这导致导航X波段雷达在降雨时无法用于海浪观测。本文提出了一种新的降低降雨影响的算法来反演海浪参数。首先,对X波段雷达图像做主成分分析,获得波浪变化的主成分,利用一维傅里叶变换得到波数谱,对其滤波减小降雨对雷达图像的影响;然后,选取JONSWAP(Joint North Sea Wave Project)谱作为理论谱,建立以观测谱与理论谱的最小化差异为目标函数的模型,求解该模型估算海浪的有效波高。与浮标测量的有效波高相比,该方法反演的有效波高的均方根误差是0.23 m,证明了该方法的可行性。     

Validation of a new generation system for bottom boundary layer beneath solitary wave

Understanding of sea bottom boundary layer characteristics, especially bottom shear stress acting on the sea bed, is an important step needed in sediment transport modeling for practical application purposes. In the present study, a new generation system for bottom boundary layer under solitary wave is proposed. Applicability of this system is examined by comparing measured and numerical solution velocities. Moreover, transitional behavior from laminar to turbulence was investigated. It is concluded that the critical Reynolds number in the experiments shows good agreement with DNS result of Vittori and Blondeaux (2008) and laboratory data of Sumer et al. (2010), indicating validity of the generation system. Since the present generation system enables continuous measurement to obtain ensemble averaged quantities, it can be effectively utilized for future experimental studies on solitary wave boundary layers, including sediment transport experiments with movable bed.     

Flow kinematics of focused wave groups on a plane beach in the U.K. Coastal Research Facility

Measurements are presented of the water particle kinematics of focused wave groups generated in the U.K. Coastal Research Facility. Single and repeated wave groups are considered at normal and 20° incidence to a 1:20 plane beach. The single focused wave groups model extreme transient events without the complication of reflections during the data acquisition process. A symmetry-based separation of harmonics method is used to interpret the water particle kinematics at the point of focus. Although the largest component is linear, there are also considerable second order kinematics terms (both low frequency and high frequency). Away from the free surface, the 2nd order difference contribution to the kinematics is a return current opposed to the direction of wave advance. For repeated wave groups, the measured kinematics confirms the presence of a low frequency free wave, followed by higher frequency waves of the main group and trailing higher order harmonic waves. In the breaker and surf zones, there is also evidence of the saw-tooth behaviour of broken waves, followed by scatter due to breaker-induced turbulence. Pulsatile wave breaking of repeated wave groups at oblique incidence is found to drive a longshore current.     

Bragg reflection in a fully nonlinear numerical wave tank based on boundary integral equation method

We investigated the phenomenon of Bragg reflection of submerged structures in a 2D fully nonlinear numerical wave tank (NWT) based on the boundary integral equation method (BIEM). This model was validated by comparing not only the free surface elevations with that of the analytic solution of Stokes’ second-order wave theory, but also the reflection coefficients of submerged bars with that from other sources. The results of the present model show that the free surface nonlinear effect on the reflection coefficient of the primary resonance reduces significantly for all of the submerged bars considered. Finally, a case study is presented to demonstrate the reflecting capacity and overall performance of various submerged bars. Results indicate that sinusoidal bar has the maximum reflection capacity at the primary resonance, but the trapezoidal submerged bar is suggested as the better option for the practical convenience of coastal underwater construction.     

Neogene-Quaternary tectonic evolution of the Leeward Antilles islands (Aruba, Bonaire, Curaçao) from fault kinematic analysis

Aruba, Bonaire, and Curaçao are islands aligned along the crest of a 200-km-long segment of the east-west-trending Leeward Antilles ridge within the broad Caribbean-South America plate boundary zone presently characterized by east-west, right-lateral strike-slip motion. The crust of the Leeward Antilles ridge represents the western segment of the Cretaceous-early Cenozoic Great Arc of the Caribbean, which obliquely collided, with the continental margin of northern South America in early Cenozoic time. Following the collision, the ridge was affected by folding and was segmented by oblique, northwest-striking normal faults that have produced steep-sided, northwest-trending, elongate islands and narrow shelves separated by deepwater, sediment-filled and fault-controlled basins. In this paper, we present the first fault slip observations on the Neogene carbonate rocks that cover large areas of all three islands. Our main objective is to quantify the timing and nature of Neogene to Quaternary phases of faulting and folding that have affected the structure and topography of this area including offshore sedimentary basins that are being explored for their petroleum potential. These data constrain three fault phases that have affected Aruba, Bonaire, and Curaçao and likely the adjacent offshore areas: 1) NW-SE-directed late Paleogene compression; 2) middle Miocene syndepositional NNW-SSE to NNE-SSW extension that produced deep rift basins transverse to the east-west-trending Leeward Antilles ridge; and 3) Pliocene-Quaternary NNE-trending compression that produced NW-SE-trending anticlines present on Aruba, Curaçao and Bonaire islands. Our new observations - that include detailed relationships between striated fault planes, paleostress tensors, and bedding planes - show that prominent bedding dips of Neogene limestone on Aruba, Bonaire and Curaçao were produced by regional tectonic shortening across the entire Leeward Antilles ridge rather than by localized, syndepositional effects as proposed by previous workers. We interpret Pliocene-Quaternary NNE-directed shortening effects on the Leeward Antilles ridge as the result of northeastward extrusion or “tectonic escape” of continental areas of western Venezuela combined with southeastward shallow subduction of the Caribbean plate beneath the ridge.     

An analysis of second-order wave forces on floating bodies by using a higher-order boundary element method

The wave diffraction and radiation problem is studied numerically by using a higher-order boundary element method. The convergence of the higher-order boundary element method is tested systematically for bodies of different shapes. For the second-order force, particular attention is paid to the contribution of the second-order potential, following the line of Molin's approach. For numerical evaluation, the free surface is divided into three subregions; inner, intermediate and outer ones. In the inner region, the integral is evaluated numerically by using higher-order boundary elements. In the intermediate region, semi-analytic form is constructed with the help of eigen functions. In the outer domain, the analytic solution is available. This subdivision scheme reduces the numerical burden remarkably.     

Internal wave excitation from a collapsing mixed region

The collapse of a uniform density fluid (a “mixed region”) into a surrounding ambient fluid with complex stratification is examined by way of laboratory experiments and fully nonlinear numerical simulations. The analysis focuses upon the consequent generation of internal gravity waves and their influence upon the evolution of the collapsing mixed region. In experiments and simulations for which the ambient fluid has uniform density over the vertical extent of the mixed region and is stratified below, we find the mixed region collapses to form an intrusive gravity current and internal waves are excited in the underlying stratified fluid. The amplitude of the waves is weak in the sense that the intrusion is not significantly affected by the waves. However, scaling the results to the surface mixed layer of the ocean we find that the momentum flux associated with the waves can be as large as 1 N/m². In simulations for which the ambient fluid is stratified everywhere, including over the vertical extent of the mixed region, we find that internal waves are excited with such large amplitude that the collapsing mixed region is distorted through strong interactions with the waves.