浅海内波垂直模式方程的一种解析解

给出了一些海区实测浮力频率剖面的数学模型.利用超几何函数对内波垂直模式方程进行了解析求解,得到内波模式方程的解析解和频散方程.利用得到的解析解给出了一种理想条件下内波前三阶简正模式的结构.     

Interaction of water waves with vertical cylinders using null-field integral equations

The scattering of water waves by bottom-mounted vertical circular cylinders is solved by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In the implementation, the null-field point can be exactly located on the real boundary owing to the introduction of degenerate kernels for fundamental solutions. An adaptive observer system of polar coordinates is considered to fully employ the properties of degenerate kernels. For the hypersingular equation, vector decomposition for the radial and tangential gradients is carefully considered. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Neither hypersingularity in the Burton and Miller approach nor the CHIEF concept was required to deal with the problem of irregular frequencies. Five advantages of free of calculating principal value, well-posed algebraic system, convergence rate of exponential order, meshfree and elimination of boundary-layer effect, are achieved by using the present approach. Numerical results are given for the forces and free-surface elevation around the circular boundaries. Also, the near-trapped behavior arisen from the physical resonance is detected. A general-purpose program for water wave impinging several circular cylinders with arbitrary number, radii, and positions was developed. Several examples of water wave structure interaction by vertical circular cylinders were demonstrated to see the validity of the present formulation.     

利用GPU实现基于物理模型的流体运动仿真

纳维-斯托克斯方程是描述流体运动的基础物理模型。首先简要介绍了在计算机上实现该模型的数值解算方法。在流体运动的计算机视觉仿真中,密度渲染才是最终结果,因此,又阐述了流体的密度场与速度场的关系,并且给出了流体仿真的基本流程。由于可编程图形处理器(GPU)具有并行性和速度快等特点,流体模拟的解算和渲染在图形处理器上运行更加高效,但是利用GPU编程实现流体仿真必须要实现3个核心转换,最后以支持3维纹理的Direct3D10为例,给出了利用GPU实现流体运动仿真两个简单实例。     

Solution of the propagation of the waves in open channels by the transfer matrix method

Many problems in mechanics can be solved by the use of the transfer matrix method. The use of this method in hydraulics engineering is not widespread and only limited studies are available. In this study, linearized St. Venant equations were used and the use of transfer matrix in ocean engineering was investigated for long waves in open channels, and numerical application was carried out. The results obtained through the transfer matrix method, which is quite easy to use, program and comprehend, showed similar results obtained from the characteristics method and finite differences method.     

港域波浪数学模型的改进与验证

通过物理模型对改进的港内波浪传播变形数学模型进行验证。该数学模型以推广的时变缓坡方程为控制方程,采用含松弛因子的ADI法求解,并对波浪反射和透射边界模拟方法进行改进。先通过物理模型试验确定斜向浪入射条件下抛石防波堤前的波浪反射系数,作为数学模型中部分反射边界模拟的依据。然后进行了一个典型港口内波浪折射、绕射和反射的模型试验,测量港内波浪分布。对比模型试验和数学模型计算的结果表明,数学模型可较好地模拟港内复杂地形和边界条件下规则波和不规则波的传播变形。     

Reevaluation of historical ocean heat content variations with time-varying XBT and MBT depth bias corrections

As reported in former studies, temperature observations obtained by expendable bathythermographs (XBTs) and mechanical bathythermographs (MBTs) appear to have positive biases as much as they affect major climate signals. These biases have not been fully taken into account in previous ocean temperature analyses, which have been widely used to detect global warming signals in the oceans. This report proposes a methodology for directly eliminating the biases from the XBT and MBT observations. In the case of XBT observation, assuming that the positive temperature biases mainly originate from greater depths given by conventional XBT fall-rate equations than the truth, a depth bias equation is constructed by fitting depth differences between XBT data and more accurate oceanographic observations to a linear equation of elapsed time. Such depth bias equations are introduced separately for each year and for each probe type. Uncertainty in the gradient of the linear equation is evaluated using a non-parametric test. The typical depth bias is +10 m at 700 m depth on average, which is probably caused by various indeterminable sources of error in the XBT observations as well as a lack of representativeness in the fall-rate equations adopted so far. Depth biases in MBT are fitted to quadratic equations of depth in a similar manner to the XBT method. Correcting the historical XBT and MBT depth biases by these equations allows a historical ocean temperature analysis to be conducted. In comparison with the previous temperature analysis, large differences are found in the present analysis as follows: the duration of large ocean heat content in the 1970s shortens dramatically, and recent ocean cooling becomes insignificant. The result is also in better agreement with tide gauge observations. On leave from the Meteorological Research Institute of the Japan Meteorological Agency.     

Lienard方程零解渐近稳定性的一个弱条件

研究Liemrd方程零解的渐近稳定性.在Liapunov函数Ⅴ满足dV/dt≤0的情况下,给出了进一步判断其渐近稳定的一个条件.     

非线性Kuamoto-Sivashinsky方程的精确控制

运用泛函分析性质以及Fourier变换的方法研究带有周期边界条件的非线性k-s方程在有限时间区间上的精确控制.首先研究线性化k-s方程的精确控制,证明对于任意给定的函数u0∈Hs,uT∈Hs,总能找到一个控制函数h使得线性化k-s方程有解u且满足u(x,0)=u0,u(x,T)=uT;然后结合线性化k-s方程的精确控制,通过定义Fredholm算子并应用Fredholm算子的一些理论找到非线性化k-s方程的控制函数,使其可精确控制.     

EDM高程导线测量中的效率和精度问题探讨

随着全站仪测角测距精度的提高,在高程联测中,用EDM高程导线测量代替三四等水准测量,成为外业高程测量的重要方法之一。分析了影响EDM高程导线测量精度的因素,讨论了提高EDM高程导线测量精度的办法,提出了效率函数的概念,并以某测区三级GPS大地控制网高程联测数据为例,从精度和效率方面进行了计算对比分析。     

Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth

Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.