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1.
A new model is presented for the propagation of monochromatic surface waves over a region of arbitrary, one-dimensional bottom topography. The smoothly varying bed profile is divided into a series of shelves separated by abrupt steps. The wave fields on either side of each step are related by a “transfer matrix”, and the propagation of waves along the shelf between adjacent steps is described by a “rotation matrix”. Starting from a point where the surface wavefield is known, the step by step application of the appropriate combination of these matrices allows computation of the wavefield over the region of interest. If the individual steps are small then the transfer matrix reduces to a simpler plane-wave form, with considerable savings in computational effort. Comparisons are made with an exact potential solution for single and double steps in order to investigate the accuracy and validity of the matrix method. Finally, the model is applied to the case of wave reflection by fixed sinusoidal bottom undulations, and good agreement is found between its predictions and existing laboratory data. 相似文献
2.
In the present paper, by introducing the effective wave elevation, we transform the extended ellip- tic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)’s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly vary- ing topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone. 相似文献
3.
This paper presents an analytical solution for scattering of oblique incident, small amplitude, monochromatic wave trains by a stationary rigid multi-layered objects with rectangular cross-section. The object is infinite long and consists of multilayers, which can be either solid or permeable. This paper extends the previous work by Hu and Liu [1] from normal incident wave condition with a special object configuration to oblique incident waves with multi-layered object. The present model is validated with several existing solutions for normal/oblique waves interacting with a single object; excellent agreement is observed. New numerical results are presented to investigate the effects of incidence angle on reflection, transmission and energy loss coefficients for a combined floating and bottom-mounted permeable breakwater. A new floating board-cage breakwater is developed from the present model and its solutions are discussed in detail. A computer program, AWAS-P, has been updated so that it is applicable for both oblique and normal incident waves, while the object is multi-layered. 相似文献
4.
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numerical experiments on propagation of an incident plane wave over a circular-type shoal are presented in comparison with the analytical result, based on Born approximation. 相似文献
5.
A time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter [J. Fluid Mech. 291 (1995) 393] using the Taylor series technique. Numerical tests are made on a horizontally one-dimensional case for regular waves over sloping beds and for both regular and irregular waves over a ripple patch. Numerical results prove that the proposed model gives accurate results for both regular and irregular waves over rapidly varying topography. 相似文献
6.
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
7.
A three-point method for estimating wave reflection is proposed to account for monochromatic oblique incident waves propagating over a sloping beach. The amplitudes of reflected wave and incident wave are separated using wave amplitudes measured at three fixed wave gauges with a distance. The applicability of the theory is verified by comparing the simulated results with the available theoretical, numerical and experimental results for the estimation of wave reflection. The sensitivity is also tested to provide a more accurate prediction of the reflection coefficient. 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.
A numerical model for wave propagation in a harbour is verified by use of physical models.The extended time-dependent mild slope equation is employed as the governing equation,and the model is solved by use of ADI method containing the relaxation factor.Firstly,the reflection coefficient of waves in front of rubble-mound breakwaters under oblique incident waves is determined through physical model tests,and it is regarded as the basis for simulating partial reflection boundaries of the numerical model.Then model tests on refraction,diffraction and reflection of waves in a harbour are performed to measure wave height distribution.Comparative results between physical and numerical model tests show that the present numerical model can satisfactorily simulate the propagation of regular and irregular waves in a harbour with complex topography and boundary conditions. 相似文献
10.
In this article, tsunamis represented as solitary waves was simulated using the fully nonlinear free surface waves based on Finite Element method developed by Sriram et al. (2006). The split up of solitary wave while it propagates over the uneven bottom topography is successfully established. Wave transmission and reflection over a vertical step introduced in the bottom topography is in good agreement with the experimental results from Seabra-Santos et al. (1987). The wave transformation over a continental shelf with different smooth slopes reveals that the solitary wave reflection increases while the continental slope varies from flat to steep. The interaction of the solitary wave with a vertical wall for different wave steepness has been analysed. The reflected shape of the profile is in good agreement with the observation made by Fenton and Rienecker (1982) and an increase in wave celerity is observed. 相似文献
11.
