Multidirectional Random Waves Research Articles

장대 케이슨 방파제에 작용하는 다방향 불규칙파랑의 파력감소계수 산정

다방향 불규칙파랑을 입사파랑으로 적용하여 장대 케이슨 방파제에 작용하는 파력감소계수에 대하여 연구하였다. 다방향 불규칙파랑의 주파수 및 방향 스펙트럼으로 JONSWAP (Joint North Sea Wave Project) 스펙트럼과 비대칭 방향 스펙트럼이 각각 적용되었다. 계산결과, 케이슨 방파제의 길이와 입사파랑 주파향의 입사각이 증가할수록 파력감소계수는 감소함을 알 수 있었다. 그리고 최대방향분포계수 <TEX>$s_{max}$</TEX>가 증가할수록 파력감소계수는 규칙파와 유사한 경향을 보였다. 다방향 불규칙파랑이 방파제에 비스듬히 입사할 경우 비대칭계수 <TEX>${\mu}$</TEX>가 증가할수록 파력감소계수는 감소하였다. By employing multi-directional random waves, a parameter controlling the force acting on a long caisson breakwater is investigated in detail. Both JONSWAP (Joint North Sea Wave Project) and asymmetric directional spectra are adopted for frequency and directional spectra. It is found that the parameter decreases as the length of caisson and the angle of main direction of incident waves increase. Furthermore, the parameter is much similar to that of regular waves as the maximum spreading parameter <TEX>$s_{max}$</TEX> increases. The parameter, however, decreases as asymmetry parameter <TEX>${\mu}$</TEX> increases when the main direction of incident waves is oblique to the breakwater.

Multidirectional random wave diffraction in harbours by the placing of submarine pit: A case study

The purpose of this study was to estimate the decreasing effects of diffracted wave fields in-and around selected harbours (Kashima and Soma Harbours) including the region of outer breakwater, when a navigation channel is dredged at the vicinity of the harbour entrance. The wave field in the problem is considered to be in a two dimensional plane, and the configuration of the submarine pit breakwater in the sea bed is designated by a single rectangular type. The numerical simulation is performed by using the solution of the boundary integral equation based on the Green function. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. Incident wave height is to be decreased in-and behind a pit region by depth discontinuity. It is observed that the wave energy is decreased when a submarine pit has been placed. Key words: Green function, harbour, navigation channel, Mitsuyasu directional spectrum, pit.

Generation of Random Wave for Several Wave Spectra on Linear Incident Boundary

Generally, wave transformation in shallow water should be estimated for a representative offshore wave spectrum. However it may be difficult for a Boussinesq wave model which requires a relative narrow computational region for calculating wave fields that an incident wave boundary is expanded to offshore. In this paper, multi-directional random waves are generated by using Boussinesq wave model on the linear incident boundary with several wave spectra transformed in shallow water. Wave height distributions behind a spherical shoal can be reproduced with spatial distribution of multi-directional spectra estimated by an energy balance equation. In an actual harbor, the significant wave height in front of a revetment can be estimated larger in generation with several wave spectra.

Boundary element modeling of multidirectional random waves in a harbor with a rectangular navigation channel

A numerical model is presented for the prediction of the wave field due to the diffraction of directional random waves in a harbor with a long navigation channel dredged in the exterior region of the harbor entrance. In this study, partially reflected boundaries are considered in the harbor region and different constant water depths are set at the channel, the harbor and the exterior region of the study domain. The method for simulating the directional random waves is based on the superposition of diffraction solutions for the monochromatic wave components obtained by a two-dimensional boundary integral approach. The incident wave conditions are specified using discretized forms of the Mitsuyasu's frequency spectrum and directional function. The present numerical model is validated through comparisons with published experimental data, where good agreement between the simulated results and experimental data are obtained. Other example calculations to examine the effect of long rectangular channels (or pits) on the wave field in the harbors are also presented. Based on the comparisons in results, it is concluded that the present numerical model is an adequate and efficient tool to predict the wave field inside a harbor and around a pit like navigation channel for many practical applications.

