弱形式时域完美匹配层——滞弹性近场波动数值模拟

本文旨在构建适用于滞弹性近场时域波动有限元模拟的高精度人工边界条件：完美匹配层（Perfectly Matched Layer：PML）,其中阻尼介质时域本构基于广义标准线性体建立.与以往研究不同,本文采用复坐标延拓技术变换弱形式波动方程构建了可直接用有限元离散的弱形式时域PML,规避以往独立对无限域内波动方程及界面条件进行延拓可导致的PML场方程和界面条件匹配不合理引发数值失稳、计算精度低下等问题.其次,针对PML中多极点有理分式与频域函数乘积的傅里叶反变换难以计算的问题,利用PML精度对复坐标延拓函数中延拓参数微调不敏感这一特点,明确给出了参数微调准则以规避多重极点,进而利用有理分式分解给出了一种普适、简便的计算方法,极大地简化了PML计算.基于该方法可实现任意高阶PML.最后,将本文构建滞弹性PML与高阶勒让德谱元（高精度集中质量有限元）结合得到滞弹性近场波动谱元离散方案.基于算例验证了滞弹性PML的计算效率、精度及新离散方案的长持时稳定特性.新离散方案可应用于计入实际介质阻尼的地震波动正、反问题数值模拟,提高波形模拟的精度以及地下波速结构反演的精度和可靠性.

     

Holderness coast erosion and the significance of ords

A sample ord, a low section of beach characteristic of the Holderness coast, is examined as it moved southwards between 1977 and 1983 and its significant role in coast erosion is demonstrated. The reduction in beach level at the cliff foot by up to 3.9 m enabled most HWN tides to reach it, as compared with only some HWS tides along the inter-ord beach, and the volume of till eroded from the cliffs increased by eight times to an annual mean of 72m³m^?1. The Holderness tills are shown to be composed of 31 per cent sand and coarser sediment which is the sediment range of the beaches. Where an ord is sited the massive injection of beach sediment goes to form the ord's most prominent constructional feature, the lower beach ridge which extends southwards from the centre of the ord. Analysis of 12 months' observer wave data collected at Withernsea in 1969/70 indicates that a net southward sand movement of 144 000 m³ occurred. Comparison of this rate with beach sediment input rates along the whole coast backed by till cliffs suggests a sediment deficit at the northern end and a surplus towards the southern end. This conclusion is supported by an overall increase in beach sediment volume southwards from Barmston. Within this longshore sediment transport system, the ords migrate southwards from their point of origin in the Barmston-Skipsea area, without losing their identity until reaching the tip of Spurn Head.     

Group Velocity of Anisotropic Waves-Part Ⅱ: Conservative Properties

It has been argued in Part I that traditional expression of multidimensional group velocity used in meteorology is only applicable for isotropic waves. While for anisotropic waves, it cannot manifest propagation of waves group along the trajectory of a reference wave point, and varies with rotation of coordinates. The general mathematical expression of group velocity which may be used also for anisotropic waves has been derived in Part I. It will be proved that the mean wave energy, momentum and wave action density are all conserved as a wave group propagates at the general group velocity. Since general group velocity represents the movement of a reference point in either isotropic or anisotropic wave trains, it may be used to define wave rays. The variations of wave parameters along the rays in a slowly varying environment are represented by ray-tracing equations. Using the general group velocity, we may derive the anisotropic ray-tracing equations, which give the traditional ray-tracing equations for     

Forecasting and hindcasting waves with the SWAN model in the Southern California Bight

The Naval Research Laboratory created a wave forecasting system in support of the Nearshore Canyon Experiment (NCEX) field program. The outer nest of this prediction system encompassed the Southern California Bight. This forecasting system is described in this paper, with analysis of results via comparison to the extensive buoy network in the region. There are a number of potential errors, two of which are poor resolution of islands in the Bight—which have a strong impact on nearshore wave climate—and the use of the stationary assumption for computations. These two problems have straightforward solutions, but the solutions are computationally expensive, so an operational user must carefully consider their cost. The authors study the impact of these two types of error (relative to other errors, such as error in boundary forcing) using several hindcasts performed after the completion of NCEX. It is found that, with buoy observations as ground truth, the stationary assumption leads to a modest increase in root-mean-square error; this is due to relatively poor prediction of the timing of swell arrivals and local sea growth/decay. The model results are found to be sensitive to the resolution of islands; however, coarse resolution does not incur an appreciable penalty in terms of error statistics computed via comparison to buoy observations, suggesting that other errors dominate. Inaccuracy in representation of the local atmospheric forcing likely has a significant impact on wave model error. Perhaps most importantly, the accuracy of directional distribution of wave energy at the open ocean boundaries appears to be a critical limitation on the accuracy of the model-data comparisons inside the Bight.     

地表下圆形夹塞区出平面散射对地面运动的影响

采用波函数展开方法,提出弹性半空间埋藏的圆形弹性夹塞区对平面ＳＨ波二维散射的封闭级数解答．利用内域型Ｇｒａｆ加法公式,将解答归结为一组无穷代数方程组的求解．通过对无穷方程组的截断计算,得到了解答的数值结果;并通过边值条件的收敛,检验了截断计算的精度．最后给出若干典型算例说明夹塞区产生的散射场对地表运动的复杂影响．     

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.     

Prediction of significant wave height using regressive support vector machines

Wave parameters prediction is an important issue in coastal and offshore engineering. In this literature, several models and methods are introduced. In the recent years, the well-known soft computing approaches, such as artificial neural networks, fuzzy and adaptive neuro-fuzzy inference systems and etc., have been known as novel methods to form intelligent systems, these approaches has also been used to predict wave parameters, as well. It is not a long time that support vector machine (SVM) is introduced as a strong machine learning and data mining tool. In this paper, it is used to predict significant wave height (H_s). The data set used in this study comprises wave wind data gathered from deep water locations in Lake Michigan. Current wind speed (u) and those belonging up to six previous hours are given as input variables, while the significant wave height is the output parameter. The SVM results are compared with those of artificial neural networks, multi-layer perceptron (MLP) and radial basis function (RBF) models. The results show that SVM can be successfully used for prediction of H_s. Furthermore, comparisons indicate that the error statistics of SVM model marginally outperforms ANN even with much less computational time required.     

Wave reflection from coastal structures in design conditions

Based on an extensive database of more than 4000 data, this paper analyses wave reflection for various types of coastal structures in design conditions, such as smooth, rock and armour unit slopes. A new simple formula has been developed that relates the reflection coefficient to the breaker parameter and seems to fit all kinds of revetment materials by changing two coefficients. These coefficients depend only on the correct roughness factor, provided by recent research on overtopping discharges. The effects on reflection due to composite slopes and to low crests are also examined and proper extensions of the formula are provided.     

Seabed shear stress and bedload transport due to asymmetric and skewed waves

A simple conceptual formulation to compute seabed shear stress due to asymmetric and skewed waves is presented. This formulation generalizes the sinusoidal wave case and uses a variable friction factor to describe the physics of the boundary layer and to parameterize the effects of wave shape. Predictions of bed shear stresses agree with numerical computations using a standard boundary layer model with a k–ε turbulence closure. The bed shear stress formulation is combined with a Meyer-Peter and Müller-type formula to predict sheet flow bedload transport under asymmetric and skewed waves for a horizontal or sloping bed. The predictions agree with oscillatory water tunnel measurements from the literature.