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1.
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. 相似文献
2.
Based on the extended mild-slope equation, the wind wave model (WWM; Hsu et al., 2005) is modified to account for wave refraction, diffraction and reflection for wind waves propagating over a rapidly varying seabed in the presence of current. The combined effect of the higher-order bottom effect terms is incorporated into the wave action balance equation through the correction of the wavenumber and propagation velocities using a refraction–diffraction correction parameter. The relative importance of additional terms including higher-order bottom components, the wave–bottom interaction source term and wave–current interaction that influence the refraction–diffraction correction parameter is discussed. The applicability of the proposed model to calculate a wave transformation over an elliptic shoal, a series of parallel submerged breakwater induced Bragg scattering and wave–current interaction is evaluated. Numerical results show that the present model provides better predictions of the wave amplitude as compared with the phase-decoupled model of Holthuijsen et al. (2003). 相似文献
3.
A consistent coupled-mode model recently developed by Athanassoulis and Belibassakis [1], is generalized in 2+1 dimensions and applied to the diffraction of small-amplitude water waves from localized three-dimensional scatterers lying over a parallel-contour bathymetry. The wave field is decomposed into an incident field, carrying out the effects of the background bathymetry, and a diffraction field, with forcing restricted on the surface of the localized scatterer(s). The vertical distribution of the wave potential is represented by a uniformly convergent local-mode series containing, except of the ususal propagating and evanescent modes, an additional mode, accounting for the sloping bottom boundary condition. By applying a variational principle, the problem is reduced to a coupled-mode system of differential equations in the horizontal space. To treat the unbounded domain, the Berenger perfectly matched layer model is optimized and used as an absorbing boundary condition. Computed results are compared with other simpler models and verified against experimental data. The inclusion of the sloping-bottom mode in the representation substantially accelerates its convergence, and thus, a few modes are enough to obtain accurately the wave potential and velocity up to and including the boundaries, even in steep bathymetry regions. The present method provides high-quality information concerning the pressure and the tangential velocity at the bottom, useful for the study of oscillating bottom boundary layer, sea-bed movement and sediment transport studies. 相似文献
4.
Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green‘s scond identity. This theory can be reduced to a number of the most typical mild-slope equations curreutly in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms. 相似文献
5.
Wave–current laboratory experiments have shown that the logarithmic current profile observed in pure current flows is modified due to the presence of waves. When waves propagate opposite the current, an increase in the current intensity is achieved near the mean water level, while a reduction is obtained for following waves and currents. With the aim of analyzing these nonlinear effects along the whole water column, an Eulerian wave–current model is presented. In contrast to previously presented wave–current models, the present is able to include the variation of the free surface elevation due to the wave motion and the effect of a non hydrostatic pressure field. Therefore it does not restrict its application to waves in shallow waters. Moreover, the model is able to simulate all the possible angles between waves and currents. 相似文献
6.
This paper presents a technique to generate waves at oblique angles in finite difference numerical models in a rectangular grid system by using internal generation technique [Lee, C., Suh, K.D., 1998. Internal generation of waves for time-dependent mild-slope equations. Coast. Eng. 34, 35–57.] along an arc-shaped line source. Tests were made for four different types of wave generation layouts. Quantitative experiments were conducted under the following conditions: the propagation of waves on a flat bottom, the refraction and shoaling of waves on a planar slope, and the diffraction of waves to a semi-infinite breakwater. Numerical experiments were conducted using the extended mild-slope equations of Suh et al. [Suh, K.D., Lee, C., Park, W.S., 1997. Time-dependent equations for wave propagation on rapidly varying topography. Coast. Eng. 32, 91–117.]. The fourth layout type consisting of two parallel lines connected to a semicircle showed the best solutions, especially for a small grid size. This technique is useful for the numerical simulation of irregular waves with broad-banded directional spectrum using conventional spectral wave models for the reasonable estimation of bottom friction and wave-breaking. 相似文献
7.
In this study, the propagation of monochromatic water waves over an arbitrarily varying topography is numerically investigated. A finite element model is developed by formulating the diffraction of waves caused by depth changes. Not only the propagating mode but also the evanescent modes are included in the model. The model developed is applied to the study of strong reflection of monochromatic waves over a sinusoidally varying topography. Predicted reflection coefficients are compared with those of available laboratory experiments and the eigenfunction expansion method. A very good agreement is observed. 相似文献
8.
Mild-slope equation for water waves propagating over non-uniform currents and uneven bottoms 总被引：5，自引：0，他引：5
I~IOXThe interaction between surface waves and ambient currents and nearshore topography lies atone of the heat of morphological medelling. Accurate predictions of how wave propagates overcurrents and topography, and of the consequent erosion and dePOSition of sand on a beach or tidalflat are vital when assessing how a coastline may be affected by changing conditions.The mild-slope equation was introduced by Berkhoff (1972) as a way of approximating therefraction-diffraction of linearized s… 相似文献
9.
The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced
currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth.
In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers
in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling
approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing
equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its
magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due
to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme
is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves
over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory
wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the
vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom
beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful
demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient
incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics
beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and
morphology evolution. 相似文献
10.
N. Booij 《Coastal Engineering》1983,7(3):191-203
The mild-slope equation is a vertically integrated refraction-diffraction equation, used to predict wave propagation in a region with uneven bottom. As its name indicates, it is based on the assumption of a mild bottom slope. The purpose of this paper is to examine the accuracy of this equation as a function of the bottom slope. To this end a number of numerical experiments is carried out comparing solutions of the three-dimensional wave equation with solutions of the mild-slope equation.For waves propagating parallel to the depth contours it turns out that the mild-slope equation produces accurate results even if the bottom slope is of order 1. For waves propagating normal to the depth contours the mild-slope equation is less accurate. The equation can be used for a bottom inclination up to 1:3. 相似文献
11.
Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave–wave and wave–current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan–Pierson–Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. 相似文献
12.
13.
A three-dimensional, multi-level model was used to study the energy dissipation of semidiurnal internal Kelvin waves due to their interaction with bottom topography. A simplified topography consisting of a channel with an additional shallow bay was used to clarify the wave’s scattering process. When the first mode semidiurnal internal wave given at an open boundary arrives at the bay mouth, higher-mode internal waves are generated at a step bottom of the bay mouth. As a result, the energy of the first mode internal Kelvin wave is effectively decayed. The decay rate of the internal Kelvin wave depends on both the width and length of the additional bay. The maximum decay rate was found when a resonance condition occurs the bay, that is, the bay length is equal to a quarter of wave length of the first mode internal wave on the shallow region. The decay rate in the wide bay cases is higher than that in a narrow case, due to a contribution from the scattering due to the Poincare wave that emanates from the corners of the bay head. The decay rate with the additional bay is 1.1–1.8 times that of the case without the additional bay. The decay rate due to the scattering process is found to be of the same order as that of the internal and bottom friction. 相似文献
14.
It is well known that wave induced bottom oscillations become more and more negligible when the water depth exceeds half the wavelength of the surface gravity wave. However, it was experimentally demonstrated for regular waves that the bottom pressure oscillations at both first and second wave harmonic frequencies could be significant even for incoming waves propagating in deep water condition in the presence of a submerged plate [16]. For a water depth h of about the wavelength of the wave, measurements under the plate (depth immersion of top of plate h/6, length h/2) have shown bottom pressure variations at the wave frequency, up to thirty times larger than the pressure expected in the absence of the plate. In this paper, not only regular but also irregular wave are studied together with wave following current conditions. This behavior is numerically verified by use of a classical linear theory of waves. The wave bottom effect is explained through the role of evanescent modes and horizontally oscillating water column under the plate which still exist whatever the water depth. Such a model, which allows the calculation of the velocity fields, has shown that not only the bottom pressure but also the near bed fluid velocity are enhanced. Two maxima are observed on both sides of the location of the plate, at a distance of the plate increasing with the water depth. The possible impact of such near bed dynamics is then discussed for field conditions thanks to a scaling based on a Froude similarity. It is demonstrated that these structures may have a significant impact at the sea bed even in very deep water conditions, possibly enhanced in the presence of current. 相似文献
15.
Lin Mingchung Hsiao Sungshan Hsu Yungcheng
Professor Dept. of Naval Architecture Ocean Engineering National Taiwan University Taiwan. Doctor Course Student Dept. of Naval Architecture Ocean Engineering National Taiwan University Taiwan 《中国海洋工程》1994,(3)
-Wave refraction-diffraction due to a large ocean structure and topography in the presence of a 'current are studied numerically. The mathematical model is the mild-slope equation developed by Kirby (1984). This equation is solved using a finite and boundary element method. The physical domain is devid-ed into two regions: a slowly varying topography region and a constant water depth region. For waves propagating in the constant water depth region, without current interfering, the mild- slope equation is then reduced to the Helmholtz equation which is solved by boundary element method. In varying topography region, this equation will be solved by finite element method. Conservation of mass and energy flux of the fluid between these two regions is required for composition of these two numerical methods. The numerical scheme proposed here is capable of dealing with water wave problems of different water depths with the main characters of these two methods. 相似文献
16.
LI Ruijie WANG Houjie
Dr. Associate Professor Engineering College of Ocean University of Qingdao Qingdao P. R. China
Ph. D. Candidate Engineering College of Ocean University of Qingdao Qingdao P. R. China 《中国海洋工程》1999,(3)
Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast. 相似文献
17.
The effect of a thin viscous fluid–mud layer on nearshore nonlinear wave–wave interactions is studied using a parabolic frequency-domain nonlinear wave model, modified to incorporate a bottom dissipation mechanism based on a viscous boundary layer approach. The boundary-layer formulation allows for explicit calculation of the mud-induced wave damping rate. The model performed well in tests based on laboratory data. Numerical tests show that damping of high frequency waves occurs, mediated by “difference” nonlinear interactions. Simulations of 2-dimensional wave propagation over a mud “patch” of finite extent show that the wave dissipation causes significant downwave diffraction effects. 相似文献
18.
A technique is developed to separate the incident and reflected waves propagating on a known current in a laboratory wave–current flume by analyzing wave records measured at two or more locations using a least squares method. It can be applied to both regular and irregular waves. To examine its performance, numerical tests are made for waves propagating on quiescent or flowing water. In some cases, to represent the signal noise and measurement error, white noise is superimposed on the numerically generated wave signal. For all the cases, good agreement is observed between target and estimation. 相似文献
19.
A coupled wave–tide–surge model has been established in this study in order to investigate the effect of tides, storm surges, and wind waves interactions during a winter monsoon on November 1983 in the Yellow Sea. The coupled model is based on the synchronous dynamic coupling of a third-generation wave model, WAM-Cycle 4, and the two-dimensional tide–surge model. The surface stress generated by interactions between wind and waves is calculated using the WAM-Cycle 4 directly based on an analytical approximation of the results obtained from the quasi-linear theory of wave generation. The changes of bottom friction factor generated by waves and current interactions are calculated by using simplified bottom boundary layer model. The model simulations showed that bottom velocity and effective bottom drag coefficient induced by combination of wave and current were increased in shallow waters of up to 50 m in the Yellow Sea during the wintertime strong storm conditions. 相似文献
20.
The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching. 相似文献