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1.
Tai-Wen Hsu Shih-Chun Hsiao Shan-Hwei Ou Swun-Kwang Wang Bin-Da Yang Shih-En Chou 《Ocean Engineering》2007,34(5-6):870-883
A numerical model based on the second-order fully nonlinear Boussinesq equations of Wei et al. [1995. Journal of Waterway, Port, Coastal and Ocean Engineering 121 (5), 251-263] is developed to simulate the Bragg reflection of both regular and irregular surface waves scattered by submerged bars. Particularly for incident regular waves, the computed results are observed to agree very well with the existing experimental data as presented by Davies and Heathershaw [1984. Journal of Fluid Mechanics 144, 419-446] and Kirby and Anton [1990. Proceedings of the 22nd International Conference on Coastal Engineering, ASCE, New York, pp. 757–768). In the case of incident irregular waves, the simulated results reveal that the distribution of Bragg reflection from irregular waves becomes more flat than that of regular waves. Due to lack of experimental data, the numerical results for incident irregular waves are compared with those of the evolution equation of the mild-slope equation [Hsu et al., 2002 Proceedings of the 24th Ocean Engineering Conference in Taiwan, pp. 70–77 (in Chinese)]. In addition, several parameters such as the number of bars, the relative height of bars and the spacing of bars affecting Bragg reflection are also discussed. 相似文献
2.
《Coastal Engineering》2006,53(4):311-318
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. Coastal Eng., 32, 91–117] and Lee et al. [Lee, C., Kim, G., Suh, K.D., 2003. Extended mild-slope equation for random waves. Coastal Eng., 48, 277–287] are compared analytically and numerically to determine their applicability to random wave transformation. The geometric optics approach is used to compare the two models analytically. In the model of Suh et al., the wave number of the component wave with a local angular frequency ω is approximated with an accuracy of O(ω − ω¯) at a constant water depth, where ω¯ is the carrier frequency of random waves. In the model of Suh et al., however, the diffraction effects and higher-order bottom effects are considered only for monochromatic waves, and the shoaling coefficient of random waves is not accurately approximated. This inaccuracy arises because the model of Suh et al. was derived for regular waves. In the model of Lee et al., all the parameters of random waves such as wave number, shoaling coefficient, diffraction effects, and higher-order bottom effects are approximated with an accuracy of O(ω − ω¯). This approximation is because the model of Lee et al. was developed using the Taylor series expansion technique for random waves. The result of dispersion relation analysis suggests the use of the peak and weighted-average frequencies as a carrier frequency for Suh et al. and Lee et al. models, respectively. All the analytical results are verified by numerical experiments of shoaling of random waves over a slightly inclined bed and diffraction of random waves through a breakwater gap on a flat bottom. 相似文献
3.
In this paper, a finite difference scheme with an efficient 2-D numerical wave absorber for solving the extended Boussinesq equations as derived by Nwogu (Nwogu, O., 1993. Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterway, Port, Coastal and Ocean Engineering, ASCE 119, 618–638) is proposed. The alternate direction iterative method combined with an efficient predictor-corrector scheme are adopted for the numerical solution of the governing differential equations. To parameterize the contribution of unresolved small-scale motions, the philosophy of the large eddy simulation is applied on the horizontal plane. The proposed method is verified by two test cases where experimental data are available for comparison. The first case is wave diffraction around a semi-infinite breakwater studied by Briggs et al. (Briggs, M.J., Thompson, E.F., Vincent, C.L., 1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE 121, 23–35). The other case is wave concentration by a navigation channel as reported by Yu et al. (Yu, Y.-X., Liu, S.-X., Li, Y.S., Wai, O.W.H., 2000. Refraction and diffraction of random waves through breakwater. Ocean Engineering 27, 489–509). Numerical results agree very well with the corresponding experimental data in both cases. 相似文献
4.
Application of desingularized approach to water wave propagation over three-dimensional topography 总被引：1，自引：0，他引：1
A numerical approach based on desingularized boundary element method and mixed Eulerian–Lagrangian formulation [Zhang et al., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Engineering 33, 2310–2331] is extended to solve the water wave propagation over arbitrary topography in a three-dimensional wave tank. A robust damping layer applicable for regular and irregular incident waves is employed to minimize the outgoing wave reflection back into the wave tank. Numerical results on the propagation of regular and irregular incident waves over the flat bottom and linear incident waves over an elliptical shoal show good concurrence with the corresponding analytical solutions and experimental data. 相似文献
5.
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
6.
