在曲线坐标系下，建立了缓变水深水域波浪传播的数值模拟模型。模型适宜于复杂变化的边界形状，克服了各种代数坐标变换的局限性。在建立模型时，将原始的椭圆型缓坡方程的近似型式——依赖时间变化的抛物型方程，作为控制方程，既克服了一般抛物近似方法的缺点，又便利了方程的求解；从开边界条件、不同反射特性的固壁边界条件相统一的表达式出发，对边界条件进行处理；用ADI法数值求解控制方程。对模型的验证表明，数值解与物模实验值吻合良好，模型对于具有复杂边界的工程实际有较强的适应性。

以一种新型的Boussinesq型方程为控制方程组，采用五阶Runge-Kutta-England格式离散时间积分，采用七点差分格式离散空间导数，并通过采用恰当的出流边界条件，从而建立了非线性波传播的新型数值模拟模型。通过对均匀水深水域内波浪传播的数值模拟说明，模型能较好地模拟大水深水域和强非线性波的传播。通过设置不同的入射波参数来进行潜堤地形上波浪传播的物理模型实验，并将数值解与物理模型实验结果进行了比较。

以一种新型的含变换速度变量的Boussinesq型方程为控制方程组，采用五阶Runge-Kutta-England格式离散时间积分，采用七点差分格式离散空间导数，并采用恰当的出流边界条件，从而建立了非线性波传播的新型数值模拟模型。对均匀水深水域内波浪传播的数值模拟，说明在引入变换速度后进一步增大了模型的水深适用范围。对潜堤地形上波浪传播的数值模拟说明，在引入变换速度后进一步提高了模型的数值模拟精度。

引入自适应网格技术，建立了曲线坐标系下考虑能耗影响的缓变水深水域波浪传播的数值模拟模型，通过在模型中引入能量耗散项以更好地处理全透射边界。基于原型缓坡方程，完善了等水深的轴对称双导堤水域内波浪传播的精确解表达式及其计算结果；提供了等水深的环形河道水域内较为详细的精确解。在极坐标系下就等水深的轴对称双导堤水域内波浪的传播，推导了缓坡方程的小角度抛物近似模型的解析解表达式。就上述两水域内波浪传播的数值模拟模型的数值解、抛物近似模型的解、精确解进行了详细比较，说明数值解与精确解相吻合、数值模拟模型比小角度和大角度抛物近似模型具有更高的精度。数值模拟模型能较好地模拟水深复杂变化的地形上波浪的传播，能有效反映波浪传播过程中的多种物理现象。

A finite-difference approach is used to develop a time-dependent mild-slope equation incorporating the effects of bottom dissipation and nonlinearity. The Euler predictor-corrector method and the three-point finite-difference method with varying spatial steps are adopted to discretize the time derivatives and the two-dimensional horizontal ones, respectively, thus leading both the time and spatial derivatives to the second-order accuracy. The boundary conditions for the present model are treated on the basis of the general conditions for open and fixed boundaries with an arbitrary reflection coefil cient and phase shift. Both the hnear and nonlinear versions of the numerical model are applied to the wave propagation and transformation over an elliptic shoal on a sloping beach, respectively, and the linear version is applied to the simulation of wave propagation in a fully open rectangular harbor. From comparison of numerical results with theoretical or experimental ones, it is found that they are in reasonable agreement.

A new approach to high-order Bonssinesq-type equations with ambient currents is presented, The current veineity is assumed to be uniform over depth and of the same magnitude as the shallow water wave celerity. The wave velocity field is expressed in terms of the horizontal and vertical wave velocity components at an arbitrary water depth level. Linear operators are introduced to improve the accuracy of the kinematic condition at the sea bottom. The dynamic and kinematic conditions at the free surface are expressed in terms of wave velneity variables defined directly on the free surface. The new equations provide high accuracy of linear properties as well as nonlinear properties from shallow to deep water, and extend the applicable range of relat/ve water depth in the case of opposing currents.

Several sets of S4 direction-wave-current-tide meters have been deployed on the coral-reef fiat of fongshu Reef in the sea area of Nansha Islands. Based on the observationat sea wave data, the attenuation, hara, teristics of the waves propagating on the coral reef flat, the bottom friction coefficeients and the transfer of wave, energy are discussed it, the paper. The results show that, in the relative depths of 0.0613～0.0867, the wave height attenuation per unit distance of wave propagation is 22.09%～46.56%, with an average of 31.35%; the wave energy attenuation coefficient, 33.74%～53.22%, with an average of 43.61%. The average of the bottom friction coefficients on the eoral-reef flat is 0.1346, which is about 10 times that on the sand or silt bottom. In the course of propagation an the reef tlat, the waves sustain more loss in high frequency than in tow frequency and the spectral energy, transfers to, the low frequency. These results may be used for reference in island and reef engineering.

针对计算域中存在直立岛式结构物的复连通区域，提出了岛体边界条件，利用缓坡方程建立了在计算域中存在直立岛式结构物时波浪传播的数值模拟模型。模型适用于变水深水域问题，克服了解析解只能适用于等水深水域的不足。直立圆柱和无穷小厚度岛式防波堤周围波浪传播的数值算例表明，数值解与解析解吻合良好，说明所建立的数值模拟模型能有效地模拟复连通区域内的波浪传播。矩形固定式防波堤周围波浪场的数值模拟说明该模型对工程实际有较强的适应性。

利用自适应网格技术，建立了曲线坐标系下缓变水深水域非均匀水流中波浪传播的数值模拟模型。将椭圆型非均匀水流中波浪传播的联合折射一绕射方程化为依赖时间变化的抛物型方程，并以此作为控制方程，克服了一般抛物近似方法的缺点；从开边界条件、不同反射特性的固壁边界条件相统一的表达式出发，对边界条件进行处理；用ADI法数值求解控制方程。验证结果表明，模型能适应复杂的边界形状，可以较好地模拟复杂边界条件下波浪传播过程中的多种物理现象，克服了以往各种代数坐标变换的局限性，有效地反映了水流对波浪传播的影响。模型的模拟结果可供实际工程参考使用。

以含底摩阻能量耗散项的时间关联型缓坡方程为控制方程，建立了一种具有二阶精度的数值离散格式。该格式对时间导数使用Euler预测一校正格式离散；对空间导数使用中心差分格式离散。基于统一边界条件表达式，对边界条件进行处理。数值解与物理模型实验值吻合较好，表明数值模拟模型可以有效地模拟波面随时间和空间的变化以及波高的空间分布。