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综合考虑多种变形因素的近岸规则波传播数学模型Ⅰ. 基本方程的导出 总被引：1，自引：0，他引：1
推广了Kirby的有环境水流影响的缓坡方程,得到了综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射、波浪破碎多种变形因素的波浪传播控制方程,并给出了非线性因子、地形因子、底摩擦因子、水流因子的确定方法。基于导出的方程做进一步推导,得到了波高和波向为变量的综合考虑多种变形因素的波浪传播基本方程,该方程有许多优点:1)其绕开了求解波势函数的困难,将椭圆型方程的边值问题化为初值问题;2)直接求解波高和波向;3)可采用有限差分法离散求解,对空间步长没有限制,适合大面积海区波场计算;4)综合考虑了多种波浪变形因素,方程更为合理,5)容易处理波浪破碎问题。 相似文献
3.
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
4.
A numerical model to compute wave field is developed. It is based on the Berkhoff diffraction-refraction equation, in which an energy dissipation term is added, to take into account the breaking and the bottom friction phenomena. The energy dissipation function, by breaking and by bottom friction, is introduced in the Berkhoff equation to obtain a new equation of propagation.The resolution is done with the hybrid finite element method, where lagrangians elements are used. 相似文献
5.
A physical parameter, μb, which was used to meet the forcing of primary short waves to be off-resonant before wave breaking, has been considered as an applicable parameter in the infra-gravity wave generation. Since a series of modulating wave groups for different wave conditions are performed to proceed with the resonant mechanism of infra-gravity waves prior to wave breaking, the amplitude growth of incident bound long wave is assumed to be simply controlled by the normalized bed slope, βb. The results appear a large dependence of the growth rate, α, of incident bound long wave, separated by the three-array method, on the normalized bed slope, βb. High spatial resolution of wave records enables identification of the cross-correlation between squared short-wave envelopes and infra-gravity waves. The cross-shore structure of infra-gravity waves over beaches presents the mechanics of incident bound- and outgoing free long waves with the formation of free standing long waves in the nearshore region. The wave run-up and amplification of infra-gravity waves in the swash zone appear that the additional long waves generated by the breaking process would modify the cross-shore structure of free standing long waves. Finally, this paper would further discuss the contribution of long wave breaking and bottom friction to the energy dissipation of infra-gravity waves based on different slope conditions. 相似文献
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I. O. Leont’ev 《Oceanology》2011,51(2):353-358
A method applicable for the estimation of the wave parameters along a set bottom profile is suggested. It takes into account
the principal processes having an influence on the waves in the coastal zone: the transformation, refraction, bottom friction,
and breaking. The ability to use a constant mean value of the friction coefficient under conditions of sandy shores is implied.
The wave breaking is interpreted from the viewpoint of the concept of the limiting wave height at a given depth. The mean
and root-mean-square wave heights are determined by the height distribution function, which transforms under the effect of
the breaking. The verification of the method on the basis of the natural data shows that the calculation results reproduce
the observed variations of the wave heights in a wide range of conditions, including profiles with underwater bars. The deviations
from the calculated values mostly do not exceed 25%, and the mean square error is 11%. The method does not require a preliminary
setting and can be implemented in the form of a relatively simple calculator accessible even for an inexperienced user. 相似文献
7.
通过在二维数值水槽内用边界元法直接求解Laplace方程,对规则波在缓坡上的变形及破碎进行了数值计算。分析了不同底坡及采用不同底摩阻系数时规则波的破碎特征,并对规则波破碎的极限坡度进行了研究。重点分析了规则波破碎时海底坡度、底摩阻系数及波形不对称性对破碎指标的影响。 相似文献
8.
