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1.
Large Eddy Simulation for Wave Breaking in the Surf Zone 总被引:1,自引:0,他引:1
BAI Yuchuan BAI Yuchuan JIANG Changbo SHEN Huanting 《中国海洋工程》2001,(4):541-552
In this paper, (he large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling leads lo the increase of wave height, and then at a certain position, the wave will be breaking. The breaking wave is a powerful agent for generating turbulence, which plays an important role in most of the fluid dynamic processes throughout the surf zone, such as transformation of wave energy, generation of near-shore current and diffusion of materials. So a proper numerical model for describing the turbulence effect is needed. In this paper, a revised Smagorinsky subgrid-scale mode! is used to describe the turbulence effect. The present study reveals that the coefficient of the Smagorinsky model for wave propagation or breaking simulation may be taken as a varying function of the water depth and distance away from the wave breaking point. The large eddy simulation model presented in this pape 相似文献
2.
近岸波浪浅水变形的非线性分析 总被引:1,自引:0,他引:1
本文就近岸波浪具有非线性特征提出了应用椭圆余弦波理论来研究波浪浅水变形的非线性问题。本文在椭圆余弦波数值计算的基础上,进一步分析了浅水波浪在HL~2/D~3>26情形下波高的变化规律,其中考虑了床面底摩擦、底坡和传质水流等因素对波高变化的影响及相应的程度分析。计算结果分析表明,浅水波浪的非线性性质和底部摩擦对波高变化的影响不能忽略,这对确定海岸工程标高有较大的实际意义和经济价值。 相似文献
3.
Shen Xianrong
Engineer Zhejiang Provincial Design Institute of Communications Hangzhou 《中国海洋工程》1995,(4)
Wave formulae derived from the dispersion relation for cnoidal waves are used to find an analytical solution to the problem of nearshore wave height variation on a simple topography, i. e., with an incrementally constant slope. The solution accounts for shoaling, frictional dissipation and will be sufficiently accurate for practical purposes considering the simplified assumptions which are necessary for the treatment of this problem by any method. 相似文献
4.
Peter Nielsen 《Coastal Engineering》1983,7(3):233-251
Explicit wave formulae derived from the dispersion relation for linear waves are used to find an analytical solution to the problem of wave height variation on a simple topography; i.e. topographies with incrementally constant slope and straight parallel contours. The solution accounts for shoaling, refraction and frictional dissipation and will be sufficiently accurate for practical purposes considering the simplifying assumptions that are necessary for treatment of this problem by any method. The solution is simple enough to be handled on a personal calculator and has the advantage over numerical solutions that it can be solved for other parameters, for example to give friction factors from observed wave height data. The last chapter contains updated formulae for wave friction factors over movable beds. 相似文献
5.
Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally‘ s analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data. 相似文献
6.
A fully nonlinear Boussinessq-type model with several free coefficients is considered as a departure point. The model is monolayer and low order so as to simplify numerical solvability. The coefficients of the model are here considered functions of the local water depth. In doing so, we allow to improve the dispersive and shoaling properties for narrow banded wave trains in very deep waters. In particular, for monochromatic waves the dispersion and shoaling errors are bounded by ~ 2.8% up to kh = 100, being k the wave number and h the water depth. The proposed model is fully nonlinear in weakly dispersive conditions, so that nonlinear wave decomposition in shallower waters is well reproduced. The model equations are numerically solved using a fourth order scheme and tested against analytical solutions and experimental data. 相似文献
7.
8.
From the phase-resolving improved Boussinesq equations (Beji and Nadaoka, Ocean Engineering 23 (1996) 691), a phase-averaged Boussinesq model for water waves is derived by more effectively describing carrier wave groups and accompanying long wave evolution with less CPU time. Linear shoaling characteristics of carrier wave equations are investigated and found to agree exactly with the analytical expression obtained from the constancy of energy flux for the improved Boussinesq equations themselves, showing that the present model equations are the results of a consistent derivation procedure regarding energy considerations. Numerical simulations of the derived equations for the single wave group and narrow-banded random waves show the validity of the present model and its high performance, especially on the CPU time. 相似文献
9.
10.
A note on linear dispersion and shoaling properties in extended Boussinesq equations 总被引:1,自引:0,他引:1
A set of optimum parameter α is obtained to evaluate the linear dispersion and shoaling properties in the extended Boussinesq equations of [Madsen and Sorensen, 1992 and Nwogu, 1993], and [Chen and Liu, 1995]. Optimum α values are determined to produce minimal errors in each wave property of phase velocity, group velocity, or shoaling coefficient relative to the analytical one given by the Stokes wave theory. Comparisons are made of the percent errors in phase velocity, group velocity, and shoaling coefficient produced by the Boussinesq equations with a different set of optimum α values. The case with a fixed value of α = −0.4 is also presented in the comparison. The comparisons reveal that the optimum α value tuned for a particular wave property gives in general poor results for other properties. Considering all the properties simultaneously, the fixed value of α = −0.4 may give overall accuracies in phase velocity and shoaling coefficient for all the types of Boussinesq equations selected in this study. 相似文献
11.
In this study, we derive an analytical solution for long waves over a circular island which is mounted on a flat bottom. The water depth on the island varies in proportion to an arbitrary power, γ, of the radial distance. Separation of variables, Taylor series expansion, and Frobenius series are used to find the solutions, which are then validated by comparing them with previously developed analytical solutions. We also investigate how different wave periods, radii of the island toe, and γ values affect the solutions. For a circular island with a small value of γ (e.g. γ = 2/3, as in the equilibrium beach (Bruun, 1954)), the wave rays approaching near the island center reach the coastline, whereas the rays approaching away from the center bend away from the coastline, leading to smaller wave amplitudes along the coast. However, for a circular island with a large value of γ, e.g. γ = 2, all the rays on the island reach the coast, giving large coastline wave amplitudes. If the island domain is small compared to the wavelength, the wave amplitudes on the coastline do not increase significantly; however, when the island domain is not small, the wave amplitudes increase significantly. If γ is also large, the amplitudes can be so large as to cause a disaster on the island. 相似文献
12.