In this study, we investigate two internal wave generation methods in numerical modeling of time-dependent equations for water wave propagation, i.e., delta source function method and source term addition method, the latter of which has been called the line source method in literatures. We derive delta source functions for the Boussinesq-type equations and extended mild-slope equations. By applying the fractional step splitting method, we show that the delta source function method is equivalent to the source term addition method employing the energy velocity. This suggests that the energy velocity should be used rather than the phase velocity for the transport of incident wave energy in the source term addition method. Finally, the performance of the delta source function method is verified by accurately generating nonlinear cnoidal waves as well as linear waves for horizontally one-dimensional cases. 相似文献
7.
Two types of analytical solutions for waves propagating over an asymmetric trench are derived. One is a long-wave solution and the other is a mild-slope solution, which is applicable to deeper water. The water depth inside the trench varies in proportion to a power of the distance from the center of the trench (which is the deepest water depth point and the origin of x-coordinate in this study). The mild-slope equation is transformed into a second-order ordinary differential equation with variable coefficients based on the longwave assumption [Hunt's, 1979. Direct solution of wave dispersion equation. Journal of Waterway, Port, Coast. and Ocean Engineering 105, 457–459] as approximate solution for wave dispersion. The analytical solutions are then obtained by using the power series technique. The analytical solutions are compared with the numerical solution of the hyperbolic mild-slope equations. After obtaining the analytical solutions under various conditions, the results are analyzed. 相似文献
8.
《Coastal Engineering》2005,52(6):513-533
Using the perturbation method, a time dependent parabolic equation is developed based on the elliptic mild slope equation with dissipation term. With the time dependent parabolic equation employed as the governing equation, a numerical model for wave propagation including dissipation term in water of slowly varying topography is presented in curvilinear coordinates. In the model, the self-adaptive grid generation method is employed to generate a boundary-fitted and varying spacing mesh. The numerical tests show that the effects of dissipation term should be taken into account if the distance of wave propagation is large, and that the outgoing boundary conditions can be treated more effectively by introduction of the dissipation term into the numerical model. The numerical model is able to give good results of simulating wave propagation for waters of complicatedly boundaries and effectively predict physical processes of wave propagation. Moreover, the errors of the analytical solution deduced by Kirby et al. (1994) [Kirby, J.T., Dalrymple, R.A., Kabu, H., 1994. Parabolic approximation for water waves in conformal coordinate systems. Coastal Engineering 23, 185–213.] from the small-angle parabolic approximation of the mild-slope equation for the case of waves between diverging breakwaters in a polar coordinate system are corrected. 相似文献
9.
Extended Boussinesq equations for rapidly varying topography 总被引：1，自引：0，他引：1
We developed a new Boussinesq-type model which extends the equations of Madsen and Sørensen [1992. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly varying bathymetry. Coastal Engineering 18, 183-204.] by including both bottom curvature and squared bottom slope terms. Numerical experiments were conducted for wave reflection from the Booij's [1983. A note on the accuracy of the mild-slope equation. Coastal Engineering 7, 191-203] planar slope with different wave frequencies using several types of Boussinesq equations. Madsen and Sørensen's model results are accurate in the whole slopes in shallow waters, but inaccurate in intermediate water depths. Nwogu's [1993. Alternative form of Boussinesq equation for nearshore wave propagation. Journal of Waterway, Port, Coastal and Ocean Engineering 119, 618-638] model results are accurate up to 1:1 (V:H) slope, but significantly inaccurate for steep slopes. The present model results are accurate up to the slope of 1:1, but somewhat inaccurate for very steep slopes. Further, numerical experiments were conducted for wave reflections from a ripple patch and also a Gaussian-shaped trench. For the two cases, the results of Nwogu's model and the present model are accurate, because these models include the bottom curvature term which is important for the cases. However, Madsen and Sørensen's model results are inaccurate, because this model neglects the bottom curvature term. 相似文献
10.
Nadarajah [Nadarajah, S., 2008. Letter to the Editor. Coastal Engineering 55, 189–190] pointed out several errors in the paper by Muraleedharan et al. [Muraleedharan, G., Rao, A. D., Kurup, P. G., Unnikrishnan Nair, N., Sinha, M., in press. Modified Weibull distribution for maximum and significant wave height simulation and prediction. Coastal Engineering] which suggested a modified Weibull distribution for maximum and significant wave height simulation and prediction. In response to Nadarajah's [Nadarajah, S., 2008. Letter to the Editor. Coastal Engineering 55, 189–190] comments, Muraleedharan [Muraleedharan, G., 2008. Reply to Saralees Nadarajah. Coastal Engineering 55, 191–193] argued that there were no errors in the original paper by Muraleedharan et al. [Muraleedharan, G., Rao, A. D., Kurup, P. G., Unnikrishnan Nair, N., Sinha, M., in press. Modified Weibull distribution for maximum and significant wave height simulation and prediction. Coastal Engineering]. Here, it is pointed out that the response by Muraleedharan [Muraleedharan, G., 2008. Reply to Saralees Nadarajah. Coastal Engineering 55, 191–193] is at least as incorrect as Muraleedharan et al. [Muraleedharan, G., Rao, A. D., Kurup, P. G., Unnikrishnan Nair, N., Sinha, M., in press. Modified Weibull distribution for maximum and significant wave height simulation and prediction. Coastal Engineering]. 相似文献
11.