A numerical model of nearshore waves, currents, and sediment transport

A two-dimensional numerical model of nearshore waves, currents, and sediment transport was developed. The multi-directional random wave transformation model formulated by Mase [Mase, H., 2001. Multi-directional random wave transformation model based on energy balance equation. Coastal Engineering Journal 43(4), 317-337.] based on an energy balance equation was employed with an improved description of the energy dissipation due to breaking. In order to describe surface roller effects on the momentum transport, an energy balance equation for the roller was included following Dally and Brown [Dally, W.R., Brown, C.A., 1995. A modeling investigation of the breaking wave roller with application to cross-shore currents. Journal of Geophysical Research 100(C12), 24873-24883.]. Nearshore currents and mean water elevation were modeled using the continuity equation together with the depth-averaged momentum equations. Sediment transport rates in the offshore and surf zone were computed using the sediment transport formulation proposed by Camenen and Larson [Camenen, B., Larson, M., 2005. A general formula for non-cohesive bed load sediment transport. Estuarine, Coastal and Shelf Science 63, 249-260.; Camenen, B., Larson, M., 2007. A unified sediment transport formulation for coastal inlet application. Technical report ERDC/CHL CR-07-1, US Army Engineer Research and Development Center, Vicksburg, MS.; Camenen, B., Larson, M., 2008. A general formula for non-cohesive suspended sediment transport. Journal of Coastal Research 24(3), 615-627.] together with the advection–diffusion equation, whereas the swash zone transport rate was obtained from the formulas derived by Larson and Wamsley [Larson, M., Wamsley, T.V., 2007. A formula for longshore sediment transport in the swash. Proceedings Coastal Sediments '07, ASCE, New Orleans, pp. 1924–1937.]. Three high-quality data sets from the LSTF experimental facility at the Coastal and Hydraulics Laboratory in Vicksburg, USA, were used to evaluate the predictive capability of the model. Good agreement between computations and measurements was obtained with regard to the cross-shore variation in waves, currents, mean water elevation, and sediment transport in the nearshore and swash zone. The present model will form the basis for predicting morphological evolution in the nearshore due to waves and currents with special focus on coastal structures.

Asymmetry in Directional Spreading Function of Random Waves due to Refraction

In this study, a more general directional spreading function is developed that allows for asymmetric directional distributions. For multidirectional random waves that approach the shore obliquely over a planar slope, we demonstrate that directional asymmetry is generated due to wave refraction. The asymmetry created by refraction increases with the offshore peak wave direction. The present spreading function is compared to a preexisting symmetric spreading function and is shown to better capture changes in the directional distribution that occur in a refracting, random wave field. Finally, the new asymmetric spreading function is compared to a long time series of wave directional spectra measured at a nearshore field site. The results demonstrate that refraction-induced asymmetry is common in the nearshore and the asymmetric spreading function gives an improved analytic representation of the overall directional distribution as compared to the symmetric function.

Modeling of random wave transformation with strong wave-induced coastal currents

The propagation and transformation of multi-directional and uni-directional random waves over a coast with complicated bathymetric and geometric features are studied experimentally and numerically. Laboratory investigation indicates that wave energy convergence and divergence cause strong coastal currents to develop and inversely modify the wave fields. A coastal spectral wave model, based on the wave action balance equation with diffraction effect (WABED), is used to simulate the transformation of random waves over the complicated bathymetry. The diffraction effect in the wave model is derived from a parabolic approximation of wave theory, and the mean energy dissipation rate per unit horizontal area due to wave breaking is parameterized by the bore-based formulation with a breaker index of 0.73. The numerically simulated wave field without considering coastal currents is different from that of experiments, whereas model results considering currents clearly reproduce the intensification of wave height in front of concave shorelines.

Development of Multidirectional Random Wave Transformation Model in Wave-Current Coexisting Field

When waves go upstream against gradually-increasing opposing current, wave breaking will occur and/or be blocked inthe case of strong current. Since wave action density is conserved in a current field, the wave action balance equation issuitable for the numerical model of wave-current interaction. In this study, the numerical simulation model based on thewave action balance equation is developed by using QUICK scheme in order to improve the accuracy of wave transformationdue to the current. The usability of the present model is verified, through the computation of the wave heightchange in the fields where the caustic exists or the area around the mouth of a river.

A three-dimensional modeling of multidirectional random wave diffraction by rectangular submarine pits

A three-dimensional modeling of multidirectional random-wave diffraction by a group of rectangular submarine pits is presented in this paper. The fluid domain is divided into N interior regions representing the pit area and an overall exterior region separated by the imaginary pit boundaries. In the interior region, the analytical expressions of the Fourier series expansion for velocity potentials in the pit regions have been derived with the unknown coefficients determined from a series of Green's function based boundary integral equations. The boundary integral approach has also been applied to obtain the velocity potential and free-surface elevation in the exterior region. The Pierson–Moskowitz (P–M) frequency spectrum was selected for the random wave simulation using the superposition of solutions of a finite number of decomposed wave components. Numerical results for the cases of regular waves and random waves are presented to examine the influences of the pit geometry and incident wave condition on the overall wave field. The general diffraction pattern of alternate bands of increase and decrease of relative wave height in front of the pit system can be observed. It is found that, in the shadow region, the relative wave height is reduced. As the number of pit increases, the effectiveness of reducing the relative wave height behind the multiple-pit system increases. However, the relative wave height within the pit area and in front of the leading pit shows increasing trend. It is noticed that under the random-wave condition, the level of increase and decrease of the relative wave height due to the existence of submarine pits is less pronounced than that observed from results in regular-wave condition.

