强非线性和色散性Boussinesq方程数值模型检验

采用同位网格有限差分法,建立了强非线性和色散性Boussinesq方程数值计算模型。以稳恒波Fourier近似解给定入射波边界条件,对均匀水深深水和浅水域不同非线性的行进波、缓坡地形上深水至浅水域的浅水变形波、以及缓坡和陡坡地形上的波浪水槽实验进行了数值计算,并将计算结果与解析解、解析数值解以及实验值进行了较为详细的比较,从而检验了模型的色散性、非线性以及不同底坡下非线性波的浅水变形性能。     

Experimental study of the transformation of bound long waves over a mild slope with ambient currents

The effect of currents on the variation of cross-shore bound long waves forced by bichromatic waves over a plane slope was investigated in the laboratory. In still water the growth rate of the shoaling bound long waves over the slope is proportional to h^– 5/2 (h is still-water depth). It was found that the opposing current makes the amplitudes of the bound long waves greater than those of still water for all cases. However, the amplitudes of bound long waves in a following current are reduced in the weakly modulated cases but are enhanced in the fully modulated case.     

Experimental study of wave–wave nonlinear interactions using the wavelet-based bicoherence

The wavelet-based bicoherence, which is a new and powerful tool in the analysis of nonlinear phase coupling, is used to study the nonlinear wave–wave interactions of breaking and non-breaking gravity waves propagating over a sill. Two cases of mechanically generated random waves based on Jonswap spectra are used for this purpose. Values of relative depth, k_ph (k_p is the wave number of the spectral peak and h is the water depth) for this study range between 0.38 and 1.22. The variations of wavelet-based total bicoherence for the test cases indicate that the degree of quadratic phase coupling increases in the shoaling region consistent with a wave profile that is pitched shoreward, relative to a vertical axis as seen in the experiments, but decreases in the de-shoaling region. For the non-breaking case, the degree of quadratic phase coupling continues to increase until waves reach the top of the sill. Breaking waves, however, achieve their highest level of quadratic phase coupling immediately before incipient breaking and the degree of phase coupling decreases sharply following breaking. In addition the wavelet-based bicoherence spectra provide evidence of the harmonics' growth which is reflected in the energy spectra. The bicoherence spectra also show that quadratic phase coupling between modes within the peak frequency as well as between modes of the peak frequency and its higher harmonics are dominant in the shoaling region, even though there are relatively high levels of quadratic phase coupling occurring between other frequencies. Furthermore, using the temporal resolution property of the wavelet-based bicoherence, we find that the quadratic wave interactions occur more readily during segments of time with large change of wave amplitude, rather than those segments having large wave amplitudes, but small gradients in amplitude.     

加强的适合复杂地形的水波方程及其一维数值模型验证

在他人给出的方程的基础上,通过在其动量方程中引入含4个参数的公式,推导出了加强的适合复杂地形的水波方程,新方程的色散、变浅作用以及非线性均比原来适合复杂地形的方程有了改善:色散关系式与斯托克斯线性波的Padé(4,4)阶展开式一致;变浅作用在相对水深(波数乘水深)不大于6时与解析解符合较好;非线性在相对水深不大于1.05时保持在5%的误差之内.基于该方程,在非交错网格下建立的时间差分格式为混合4阶Adams-Bashforth-Moulton的一维数值模型,并在数值计算中利用了五对角宽带解法.数值模拟了潜堤上波浪传播变形,并将数值计算结果与实验结果进行了对比,验证了该数值模型是合理的.     

Field observations of infragravity waves and their behaviour on rock shore platforms

Infragravity wave (IGW) transformation was quantified from field measurements on two shore platforms on New Zealand's east coast, making this the first study to describe the presence, characteristics and behaviour of IGWs on rock platform coasts. Data was collected using a cross‐shore array of pressure transducers during a 22 hour experiment on Oraka shore platform and a 36 hour experiment at Rothesay Bay shore platform. A low pass Fourier filter was used to remove gravity wave frequency oscillations, allowing separate analysis of IGWs and the full wave spectrum. Offshore IGW heights were measured to be 7 cm (Oraka) and 9 cm (Rothesay Bay), which were 21% (Oraka) and 7.5% (Rothesay Bay) the height of incident wave height. At the cliff toe, significant IGW height averaged 15 cm at Oraka and 13 cm at Rothesay Bay. This increase in IGW height over the platform during both experiments is attributed to shoaling of 40 to 55% over the last 50–60 m before the cliff toe, respectively. Shoaling across the platform was quantified as the change in IGW height from the platform edge to cliff toe, resulting in a maximum increase of 1·88 and 2·63 on Rothesay Bay and Oraka platforms. IGW height at the cliff toe showed a strong correlation with incident wave height. The proportional increase in IGW height shows a strong correlation to water level on each platform. The rate of shoaling of long period waves on the shallow, horizontal platforms increased at higher water levels resulting in a super elevation in water level at the cliff toe during high tide. Greater IGW shoaling was also observed on the wider (Oraka) shore platform. Results from this study show the first measurements of IGWs on shore platforms and identify long wave motion a significant process in a morphodynamic understanding of rock coast. Copyright © 2011 John Wiley & Sons, Ltd.     

Wave Runup-Rundown Ampu''''tude on Slopes

This paper gives an overall discussion about water level change on slopes under wave action, including wave runup, wave rundown and wave up-down amplitude, and a suggested formula for their calculation.     

Calculations of wave transformation across the surf zone

The accuracy of predicting wave transformation in the nearshore is very important to wave hydrodynamics, sediment transport and design of coastal structures. An efficient numerical model based on the time-dependent mild-slope equation is presented in this paper for the estimation of wave deformation across the surf zone. This model incorporates an approximate nonlinear shoaling formula and an energy dissipation factor due to wave breaking to improve the accuracy of the calculation of wave height deformation prior to wave breaking and also in the surf zone. The model also computes the location of first wave breaking, wave recovery and second wave breaking, if physical condition permits. Good agreement is found upon comparison with experimental data over several one-dimensional beach profiles, including uniform slope, bar and step profiles.     

Wave energy losses in intermediate depths

Recent work on wave power devices has encouraged interest in the processes whereby waves lose energy and change direction in shoaling water, and especially in detailed calculations of their effects.^1,2 Here one of the most comprehensive sets of measurements available is examined, for four sites in depths of 15 to 100 m off South Uist in the Hebrides. The mean directional spectrum is recalculated for each site, and a proper allowance found for refraction which raises the estimates of net energy flux in intermediate depths by up to 10%. Indeed, the pattern of losses between 100 m and 23 m depths fits well with that expected from bottom friction. The estimated friction coefficient is quite high, as might be expected in view of the very rough sea bottom in the area.³