多圆环柱域上解析函数边值问题再论

讨论多圆环柱域上多个复变量的解析函数的一般形式的 Riemann- Hilbert边值问题。通过函数的解析变换 ,导出了解析函数一般形式的 Riemann- Hilbert边值问题的可解性 ,并给出了解的积分表达式。     

波浪水槽中非线性浅水波传播特性与模拟

通过建立解析解、进行数值模拟和物理实验，研究了波浪水槽中非线性浅水波浪传播特性，给出了数值模拟中对应造波板做正弦运动的二阶入射边界条件。数值模拟采用高阶Boussinesq方程。实验结果、数值结果和解析解进行对比，并讨论了解析解的适用范围、高次谐波的产生及三波相互作用问题。     

三维物体上二阶波浪绕射的实时模拟

采用二阶时域理论对非线性波浪在任意三维物体周围的绕射问题进行了研究，对自由表面边界条件进行Taylor级数展开，应用摄动展开可以建立相应的边值问题，而且此边值问题的计算域不随时间变化，运用基于B－样条的边界元方法求解每一时刻的波浪场，二阶自由表面边界条件在时间上进行数值积分，在自由表面加了一个人工阻尼层以避免波浪的反射，速度势分解为已知的入射势和未知的散射势，初始条件采用二阶Stokes波浪场，通过加入物体表面边界条件，得到散射势在时间和空间上的发展，本文对圆柱所受规则波的二阶波浪力和波浪爬高进行了计算，数值结果表明此理论计算准确，效率高，数值稳定。     

拖曳线列阵振荡幅值响应特性

通过欧拉角的变换把拖曳线列阵微元段矢量动力平衡方程在局部坐标系下展开，在时间和空间上作中心差分数值离散平衡方程。将尾绳阻力作为线列阵尾端点的张力，改善因尾端张力为零引起的差分方程奇异性。取有关文献资料中的两个拖曳线列阵进行了拖点振荡响应计算，计算结果与相应文献资料中线性理论的计算和试验结果基本吻合。最后由仿真计算讨论了拖曳线列阵参数变化对拖点垂向和横向的谐振稳态响应特性。计算结果表明影响拖曳线列阵振荡响应的主要参数是由拖缆长度、拖点航速和拖点振荡因频率构成的无因次振荡频率。     

测度链上微分方程的进展

综述测度链上微分方程理论的基本概念及其最新进展，包括作者的研究集体所做的工作，也提出一些值得进一步研究的课题。     

渤、黄、东海潮汐开边界的1种反演方法

潮汐潮流数值模拟中的 1个主要难点在于开边界条件的确定。本文采用伴随方法 ,利用渤、黄、东海的 64个验潮站资料 (潮汐调和常数 ) ,通过反演渤、黄、东海的开边界条件 ,来实现渤、黄、东海 M2 潮波的数值模拟。为了取得较好的数值模拟结果 ,同时对给定的底摩擦系数进行校正 ,计算出调和常数的模拟值与实测值之差的绝对平均值 :振幅差为 4 .0 cm,迟角差为 2 .5°。实验结果较好地体现了渤、黄、东海 M2 潮波的特征。     

An analysis of second-order wave forces on floating bodies by using a higher-order boundary element method

The wave diffraction and radiation problem is studied numerically by using a higher-order boundary element method. The convergence of the higher-order boundary element method is tested systematically for bodies of different shapes. For the second-order force, particular attention is paid to the contribution of the second-order potential, following the line of Molin's approach. For numerical evaluation, the free surface is divided into three subregions; inner, intermediate and outer ones. In the inner region, the integral is evaluated numerically by using higher-order boundary elements. In the intermediate region, semi-analytic form is constructed with the help of eigen functions. In the outer domain, the analytic solution is available. This subdivision scheme reduces the numerical burden remarkably.     

Improvement on open boundaries on a time dependent numerical model of wave propagation in the nearshore region

An improvement on the simulation of outgoing waves on a time dependent numerical model for water wave propagation in the nearshore region is presented. The governing equations consist of a system of first order partial differential equations (PDEs), the equation of continuity and the equation of motion. A comparative study of first order radiation boundary conditions (BCs) and first order radiation BCs combined with sponge layers is presented for cases where outgoing waves leave the numerical domain of calculation through the open boundary. A reduction of spurious reflections from the numerical open boundaries can be obtained with an irrelevant increase in terms of computational cost.     

Current structure and volume transport of the Soya Warm Current in summer

ADCP, CTD and XBT observations were conducted to investigate the current structure and temperature, salinity and density distributions in the Soya Warm Current (SWC) in August, 1998 and July, 2000. The ADCP observations clearly revealed the SWC along the Hokkaido coast, with a width of 30–35 km and an axis of maximum speed of 1.0 to 1.3 ms⁻¹, located at 20–25 km from the coast. The current speed gradually increased from the coast to a maximum and steeply decreased in the offshore direction. The SWC consisted of both barotropic and baroclinic components, and the existence of the baroclinic component was confirmed by both the density front near the current axis and vertical shear of the alongshore current. The baroclinic component strengthened the barotropic component in the upper layer near the axis of the SWC. The volume transport of the SWC was 1.2–1.3 SV in August, 1998 and about 1.5 SV and July, 2000, respectively. Of the total transport, 13 to 15% was taken up by the baroclinic component. A weak southeastward current was found off the SWC. It had barotropic characteristics, and is surmised to be a part of the East Sakhalin Current.     

Bottom friction and its effects on periodic long wave propagation

A new set of Boussinesq-type equations describing the free surface evolution and the corresponding depth-integrated horizontal velocity is derived with the bottom boundary layer effects included. Inside the boundary layer the eddy viscosity gradient model is employed to characterize Reynolds stresses and the eddy viscosity is further approximated as a linear function of the distance measured from the seafloor. Boundary-layer velocities are coupled with the irrotational velocity in the core region through boundary conditions. The leading order boundary layer effects on wave propagation appear in the depth-integrated continuity equation to account for the velocity deficit inside the boundary layer. This formulation is different from the conventional approach in which a bottom stress term is inserted in the momentum equation. An iterative scheme is developed to solve the new model equations for the free surface elevation, depth-integrated velocity, the bottom stress, the boundary layer thickness and the magnitude of the turbulent eddy viscosity. A numerical example for the evolution of periodic waves propagating in one-dimensional channel is discussed to illustrate the numerical procedure and physics involved. The differences between the conventional approach and the present formulation are discussed in terms of the bottom frictional stress and the free surface profiles.