Numerical modelling of deformation of multi-directional random waves over a varying topography

Two numerical formulations of the breaking phenomenon were implemented in a numerical model for random wave propagation based on the elliptic formulation of the mild-slope equation. The randomness of the wave field was simulated based on a spectral component method, in which the 3-D spectrum is discretised in components of equal energy. One of the breaking process formulations is based on the concept of breaking each independent spectral component. The other is based on the distribution of the local amount of energy dissipated through the independent spectral components. The model based on the concept of breaking each independent spectral component produces the best estimates of the wave field, when the numerical results are compared with laboratory data.

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.

直線上に分布するスペクトルを入射波条件とした多方向不規則波浪変形時系列解析

Wave prediction models based on the energy balance equation are suitable for applications involving a large sea area. Time domain models like the Boussinesq wave model can estimate wave fields in detail for a not so large area. As a first step to link together these models seamlessly, this study presents a time domain analysis of multidirectional random wave transformations, in which the incident wave spectrum are intermittently distributed over the rectilinearity. Multidirectional random wave transformation over a spherical shoal is numerically simulated by a Boussinesq model with the present method which starts calculation from cross sections around the shoal. The results on the significant wave height distributions and wave spectrum are compared to those calculated by an energy balance equation model in the whole area.

Extended energy-balance-equation wave model for multidirectional random wave transformation

This study extends an energy-balance-equation wave model (a phase-averaging wave model) for multidirectional random wave transformations to account for wave shoaling, refraction, diffraction, reflection and breaking. Quadratic upstream interpolation for convective kinematics is used in the discretization to reduce numerical diffusion. Predictions using the present wave model are compared with Sommerfeld's solutions for wave transformation through a gap between breakwaters, experimental observations for wave transformation due to a circular shoal, and field measurements for waves behind a breakwater. The results of these comparisons show fairly good agreement.

A three-dimensional numerical modeling of multidirectional random wave diffraction by rectangular submarine pits

A three-dimensional numerical model of multidirectional random wave diffraction by rectangular submarine pits has been investigated theoretically in the uniform water depth. In the exterior region, the three-dimensional Green function has been us ed for the solution of the velocity potential and its derivative in fluid interface between regions. The form of the Fourier expansion has also been utilized for the solution of the velocity potential in the interior region. The Mitsuyasu directional spectrum has been di scretized to specify the incident wave conditions for obtaining linear diffraction solutions, and then subsequent cumulative superposition is performed to obtain the random wave results. The results of the present model have been compared with those of previous theoretical studies for both regular and random wave diffraction by single or multiple pits. reasonable agreement was consistently obtained in all cases. In accordance with good agreement from these comparisons, the present numerical model may accurately be utilized to predict the three-dimensional wave field around multiple submarine pits or navigation channels.

Boundary element modeling of multidirectional random wave diffraction by multiple rectangular submarine pits

The diffraction of multidirectional random surface waves by one or more rectangular submarine pits is investigated theoretically. The present method is based on the principle of cumulative superposition of diffraction solutions for linear Airy wave theory obtained by a two-dimensional boundary integral equation in water of uniform depth. The constant segment mode has been utilized to obtain the velocity potentials on the interface of each pit, and a specified discrete form of the Mitsuyasu directional spectrum is used for the incident wave conditions. The results of the present model have been validated through the comparison with those obtained by previous works ( kh<1, long wave) for random wave diffraction by single or multiple pits. A further investigation for random wave diffraction has been also studied by considering short wave range kh>1. In accordance with reasonable agreement from these comparisons, it is concluded that the present BEM numerical model may accurately be utilized to predict the wave field around multiple submarine pits or navigation channels in many practical applications.