Numerical simulation of breaking wave generated sediment suspension and transport process based on CLSVOF algorithm 总被引：1，自引：0，他引：1
The sediment suspension and transport process under complex breaking wave situation is investigated using large eddy simulation （abbreviated as LES hereafter） method. The coupled level set （LS） and volume of fluid （VOF） method is used to accurately capture the evolution of air？water interface. The wall effect at the bottom is modeled based on the wave friction term while the complicate bottom boundary condition for sediment is tackled using Chou and Fringer’s sediment erosion and deposition flux method. A simulation is carried out to study the sediment suspension and transport process under periodic plunging breaking waves. The comparison between the results by CLSVOF method and those obtained by the LS method is given. It shows that the latter performs as well as the CLSVOF method in the pre-breaking weak-surface deformation situation. However, a serious mass conservation problem in the later stages of wave breaking makes it inappropriate for this study by use of the LS method and thus the CLSVOF method is suggested. The flow field and the distribution of suspended sediment concentration are then analyzed in detail. At the early stage of breaking, the sediment is mainly concentrated near the bottom area. During the wave breaking process, when the entrapped large-scale air bubble travels downward to approach the bottom, strong shear is induced and the sediment is highly entrained. 相似文献
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A numerical experiment of the M2 tide in the Yellow sea 总被引：1，自引：0，他引：1
Hui Soo An 《Journal of Oceanography》1977,33(2):103-110
Semi-diurnal tides in the Yellow Sea are calculated by integrating the shallow water wave equations with frictional and inertial terms.It is found that the results depend on the bottom friction. In the frictionless case the tidal range is unstably amplified because of the occurrence of resonance of the semi-diurnal tidal component in Inchon Bay. When the bottom friction is in the form of the square of velocity, the results agree fairly well with the observations.The following results are obtained. First, the tidal range is larger at the coast of the Korean Peninsula than at the China Coast. Second, resonance of the semi-diurnal tide occurs in Inchon Bay. Third, bottom friction is very important in the shallow ocean,i.e., when the bottom friction become large, the phase lag is retarded and the tidal range decreases.The amplitude and the phase lag calculated in this study agree well with the observations in the case of
b
=b
2
V¦V¦,
b
2=0.0026, especially in the coast of the Korean Peninsula. 相似文献
10.
Parabolic Approximation of the Weakly Nonlinear Mild Slope Equation with Bottom Friction 总被引：2，自引：0，他引：2
This paper presents a refined parabolic approximation model of the mild slope equation to simu-late the combination of water wave refraction and diffraction in the large coastal region.The bottom frictionand weakly nonlinear term are included in the model.The difference equation is established with the Crank-Nicolson scheme.The numerical test shows that some numerical prediction results will be inaccurate in com-plicated topography without considering weak nonlinearity;the bottom friction will make wave height damp-ing and it can not be neglected for calculation of wave field in large areas. 相似文献
11.
Dependence of Whitecap Coverage on Wind and Wind-Wave Properties 总被引：13，自引：0，他引：13
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Estimates of area-averaged tidal bottom stress are made for four channel segments of the Great Bay Estuary, N.H. Current and sealevel measurements are used to estimate acceleration and pressure gradient terms in the equation of motion, while the equation of motion itself is used to infer the remaining stress term. Dynamic terms, bottom stress values, friction coefficients and energy dissipation rates are estimated for each site. The analysis shows that while throughout the estuary the principal force balance is between the frictional stress and the pressure gradient forcing, RMS values of total bottom stress range from 2·67 to 10·38 Nm?2 and friction coefficients vary from 0·015 to 0·054. Both stress and energy dissipation are largest in the seaward portion of the estuary with an order of magnitude decrease in dissipation at the most inland site.These distributions of stress and energy dissipation are consistent with cotidal charts of the principal semi-diurnal tidal constituent (M2) which indicate that the estuary is composed of a highly dissipative more progressive tidal wave regime seaward and a less dissipative standing wave regime landward. 相似文献
13.
Momoki Koga 《Journal of Oceanography》1984,40(2):105-114
The relation between the intensity of breaking of individual wind-wave crests and parameters of wave size and wave form (e. g., height, period, steepness and skewness) is examined, and the process of change of these parameters is studied in a wind-wave
tank (reference wind speed 15 m sec−1, fetch 16 m). Distributions of the wave form parameters are different for breaking and nonbreaking waves. Fully breaking
waves seem to hold the relationH ∞T
2, whereH is the individual wave height andT is the period. The condition of breaking is not simply determined by the simple criterion of Stokes' limit. Wave height and
steepness of a breaking wave are not always larger than those of a nonbreaking wave. This suggests the existence of an overshooting
phenomenon in the breaking wave. The wave form parameters are found to change cyclically in a statistical sense during the
wave propagation. The period of the cycle in the present case is estimated to be longer than four wave periods. An intermittency
of wave breaking is associated with this cyclic process. Roughly speaking, two or three succeeding breaking-waves sporadically
exist among a series of nonbreaking waves along the fetch. 相似文献
14.