A mathematical model has been developed to analyze the influence of extreme water waves over multiconnected regions in Visakhapatnam Port, India by considering an average water depth in each multiconnected regions. In addition, partial reflection of incident waves on coastal boundary is also considered. The domain of interest is divided mainly into two regions, i.e., open sea region and harbor region namely as Region-I and Region-II, respectively. Further, Region-II is divided into multiple connected regions. The 2-D boundary element method (BEM) including the Chebyshev point discretization is utilized to solve the Helmholtz equation in each region separately to determine the wave amplification. The numerical convergence is performed to obtain the optimum numerical accuracy and the validation of the current numerical approach is also conducted by comparing the simulation results with existing studies. The four key spots based on the moored ship locations in Visakhapatnam Port are identified to perform the numerical simulation. The wave amplification at these locations is estimated for monochromatic incident waves, considering approximate water depth and different reflection coefficients on the wall of port under the resonance conditions. In addition, wave field analysis inside the Visakhapatnam Port is also conducted to understand resonance conditions. The current numerical model provides an efficient tool to analyze the amplification on any realistic ports or harbors.
相似文献12.
In this paper, following the procedure outlined by Li (1994. An evolution equation for water waves. Coastal Engineering, 23, 227-242) and Hsu and Wen (2000. A study of using parabolic model to describe wave breaking and wide-angle wave incidence. Journal of the Chinese Institute of Engineers, 23(4), 515–527) and Hsu and Wen (2000) the extended refraction–diffraction equation is recasted into a time-dependent parabolic equation. This model, which includes higher-order bottom effect terms, is extended to account for a rapidly varying topography and wave energy dissipation in the surf zone. The importance of the higher-order bottom effect terms is examined in terms of the relative water depth. The present model was tested for wave reflection in a number of different environments, namely from a plane slope with different inclinations, from a patch of periodic ripples. The model was also tested for wave height distribution around a circular shoal and wave breaking on a barred beach. The comparison of predictions with other numerical models and experimental data show that the validity of the present model for describing wave propagation over a rapidly varying seabed is satisfactory. 相似文献
13.
14.
A coupled-mode model is developed for treating the wave–current–seabed interaction problem, with application to wave scattering by non-homogeneous, steady current over general bottom topography. The vertical distribution of the scattered wave potential is represented by a series of local vertical modes containing the propagating mode and all evanescent modes, plus additional terms accounting for the satisfaction of the free-surface and bottom boundary conditions. Using the above representation, in conjunction with unconstrained variational principle, an improved coupled system of differential equations on the horizontal plane, with respect to the modal amplitudes, is derived. In the case of small-amplitude waves, a linearised version of the above coupled-mode system is obtained, generalizing previous results by Athanassoulis and Belibassakis [J Fluid Mech 1999;389:275–301] for the propagation of small-amplitude water waves over variable bathymetry regions. Keeping only the propagating mode in the vertical expansion of the wave potential, the present system reduces to an one-equation model, that is shown to be compatible with mild-slope model concerning wave–current interaction over slowly varying topography, and in the case of no current it exactly reduces to the modified mild-slope equation. The present coupled-mode system is discretized on the horizontal plane by using second-order finite differences and numerically solved by iterations. Results are presented for various representative test cases demonstrating the usefulness of the model, as well as the importance of the first evanescent modes and the additional sloping-bottom mode when the bottom slope is not negligible. The analytical structure of the present model facilitates its extension to fully non-linear waves, and to wave scattering by currents with more general structure. 相似文献
15.
Diapycnal mixing plays an important role in the ocean circulation.Internal waves are a kind of bridge relating the diapycnal mixing to external sources of mechanical energy.Difficulty in obtaining eigen solutions of internal waves over curved topography is a limitation for further theoretical study on the generation problem and scattering process.In this study,a kind of transform method is put forward to derive the eigen solutions of internal waves over subcritical topography in twodimensional and linear framework.The transform converts the curved topography in physical space to flat bottom in transform space while the governing equation of internal waves is still hyperbolic if proper transform function is selected.Thus,one can obtain eigen solutions of internal waves in the transform space.Several examples of transform functions,which convert the linear slope,the convex slope,and the concave slope to flat bottom,and the corresponding eigen solutions are illustrated.A method,using a polynomial to approximate the transform function and least squares method to estimate the undetermined coefficients in the polynomial,is introduced to calculate the approximate expression of the transform function for the given subcritical topography. 相似文献
16.
