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1.
A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool. 相似文献
2.
In this paper we propose an integral form of the fully non-linear Boussinesq equations in contravariant formulation, in which Christoffel symbols are avoided, in order to simulate wave transformation phenomena, wave breaking and nearshore currents in computational domains representing the complex morphology of real coastal regions. Following the approach proposed by Chen (2006), the motion equations retain the term related to the approximation to the second order of the vertical vorticity. A new Upwind Weighted Essentially Non-Oscillatory scheme for the solution of the fully non-linear Boussinesq equations on generalised curvilinear coordinate systems is proposed. The equations are rearranged in order to solve them by a high resolution hybrid finite volume–finite difference scheme. The conservative part of the above-mentioned equations, consisting of the convective terms and the terms related to the free surface elevation, is discretised by a high-order shock-capturing finite volume scheme in which an exact Riemann solver is involved; dispersive terms and the term related to the approximation to the second order of the vertical vorticity are discretised by a cell-centred finite difference scheme. The shock-capturing method makes it possible to intrinsically model the wave breaking, therefore no additional terms are needed to take into account the breaking related energy dissipation in the surf zone. The model is verified against several benchmark tests, and the results are compared with experimental, theoretical and alternative numerical solutions. 相似文献
3.
This paper describes the formulation and validation of a nearshore wave model for tropical coastal environment. The governing Boussinesq-type equations include the conservative form of the nonlinear shallow-water equations for shock capturing. A Riemann solver supplies the inter-cell flux and bathymetry source term, while a Godunov-type scheme integrates the evolution variables in time. The model handles wave breaking through momentum conservation with energy dissipation based on an eddy viscosity concept. The computed results show very good agreement with laboratory data for wave propagation over a submerged bar, wave breaking and runup on plane beaches as well as wave transformation over fringing reefs. The model accurately describes transition between supercritical and subcritical flows as well as development of dispersive waves in the processes. 相似文献
4.
5.
Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure 总被引：2，自引：0，他引：2
A numerical method for non-hydrostatic, free-surface, irrotational flow governed by the nonlinear shallow water equations including the effects of vertical acceleration is presented at the aim of studying surf zone phenomena. A vertical boundary-fitted grid is used with the water depth divided into a number of layers. A compact finite difference scheme is employed for accurate computation of frequency dispersion requiring a limited vertical resolution and hence, capable of predicting the onset of wave breaking. A novel wet–dry algorithm is applied for a proper handling of moving shoreline. Mass and momentum are strictly conserved at discrete level while the method only dissipates energy in the case of wave breaking. The numerical results are verified with a number of tests and show that the proposed model using two layers without ad-hoc assumptions enables to resolve propagating nonlinear shoaling, breaking waves and wave run-up within the surf and swash zones in an efficient manner. 相似文献
6.
Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone 总被引：2，自引：0，他引：2
In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data. 相似文献
7.
A higher-order non-hydrostatic model in a σ-coordinate system is developed. The model uses an implicit finite difference scheme on a staggered grid to simultaneously solve the unsteady Navier-Stokes equations (NSE) with the free-surface boundary conditions. An integral method is applied to resolve the top-layer non-hydrostatic pressure, allowing for accurately resolving free-surface wave propagation. In contrast to the previous work, a higher-order spatial discretization is utilized to approximate the large horizontal pressure gradient due to steep surface waves or rapidly varying topographies. An efficient direct solver is developed to solve the resulting block hepta-diagonal matrix system. Accuracy of the new model is validated by linear and nonlinear standing waves and progressive waves. The model is then used to examine freak (extreme) waves. Features of downshifting focusing location and wave asymmetry characteristics are predicted on the temporal and spatial domains of a freak wave. 相似文献
8.
Novel laboratory experiments and numerical modelling have been performed to study the advection scales of suspended sediment in the swash zone. An experiment was designed specifically to measure only the sediment picked up seaward of the swash zone and during bore collapse. The advection scales and settling of this sediment were measured during the uprush along a rigid sediment-free beach face by a sediment trap located at varying cross-shore positions. Measurements were made using a number of repeated solitary broken waves or bores. Approximately 25% of the pre-suspended sediment picked up by the bores reaches the mid-swash zone (50% of the horizontal run-up distance), indicating the importance of the sediment advection in the lower swash zone. The pre-suspended sediment is sourced from a region seaward of the shoreline (still water line) which has a width of about 20% of the run-up distance. An Eulerian–Lagrangian numerical model is used to model the advection scales of the suspended sediment. The model resolves the hydrodynamics by solving the non-linear shallow water equations in an Eulerian framework and then solves the advection–diffusion equation for turbulence and suspended sediment in a Lagrangian framework. The model provides good estimates of the measured mass and distribution of sediment advected up the beach face. The results suggest that the correct modelling of turbulence generation prior to and during bore collapse and the advection of the turbulent kinetic energy into the lower swash is important in resolving the contribution of pre-suspended sediment to the net sediment transport in the swash zone. 相似文献
9.