Osamu Abe Atsushi Watanabe V. V. S. S. Sarma Yohei Matsui Hiroya Yamano Naohiro Yoshida Toshiro Saino 《Journal of Oceanography》2010,66(3):363-372
We estimated gas exchange rates in Kabira Reef at Ishigaki Island, southwest Japan, using a mass balance calculation with
dual “biological” tracers: dissolved inorganic carbon (DIC) and dissolved oxygen (DO). The nighttime results allowed us to
obtain reasonable gas transfer velocity k
w values, all of which exceeded those obtained in wind-dominant studies. The difference is likely due to the contribution of
turbulence generated by the interaction between the current and bottom topography. The k
w obtained during high tides is consistent with that reported by Raymond and Cole (2001), whereas k
w during low tides is significantly higher, which seems to be caused by enhanced friction with the bottom of the reef and/or
bubble-induced gas transfer by wave breaking at the reef crest. 相似文献
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Wave-Current Propagation over a Frictional Topography 总被引：1，自引：0，他引：1
ZUO Qihua DING Bingcan Prof. Senior Engineer River Harbour Department Nanjing Hydraulic Research Institute 《中国海洋工程》1998,(4)
—In this paper the parabolic approximation model based on mild-slope equation is used tostudy wave propagation over a slowly varying and frictional topography under wave-current interaction.A governing equation considering the friction effects is derived by the authors for the first time.A simpli-fied form for the rate of wave energy dissipation is presented on the basis of the wave-current action conser-vation equation and the bottom friction model given by Yoo and O＇connor(1987).Examples reveal thatthe present computational method can be used for the calculation of wave elements for actual engineeringprojects with large water areas. 相似文献
17.
A spatial fixed σ-coordinate is used to transform the Navier–Stokes equations from the sea bed to the still water level. In the fixed σ-coordinate system only a very small number of vertical grid points are required for the numerical model. The time step for using the spatial fixed σ-coordinate is efficiently larger than that of using a time dependent σ-coordinate, as there is substantial truncation error involved in the time dependent σ-coordinate transformation. There is no need to carry out the σ-coordinate transformation at each time step, which can reduce computational times. It is important that wave breaking can be potentially modeled in the fixed σ-coordinate system, but in a time-dependent σ-coordinate system the wave breaking cannot be modeled. A projection method is used to separate advection and diffusion terms from the pressure terms in Navier–Stokes equations. The pressure variable is further separated into hydrostatic and hydrodynamic pressures so that the computer rounding errors can be largely avoided. In order to reduce computational time of solving the hydrodynamic pressure equation, at every time step the initial pressure is extrapolated in time domain using computed pressures from previous time steps, and then corrected in spatial domain using a multigrid method. For each time step, only a few of iterations (typically six iterations) are required for solving the pressure equation. The model is tested against available experimental data for regular and irregular waves and good agreement between calculation results and the measured data has been achieved. 相似文献
18.
LAGFD-WAM海浪数值模式是一种第三代海浪数值模式，通过求解波数谱平衡方程，并考虑风输入、波浪破碎耗散、底摩擦耗散、波波非线性相互作用和波流相互作用等源函数，模拟波数空间下的海浪方向谱，并依此获得海浪的波高、周期和平均波向。该模式的一个显著特点是采用特征线嵌入格式求解海浪的传播。在进行浅水区域的海浪模拟时，特征线嵌入格式的数值计算方案是否合理对海浪数值模拟结果产生直接的影响。为此LAGFD-WAM海浪数值模式提出了一种新的特征线混合数值计算格式，并应用于浅水海浪数值模拟。结果表明，采用该计算方法，能够使数值模拟结果与实测结果很好符合。 相似文献
19.
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
20.
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