The Breaking Celerity Index (BCI) is proposed as a new wave breaking criterion for Boussinesq-type equations wave propagation models (BTE).The BCI effectiveness in determining the breaking initiation location has been verified against data from different experimental investigations conducted with incident regular and irregular waves propagating along uniform slope [Utku, M. (1999). “The Relative Trough Froude Number. A New Criteria for Wave Breaking”. Ph.D. Dissertation, Dept. of Civil and Enviromental Engineering, Old Dominion University, Norfolk, VA; Gonsalves Veloso dos Reis, M.T.L. (1992). “Characteristics of waves in the surf zone”. MS Thesis, Department of Civil Engineering, University of Liverpool., Liverpool; Lara, J.L., Losada, I.J., and Liu, P.L.-F. (2006). “Breaking waves over a mild gravel slope: experimental and numerical analysis”. Journal of Geophysical Research, VOL 111, C11019] and barred beaches [Tomasicchio, G.R., and Sancho, F. (2002). “On wave induced undertow at a barred beach”. Proceedings of 28th International Conference on Coastal Engineering, ASCE, New York, 557–569]. The considered experiments were carried out in small-scale and large-scale facilities. In addition, one set of data has been obtained by the use of the COBRAS model based upon the Reynolds Averaged Navier Stokes (RANS) equations [Liu, P.L.-F., Lin, P., Hsu, T., Chang, K., Losada, I.J., Vidal, C., and Sakakiyama, T. (2000). “A Reynolds averaged Navier–Stokes equation model for nonlinear water wave and structure interactions”. Proceedings of Coastal Structures ‘99, Balkema, Rotterdam, 169–174; Losada, I.J., Lara, J.L., and Liu, P.L.-F. (2005). “Numerical simulation based on a RANS model of wave groups on an impermeable slope”. Proceedings of Fifth International Symposium WAVES 2005, Madrid].Numerical simulations have been performed with the 1D-FUNWAVE model [Kirby, J.T., Wei, G., Chen, Q., Kennedy, A.B., and Dalrymple, R.A. (1998). “FUNWAVE 1.0 Fully Nonlinear Boussinesq Wave Model Documentation and User's Manual”. Research Report No CACR-98-06, Center for Applied Coastal Research, University of Delaware, Newark]. With regard to the adopted experimental conditions, the breaking location has been calculated for different trigger mechanisms [Zelt, J.A. (1991). “The run-up of nonbreaking and breaking solitary waves”. Coastal Engineering, 15, 205–246; Kennedy, A.B., Chen, Q., Kirby, J.T., and Dalrymple, R.A. (2000). “Boussinesq modeling of wave transformation, breaking and run-up. I: 1D”. Journal of Waterway, Port, Coastal and Ocean Engineering, 126, 39–47; Utku, M., and Basco, D.R. (2002). “A new criteria for wave breaking based on the Relative Trough Froude Number”. Proceedings of 28th International Conference on Coastal Engineering, ASCE, New York, 258–268] including the proposed BCI.The calculations have shown that BCI gives a better agreement with the physical data with respect to the other trigger criteria, both for spilling and plunging breaking events, with a not negligible reduction of the calculation time. 相似文献
12.
Conventional spectral wave models, which are used to determine wave conditions in coastal regions, can account for all relevant processes of generation, dissipation and propagation, except diffraction. To accommodate diffraction in such models, a phase-decoupled refraction–diffraction approximation is suggested. It is expressed in terms of the directional turning rate of the individual wave components in the two-dimensional wave spectrum. The approximation is based on the mild-slope equation for refraction–diffraction, omitting phase information. It does therefore not permit coherent wave fields in the computational domain (harbours with standing-wave patterns are excluded). The third-generation wave model SWAN (Simulating WAves Nearshore) was used for the numerical implementation based on a straightforward finite-difference scheme. Computational results in extreme diffraction-prone cases agree reasonably well with observations, analytical solutions and solutions of conventional refraction–diffraction models. It is shown that the agreement would improve further if singularities in the wave field (e.g., at the tips of breakwaters) could be properly accounted for. The implementation of this phase-decoupled refraction–diffraction approximation in SWAN shows that diffraction of random, short-crested waves, based on the mild-slope equation can be combined with the processes of refraction, shoaling, generation, dissipation and wave–wave interactions in spectral wave models. 相似文献
13.
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. 相似文献
14.