Graham J.M. Copeland 《Coastal Engineering》1985,9(2):125-149
The “mild-slope” equation which describes wave propagation in shoaling water is normally expressed in an elliptic form. The resulting computational effort involved in the solution of the boundary value problem renders the method suitable only for small sea areas. The parabolic approximation to this equation considerably reduces the computation involved but must omit the reflected wave. Hence this method is not suited to the modelling of harbour systems or areas near to sea walls where reflections are considerable. This paper expresses the “mild-slope” equation in the form of a pair of first-order equations, which constitute a hyperbolic system, without the loss of the reflected wave. A finite-difference numerical scheme is described for the efficient solution of the equations which includes boundaries of arbitrary reflecting power. 相似文献
13.
Fabrice Ardhuin 《Journal of Oceanography》2006,62(6):917-922
In a recent paper, Kenyon (2004) proposed that the wave-induced energy flux is generally not conserved, and that shoaling
waves cause a mean force and torque on the bottom. That force was equated to the divergence of the wave momentum flux estimated
from the assumption that the wave-induced mass flux is conserved. This assumption and conclusions are contrary to a wide body
of observations and theory. Most importantly, waves propagate in water, so that the momentum balance generally involves the
mean water flow. Although the expression for the non-hydrostatic bottom force given by Kenyon is not supported by observations,
a consistent review of existing theory shows that a smaller mean wave-induced force must be present in cases with bottom friction
or wave reflection. That force exactly balances the change in wave momentum flux due to bottom friction and the exchange of
wave momentum between incident and reflected wave components. The remainder of the wave momentum flux divergence, due to shoaling
or wave breaking, is compensated by the mean flow, with a balance involving hydrostatic pressure forces that arise from a
change in mean surface elevation that is very well verified by observations. 相似文献
14.
15.
A two-dimensional vertical (2DV) non-hydrostatic boundary fitted model based on a Godunov-type shock-capturing scheme is introduced and applied to the simulation of waves from deep water up to the swash zone. The effects of shoaling, breaking, surf zone dissipation and swash motions are considered. The application of a Godunov-type shock-capturing algorithm together with an implicit solver on a standard staggered grid is proposed as a new approach in the 2DV simulation of large gradient problems such as wave breaking and hydraulic jumps. The complete form of conservative Reynolds averaged Navier–Stokes (RANS) equations are solved using an implicit finite volume method with a pressure correction technique. The horizontal advection of the horizontal velocity is solved by an explicit predictor–corrector method. Fluxes are predicted by an exact Riemann solver and corrected by a downwind scheme. A simple total variation diminishing (TVD) method with a monotonic upstream-centered scheme for conservation laws (MUSCL) limiter function is employed to eliminate undesirable oscillations across discontinuities. Validation of the model is carried out by comparing the results of the simulations with several experimental test cases of wave breaking and run-up and the analytical solution to linear short waves in deep water. Promising performance of the model has been observed. 相似文献
16.
The random long wave runup on a beach of constant slope is studied in the framework of the rigorous solutions of the nonlinear shallow water theory. These solutions are used for calculation of the statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. It is shown that probability characteristics of the runup heights and extreme values of the shoreline velocity coincide in the linear and nonlinear theory. If the incident wave is represented by a narrow-band Gaussian process, the runup height is described by a Rayleigh distribution. The significant runup height can also be found within the linear theory of long wave shoaling and runup. Wave nonlinearity nearshore does not affect the Gaussian probability distribution of the velocity of the moving shoreline. However the vertical displacement of the moving shoreline becomes non-Gaussian due to the wave nonlinearity. Its statistical moments are calculated analytically. It is shown that the mean water level increases (setup), the skewness is always positive and kurtosis is positive for weak amplitude waves and negative for strongly nonlinear waves. The probability of the wave breaking is also calculated and conditions of validity of the analytical theory are discussed. The spectral and statistical characteristics of the moving shoreline are studied in detail. It is shown that the probability of coastal floods grows with an increase in the nonlinearity. Randomness of the wave field nearshore leads to an increase in the wave spectrum width. 相似文献
17.
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
18.
A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas. 相似文献
19.
《Ocean Engineering》1999,26(3):255-276
A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas. 相似文献
20.
A modified Boussinesq-type model is derived to account for the propagation of either regular or irregular waves in two horizontal dimensions. An improvement of the dispersion and shoaling characteristics of the model is obtained by optimizing the coefficients of each term in the momentum equation, expanding in this way its applicability in very deep waters and thus overcoming a shortcoming of most models of the same type. The values of the coefficients are obtained by an inverse method in such a way as to satisfy exactly the dispersion relation in terms of both first and second-order analyses matching in parallel the associated shoaling gradient. Furthermore a physically more sound way to approach the evaluation of wave number in irregular wave fields is proposed. A modification of the wave generator boundary condition is also introduced in order to correctly simulate the phase celerity of each input wave component. The modified model is applied to simulate the propagation of breaking and non-breaking, regular and irregular, long and short crested waves in both one and two horizontal dimensions, in a variety of bottom profiles, such as of constant depth, mild slope, and in the presence of submerged obstacles. The simulations are compared with experimental data and analytical results, indicating very good agreement in most cases. 相似文献