New laboratory and field data are presented on fluid advection into the swash zone. The data illustrate the region of the inner surf zone from which sediment can be directly advected into the swash zone during a single uprush, which is termed the advection length. Experiments were conducted by particle tracking in a Lagrangian reference frame, and were performed for monochromatic breaking waves, solitary bores, non-breaking solitary waves and field conditions. The advection length is normalised by the run-up length to give an advection ratio, A, and different advection ratios are identified on the basis of the experimental data. The data show that fluid enters the swash zone from a region of the inner surf zone that can extend a distance seaward of the bore collapse location that is approximately equal to half of the run-up length. This region is about eight times wider than the region predicted by the classical swash solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. Journal of Fluid Mechanics 16, 113–125], as illustrated by Pritchard and Hogg [Pritchard, D., Hogg, A.J., 2005. On the transport of suspended sediment by a swash event on a plane beach. Coastal Engineering 52, 1–23]. Measured advection ratios for periodic waves show no significant trend with Iribarren number, consistent with self-similarity in typical swash flows. The data are compared to recent characteristic solutions of the non-linear shallow water wave (NLSW) equations and both finite difference and finite volume solutions of the NLSW equations. 相似文献
10.
This is the second of three papers on the modelling of various types of surf zone phenomena. In the first paper the general model was described and it was applied to study cross-shore motion of regular waves in the surf zone. In this paper, part II, we consider the cross-shore motion of wave groups and irregular waves with emphasis on shoaling, breaking and runup as well as the generation of surf beats. These phenomena are investigated numerically by using a time-domain Boussinesq type model, which resolves the primary wave motion as well as the long waves. As compared with the classical Boussinesq equations, the equations adopted here allow for improved linear dispersion characteristics and wave breaking is modelled by using a roller concept for spilling breakers. The swash zone is included by incorporating a moving shoreline boundary condition and radiation of short and long period waves from the offshore boundary is allowed by the use of absorbing sponge layers. Mutual interaction between short waves and long waves is inherent in the model. This allows, for example, for a general exchange of energy between triads rather than a simple one-way forcing of bound waves and for a substantial modification of bore celerities in the swash zone due to the presence of long waves. The model study is based mainly on incident bichromatic wave groups considering a range of mean frequencies, group frequencies, modulation rates, sea bed slopes and surf similarity parameters. Additionally, two cases of incident irregular waves are studied. The model results presented include transformation of surface elevations during shoaling, breaking and runup and the resulting shoreline oscillations. The low frequency motion induced by the primary-wave groups is determined at the shoreline and outside the surf zone by low-pass filtering and subsequent division into incident bound and free components and reflected free components. The model results are compared with laboratory experiments from the literature and the agreement is generally found to be very good. Finally the paper includes special details from the breaker model: time and space trajectories of surface rollers revealing the breakpoint oscillation and the speed of bores; envelopes of low-pass filtered radiation stress and surface elevation; sensitivity of surf beat to group frequency, modulation rate and bottom slope is investigated. Part III of this work (Sørensen et al., 1998) presents nearshore circulations induced by the breaking of unidirectional and multi-directional waves. 相似文献
11.