The study describes a new fixed-frequency Stokes wave theory that differs from previous Stokes wave theories that fix the wave number. The present wave expansion analytically reveals that the wavelength increases with wave height and exceeds than the wavelength obtained by linear wave theory. A method proposed to comparably transform the wave celerity of Fenton's [Fenton, J.D., 1985. A fifth-order Stokes theory for steady waves. Journal of Waterway, Port, Coastal and Ocean Engineering 111, 216–234.] wave theory to the present one. A direct calculation of the wavelength is introduced for practical solutions, avoiding the need to solve a nonlinear equation using an iterative numerical method. 相似文献
15.
An approach by which the scour depth and scour width below a fixed pipeline and scour depth around a circular vertical pile in random waves can be derived is presented. Here, the scour depth formulas by Sumer and Fredsøe [ASCE J. Waterw., Port, Coastal Ocean Eng. 116 (1990) 307] for pipelines and Sumer et al. [ASCE J. Waterw., Port, Coastal Ocean Eng. 114 (1992) 599] for vertical piles as well as the scour width formula by Sumer and Fredsøe [The Mechanics of Scour in the Marine Environment, World Scientific, Singapore, 2002] for pipelines combined with describing the waves as a stationary Gaussian narrow-band random process are used to derive the cumulative distribution functions of the scour depths and width. Comparisons are made between the present approach and random wave scour data. Tentative approaches to related random wave scour cases are also suggested. 相似文献
16.
The numerical investigation of random wave slamming on superstructures of marine structures in the splash zone is presented in this paper. The impact pressures on the underside of the structure are computed based on the improved volume of fluid method (VOF). The governing equations are Reynolds time-averaged equations and the two equation k– model. The third order upwind difference scheme is applied to the convection term to reduce the effect of numerical viscosity. The numerical wave flume with random wave-maker suitable for VOF is established. Appropriate moving contact-line boundary conditions are introduced to the model wave in contact with and separated from the underside of structure. Parametric studies have been carried out for different incident waves, structure dimensions and structure clearance. The numerical results are verified by the experimental results. 相似文献
17.
In designing the coastal structures, the accurate estimation of the wave forces on them is of great importance. In this paper, the influences of the phase difference on wave pressure acting on a composite breakwater installed in the three-dimensional (3-D) wave field are studied numerically. We extend the earlier model [Hur, D.S., Mizutani, N., 2003. Coastal Engineering 47, 329–345] to simulate 3-D wave fields by introducing 3-D Navier–Stokes solver with the Smagorinsky's sub-grid scale (SGS) model. For the validation of the model, the wave field around a 3-D asymmetrical structure installed on a submerged breakwater, in which the complex wave deformations generate, is simulated, and the numerical solutions are compared to the experimental data reported by Hur, Mizutani, Kim [2004. Coastal Engineering (51, 407–420)]. The model is then adopted to investigate 3-D characteristics of wave pressure and force on a caisson of composite breakwater, and the numerical solutions were discussed with respect to the phase difference between harbor and seaward sides induced by the transmitted wave through the rubble mound or the diffraction. The numerical results reveal that wave forces acting on the composite breakwater are significantly different at each cross-section under influence of wave diffraction that is important parameter on 3-D wave interaction with coastal structures. 相似文献
18.
19.
This paper presents a mathematical model which computes the hydrodynamic characteristics of a curtainwall–pile breakwater (CPB) using circular piles, by modifying the model developed for rectangular piles by Suh et al. [2006. Hydrodynamic characteristics of pile-supported vertical wall breakwaters. Journal of Waterway, Port, Coastal and Ocean Engineering 132(2), 83–96]. To examine the validity of the model, laboratory experiments have been conducted for CPB with various values of draft of curtain wall, spacing between piles, and wave height and period. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. The mathematical model based on linear wave theory tends to over-predict the reflection coefficient as the wave height increases. As the draft of the curtain wall increases and the porosity between piles decreases, the reflection and transmission coefficient increases and decreases, respectively, as expected. As the relative water depth increases, however, the effect of porosity disappears because the wave motion is minimal in the lower part of a water column for short waves. 相似文献
20.
Coastal disposal of waste water can be idealized as the problem of a jet under random waves. Understanding of this phenomenon is important for engineering design and environmental impact assessment. The present study aims to simulate such phenomenon by using a 3D numerical model based on the solution of the spatially filtered and σ-transformed Navier–Stokes equations with dynamic sub-grid scale model of turbulence. The numerical solution procedures are split into three steps: advection, diffusion and pressure propagation, and a Lagrange–Euler method is used to track the free surface. Cases of vertical jet in stagnant water, pure random waves and vertical jet in random waves are simulated with the same grid system for comparative study. Different methods of generating jet inflow turbulence have been tested and the method of jet azimuthal modes is found to be the optimum. The numerical results reproduce the distinct characteristics of jet in waves, including faster decay of centerline velocity, wider lateral spreading and the occurrence of wave tractive mechanism. 相似文献