Numerical reproduction of fully nonlinear multi-directional waves by a viscous 3D numerical wave tank

Fully nonlinear multi-directional waves are reproduced by use of a viscous 3D numerical wave tank (NWT) simulation technique. The governing equations, Navier–Stokes and continuity equations, are discretized by a finite-difference/volume method in the framework of a rectangular/body-fitted coordinate system, and the boundary values are updated at each time step in a time-marching procedure. The fully nonlinear kinematic free-surface condition is satisfied by the marker-density function technique. The directed incident waves are generated by multi-segmented wavemaker on the basis of the so-called “snake-principle”, and the outgoing waves are numerically dissipated inside an artificial damping zone located at the opposite side of the wavemaker. In this study, the results for the generation of regular waves, including numerical convergence tests, irregular waves, and multi-directional random waves are presented. Furthermore, the generation of following waves, which are one kind of directional waves, is examined using a fluid acceleration wavemaker, and the hydrodynamic forces acting on an advancing ship in such a wave condition are discussed.

Deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on a sloping bed

This study investigates the wave deformation of multi-directional random waves passing over an impermeable submerged breakwater installed on the slope. Experiments were conducted in a three-dimensional wave basin equipped with a multi-directional random wave generator. Measurements of the free surface elevations around an impermeable submerged breakwater were carried out using 19 capacitance-type wave gages. In addition, a numerical model is proposed in three-dimensional random wave field. It is shown that the numerical results reproduce the general trend of the experimental results well. Investigations are made to study the effect of the spreading parameter S max and bottom topography (bottom slope and submerged breakwater) on the wave deformation. It is pointed out that concentration of wave energy with larger values of the spreading parameter S max is located within narrow limits in onshore side of the submerged breakwater. Furthermore, the supplementary discussion is made by means of numerical results.

The Diffraction of Multidirectional Random Waves by Rectangular Submarine Pits

The diffraction of multidirectional random surface waves with one or more rectangular submarine pits is investigated theoretically. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The numerical model involves the superposition of regular-wave diffraction solutions based on linearized shallow water wave theory obtained by a two-dimensional boundary integral approach for water of uniform depth. Numerical results are presented for multi-directional random waves that illustrate the effect of the various wave and pit parameters on the diffraction characteristics of typical single and multiple pit systems.

複雑な海底地形に設置された長大防波堤の波力平滑化特性

As the length of a caisson becomes long, the wave force per unit length becomes smaller because of the wave phase difference. In this study, we performed hydraulic model test on a long caisson placed on the complicated submarine topography model under various wave conditions in order to investigate the characteristics of wave reduction.It is found that the wave force on a long caisson placed on the complicated submarine topography is reduced significantly in the case of oblique waves. The reduction ratio for multi-directional random waves is smaller than that for uni-directional random waves due to directional spreading. In the case of head-on waves, wave force per unit length on the long caisson becomes smaller because of the dispersion of the wave height and the phase due to wave refraction.

선박의 항행안전지원을 위한 파랑추산에 관한 연구

해상수송의 안전성을 개선하는 하나의 수란으로서, 해상풍 정보로부터 예정 항로상에서 조우하게될 파랑정보를 높은 정밀도로 예측하여 단시간에 본선에 제공할 수 있는 시스템을 개발할 필요가 있다. 본 연구에서는 이의 제1단계로서 대양에서의 다방향 불규칙파 예측을 위한 파랑추산모델을 제시하였다. 검토방법으로는 과거 실제 해역에서 발생한 황천에 기인한 선박 침몰사고를 대상으로 선박의 항행 일정에 따른 해상풍의 분석 및 파랑추산시뮬레이션을 수행하였으며, 이로부터 사고 선박이 조우한 해상을 평가하고 모델의 재현성 및 정도를 검토하였다. 연구비 결과, 사고 선박은 침몰사고의 원인이 Okhotsk해에서 발달한 저기압에 의해 급속히 성장한 고파랑 해역을 회피하지 못하여 발생한 것에 있음을 명백히 하였으며, 본 계산에 이용한 제3세대 파랑추산모델(WAM)로부터의 결과는 실제 관측 파랑의 유의파고, 주기, 방향 스펙트럼 등 항행관련의 파랑제원과 잘 부합되었으며, 실용 선박에서의 예측시스템 구축에 적용성이 양호한 것으로 나타났다. In order to improve navigational safety of ships, an ocean wave prediction model of high precision within a short time, dealing with multi-directional random waves from the information of the sea surface winds encountered at the planned ship's course, was introduced for construction of ocean wave forecasting system on the ship. In this paper, we investigated a sea disaster occurred by a stormy weather in the past. We analyzed the sea surface wind first and then carried out ocean wave hindercasting simulations according to the routes the sunken vessel. From the result of this study, we concluded that the sea disaster was caused by rapidly developed iou pressure system Okhotsk Sea and the predicted values by the third generation wave prediction model(WAM) was agreed well with the observed significant wave height, wave period, and directional wave spectrum. It gives a good applicability for construction of a practical on-board calculation system.