A probabilistic model (
-model) was developed to describe the propagation and transformation of individual waves (wave by wave approach). The individual waves shoal until an empirical criterion for breaking is satisfied. Wave height decay after breaking is modelled by using an energy dissipation method. Wave-induced set-up and set-down and breaking-associated longshore currents are also modelled. Laboratory and field data were used to calibrate and verify the model. The model was calibrated by adjusting the wave breaking coefficient (as a function of local wave steepness and bottom slope) to obtain optimum agreement between measured and computed wave height. Four tests carried out in the large Delta flume of Delft Hydraulics were considered. Generally, the measured H1/3-wave heights are reasonably well represented by the model in all zones from deep water to the shallow surf zone. The fraction of breaking waves was reasonably well represented by the model in the upsloping zones of the bottom profile. Verification of the model results with respect to wave-induced longshore current velocities was not extensive, because of a lack of data. In case of a barred profile the measured longshore velocities showed a relatively uniform distribution in the (trough) zone between the bar crest and the shoreline, which could to some extent be modelled by including space-averaging of the radiation force gradient, horizontal mixing and longshore water surface gradients related to variations in set-up. In case of a monotonically upsloping profile the cross-shore distribution of the longshore current velocities is reasonably well represented. 相似文献
12.
In this paper, a hybrid scheme based on a set of 2DH extended Boussinesq equations for slowly varying bathymetries is introduced. The numerical code combines the finite volume technique, applied to solve the advective part of the equations, with the finite difference method, used to discretize dispersive and source terms. Time integration is performed using the fourth-order Adams–Bashforth–Moulton predictor–corrector method; the Riemann problem is solved employing an approximate HLL solver, a fourth-order MUSCL-TVD technique is applied. Five test cases, for non-breaking and breaking waves, are reproduced to verify the model comparing its results to laboratory data or analytical solutions. 相似文献
13.
《Coastal Engineering》2006,53(2-3):265-275
Sand waves form a prominent regular pattern in the offshore seabeds of sandy shallow seas and pose a threat to a range of offshore activities. A two-dimensional vertical (2DV) flow and morphological simulation model describing the behaviour of these sand waves has been developed. The simulation model contains the 2DV shallow water equations, with a free water surface and a general bed load formula. The water movement is coupled to the sediment transport equation with a seabed evolution equation. The domain is non-periodic in both directions. The spatial discretisation is performed by a spectral method based on Chebyshev polynomials. A fully implicit method is chosen for the discretisation in time. Firstly, we validate the simulation model mathematically by reproducing the results obtained using a linear stability analysis for infinitely small sand waves. Hereby, we investigate a steady current situation induced by a wind stress applied at the sea surface. The bed forms we find have wavelengths in the order of hundreds of metres when the resistance at the seabed is relatively large. The results show that it is possible to model the initial evolution of sand waves with a numerical simulation model. This paper forms the necessary first step to investigate the intermediate term behaviour of sand waves. 相似文献
14.
《Coastal Engineering》2005,52(5):391-407
A numerical solver is presented of the modified time-independent mild-slope equation, which incorporates energy dissipation. Using a second-order parabolic approximation, the following external boundary conditions are modelled: open and fully transmitting to both incoming and outgoing waves; partially reflecting, and; fully absorbing. Discretisation of the governing equation and boundary conditions is by means of a second-order accurate central difference scheme. The resulting sparse-banded matrix is solved using an inexpensive banded solver with Gaussian elimination. The numerical predictions are in excellent agreement with the analytical solution for the interaction of non-breaking waves with an array of vertical surface-piercing circular cylinders on a horizontal bed. Results are compared with those for the same array on various seabed topographies. The model is robust and can be used for wave propagation in complex geometries. It has fewer restrictions associated with wave obliqueness at boundaries than traditional models based on the mild-slope equation. 相似文献
15.
数值模拟作为海啸预报的主要研究方法在海啸预警中起着关键作用。本文采用Godunov格式的有限体积方法,使用MUSCL-Hancock格式,并利用HLLC Riemann近似求解器计算单元界面上的流体通量,建立了球坐标系下二阶精度的海啸数值模型。模型所基于的全和谐型浅水方程保证了数值的稳定性,而地形重构方法实现了干湿边界的精准模拟。本文模拟了2015年9月16日智利Mw8.3级地震海啸,通过与智利近岸14个测站和环太平洋20个DART浮标实测数据比较,验证了模型对实际越洋海啸模拟预报的能力。 相似文献
16.
本文基于具备间断捕捉能力的二阶全非线性Boussinesq数值模型,对规则波和随机波在礁坪地形上的传播变形进行了数值模拟。该模型采用高阶有限体积法和有限差分方法求解守恒格式的控制方程,将波浪破碎视为间断,同时采用静态重构技术处理了海岸动边界问题。重点针对礁坪上波浪传播过程中的波高空间分布和沿程衰减,礁坪上的平均水位变化,以及波浪能量频谱的移动和空间差异等典型水动力现象开展数值计算。将数值结果与实验结果对比,两者吻合情况良好,验证了模型具有良好的稳定性,具备模拟破碎波浪和海-岸动边界的能力,能较为准确地模拟波浪在礁坪地形上的传播过程中发生的各种水动力现象。 相似文献
17.