Predictions of nearshore and surf zone processes are important for determining coastal circulation, impacts of storms, navigation, and recreational safety. Numerical modeling of these systems facilitates advancements in our understanding of coastal changes and can provide predictive capabilities for resource managers. There exists many nearshore coastal circulation models, however they are mostly limited or typically only applied as depth integrated models. SHORECIRC is an established surf zone circulation model that is quasi-3D to allow the effect of the variability in the vertical structure of the currents while maintaining the computational advantage of a 2DH model. Here we compare SHORECIRC to ROMS, a fully 3D ocean circulation model which now includes a three dimensional formulation for the wave-driven flows. We compare the models with three different test applications for: (i) spectral waves approaching a plane beach with an oblique angle of incidence; (ii) monochromatic waves driving longshore currents in a laboratory basin; and (iii) monochromatic waves on a barred beach with rip channels in a laboratory basin. Results identify that the models are very similar for the depth integrated flows and qualitatively consistent for the vertically varying components. The differences are primarily the result of the vertically varying radiation stress utilized by ROMS and the utilization of long wave theory for the radiation stress formulation in vertical varying momentum balance by SHORECIRC. The quasi-3D model is faster, however the applicability of the fully 3D model allows it to extend over a broader range of processes, temporal, and spatial scales. 相似文献
17.
A Boussinesq model for simulating wave and current interaction 总被引：1，自引：0，他引：1
A new formulation of a pair of Boussinesq equations for three-dimensional nonlinear dispersive shallow-water waves is presented. This set of model equations permits spatial and temporal variations of the bottom topography and the presence of uniform currents. The newly derived equations are used to simulate the propagation of cnoidal waves and their interactions with a uniform current in a wave channel. The modified Euler's predictor-corrector algorithm for time advancing and a central difference representation for the space derivatives are applied to the computation of the basic equations. A set of open boundary conditions is developed to effectively transmit the cnoidal waves out of the computational domain. It is found that, as expected, the wave length decreases with an opposing current and increases with a following current. The wave height increases in magnitude with an opposing current and decreases with a following current. The Mach reflection due to oblique cnoidal waves propagating into an open channel with an opposing current is also investigated. Due to the opposing current, the wave patterns are compressed into smaller saddle-like regions in comparison with the Mach reflection without current effect. 相似文献
18.
《Coastal Engineering》2005,52(4):331-351
The development of an analytic model (Axisymmetric 3-D Step Model) for the propagation of linear water waves over an axisymmetric bathymetric anomaly in arbitrary water depth is presented. The Axisymmetric 3-D Step Model is valid in a region of uniform depth containing an axisymmetric bathymetric anomaly with gradual transitions in depth allowed as a series of steps approximating arbitrary slopes. The velocity potential is calculated by applying matching conditions at the interface between regions of constant depth. The velocity potential obtained determines the wave field in the domain for monochromatic incident waves of linear form. A second analytic model (3-D Shallow Water Exact Model) is developed for comparison within the shallow water limit.The Axisymmetric 3-D Step Model determines the wave transformation caused by the processes of wave refraction, diffraction and reflection. Wave transformation is demonstrated in plots of the relative amplitude for bathymetric anomalies in the form of pit or a shoal, highlighting areas of wave sheltering and wave focusing. Anomalies of constant volume, but variable cross-section are employed to isolate the effect of the transition slope on the wave transformation.Comparisons to a shallow water model, numerical models, and experimental data verify the results of the Axisymmetric 3-D Step Model for several bathymetries including both pits and shoals. Also included are estimates of the energy reflection induced by an axisymmetric depth anomaly. The 3-D Axisymmetric Step Model has been applied previously to account for nearshore transformation (sloping bathymetry) and associated shoreline changes [C.J. Bender, R.G. Dean, Coastal Engineering 51 (2004) 1143]. 相似文献
19.
Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem 总被引：3，自引：0，他引：3
A series of laboratory experiments was carried out to investigate the strong reflection of regular water waves over a train of submerged breakwaters. Rectangular and trapezoidal shapes of submerged breakwaters are employed and compared for reflecting capability of incident waves. Measured reflection coefficients of regular waves over impermeable submerged breakwaters are verified by comparing with those of the eigenfunction expansion method. A very good agreement is observed. Reflection coefficients of permeable submerged breakwaters are less than those of impermeable breakwaters. The trapezoidal shape is recommended for a submerged breakwater in terms of reflecting capability and practical application. 相似文献
20.
适合复杂地形的高阶Boussinesq水波方程 总被引：17，自引：4，他引：17
针对海底坡度较大(量阶为O(1))或海底曲率较大的复杂地形,建立了一个新型高阶Boussinesq水波方程.该方程可用于研究海底存在若干相互平行沙坝引起的Bragg反射问题.方程的水平速度沿水深的分布为四次多项式,色散性和变浅作用性能的精度比经典Boussinesq方程高了一阶.方程在浅水水域可以是完全非线性的. 相似文献