Nearshore shoaling and breaking waves can drive a complex circulation system of wave-induced currents. In the cross-shore direction, the local vertical imbalance between the gradient of radiation stress and that of pressure due to the setup drives an offshore flow near the bottom, called ‘undertow’, which plays a significant role in the beach profile evolution and the structure stability in coastal regions. A 1DV undertow model was developed based on the relationship between the turbulent shear stress and t... 相似文献
18.
The highest short-crested waves have been studied analytically and numerically by several workers, but without a conclusive view. An efficient numerical scheme is proposed in this paper which retains the water-surface elevations in an implicit form in the governing equations, rather than using a series approximation, thus improving the accuracy of the numerical results. Convergence of the numerical scheme is verified. The almost highest short-crested waves in deep water are then evaluated, which are defined for the condition with the largest wave energies. It is found that the critical angle for wave frequency reversal also demarcates the wave characteristics near breaking, for either kinematic or dynamic prominence. The known results available for the limiting two-dimensional cases of standing and progressive waves are compared favourably. 相似文献
19.
R. Bakhtyar D.A. Barry L. Li D.S. Jeng A. Yeganeh-Bakhtiary 《Ocean Engineering》2009,36(9-10):767-783
A critical review of conceptual and mathematical models developed in recent decades on sediment transport in the swash zone is presented. Numerous studies of the hydrodynamics and sediment transport in the swash zone in recent years have pointed out the importance of swash processes in terms of science advancement and practical applications. Evidently, the hydrodynamics of the swash zone are complex and not fully understood. Key hydrodynamic processes include both high-frequency bores and low-frequency infragravity motions, and are affected by wave breaking and turbulence, shear stresses and bottom friction. The prediction of sediment transport that results from these complex and interacting processes is a challenging task. Besides, sediment transport in this oscillatory environment is affected by high-order processes such as the beach groundwater flow. Most relationships between sediment transport and flow characteristics are empirical, based on laboratory experiments and/or field measurements. Analytical solutions incorporating key factors such as sediment characteristics and concentration, waves and coastal aquifer interactions are unavailable. Therefore, numerical models for wave and sediment transport are widely used by coastal engineers. This review covers mechanisms of sediment transport, important forcing factors, governing equations of wave-induced flow, groundwater interactions, empirical and numerical relations of cross-shore and longshore sediment transport in the swash zone. Major advantages and shortcomings of various numerical models and approaches are highlighted and reviewed. These will provide coastal modelers an impetus for further detailed investigations of fluid and sediment transport in the swash zone. 相似文献
20.
This paper builds on the work of Masselink [Masselink, G., 1993. Simulating the effects of tides on beach morphodynamics. J. Coast. Res. SI 15, 180–197.] on the use of the residence times of shoaling waves, breaking waves and swash/backwash motions across a cross-shore profile to qualitatively understand temporal beach behaviour. We use a data set of in-situ measurements of wave parameters (height and period) and water depth, and time-exposure video images overlooking our single-barred intertidal measurement array at Egmond aan Zee (Netherlands) to derive boundaries between the shoaling zone, the surf zone and the swash zone. We find that the boundaries are functional dependencies of the local relative wave height on the local wave steepness. This contrasts with the use of constant relative wave heights or water levels in earlier work. We use the obtained boundaries and a standard cross-shore wave transformation model coupled to an inner surf zone bore model to show that large (> 5) relative tide ranges (RTR, defined as the ratio tide range–wave height) indicate shoaling wave processes across almost the entire intertidal profile, with surf processes dominating on the beach face. When the RTR is between 2 and 5, surf processes dominate over the intertidal bar and the lower part of the beach face, while swash has the largest residence times on the upper beach face. Such conditions, associated with surf zone bores propagating across the bar around low tide, were observed to cause the intertidal bar to migrate onshore slowly and the upper beach face to steepen. For RTR values less than about 2, surf zone processes dominate across the intertidal bar, while the dominance of swash processes now extends across most of the beach face. The surf zone processes were now observed to lead to offshore bar migration, while the swash eroded the upper beach face. 相似文献