任意空间取向TI介质qP和qSV波解耦的波动方程

由于构造运动等作用,TI介质对称轴往往沿空间任意方向分布,具有任意空间取向对称轴的TI（ATI）介质更符合实际地质情况.VTI介质与ATI介质的相速度在形式上具有一致性,VTI介质中地震波的相角对应ATI介质对称轴与地震波传播方向的夹角.本文基于Tsvankin的VTI介质精确相速度公式,利用TI介质对称轴和地震波传播方向上单位向量的数量积和向量积来计算ATI介质的精确相速度.根据弱各向异性假设,导出qP波和qSV波的近似相速度,分析了近似公式的误差,讨论总结了ATI介质qP波和qSV波的相速度特征.本文中的单位向量采用观测坐标系表示,通过相角关系,可以较为方便地由ATI介质近似相速度导出频散关系,然后借助傅里叶逆变换推导出时间-波数域qP波和qSV波解耦的波动方程.数值算例表明本文的波动方程是qP波和qSV波解耦的,波场计算结果稳定,未出现明显的数值频散,验证了本文方法的有效性.     

Steady streaming around a circular cylinder in an oscillatory flow

Steady streaming induced by an oscillatory flow around a circular cylinder is investigated using a numerical method. Two-dimensional Reynolds-averaged Navier-Stokes equations are solved using a finite element method with a k-ω turbulent model closure. The range of the Keulegan-Carpenter (KC) number investigated is between 2 and 40, which is substantially higher than those reported in literature related to steady streaming to date. A constant value of Stokes number (β) of 196 is chosen in this study. The steady streaming structures and velocity distribution are analysed in detail. It is found that the characteristics of steady streaming are strongly related to the vortex shedding flow regimes.     

A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows

A set of weakly dispersive Boussinesq-type equations, derived to include viscosity and vorticity terms in a physically consistent manner, is presented in conservative form. The model includes the approximate effects of bottom-induced turbulence, in a depth-integrated sense, as a second-order correction. Associated with this turbulence, vertical and horizontal rotational effects are captured. While the turbulence and horizontal vorticity models are simplified, a model with known physical limitations has been derived that includes the quadratic bottom friction term commonly added in an ad hoc manner to the inviscid equations. An interesting result of this derivation is that one should take care when adding such ad hoc models; it is clear from this exercise that (1) it is not necessary to do so – the terms can be included through a consistent derivation from the viscous primitive equations – and (2) one cannot properly add the quadratic bottom friction term without also adding a number of additional terms in the integrated governing equations. To solve these equations numerically, a highly accurate and stable model is developed. The numerical method uses a fourth-order MUSCL-TVD scheme to solve the leading order (shallow water) terms. For the dispersive terms, a cell averaged finite volume method is implemented. To verify the derived equations and the numerical model, four cases of verifications are given. First, solitary wave propagation is examined as a basic, yet fundamental, test of the models ability to predict dispersive and nonlinear wave propagation with minimal numerical error. Vertical velocity distributions of spatially uniform flows are compared with existing theory to investigate the effects of the newly included horizontal vorticity terms. Other test cases include comparisons with experiments that generate strong vorticity by the change of bottom bathymetry as well as by tidal jets through inlet structures. Very reasonable agreements are observed for the four cases, and the results provide some information as to the importance of dispersion and horizontal vorticity.     

二维浅水波方程的间断-连续Galerkin方法

将基于二维简化浅水波模型的间断Galerkin有限元与连续Galerkin有限元耦合方法推广至形式更为复杂的浅水波方程,并给出了误差分析以及模型问题的数值算例。     

直接利用旋转矩阵进行空间后方交会的原理和方法

空间后方交会是摄影测量学的基本内容,其解算的理论基础是共线条件方程及其线性化。传统的解算方法是直接以6个外方位元素为未知参数,使用泰勒级数展开进行线性化,然后迭代求解。而这里则直接以旋转矩阵为未知数进行迭代求解,这样既可直接解算出旋转矩阵,又避免欧拉角和旋转矩阵相互转换所引起的计算误差和时间耗费。试验结果表明该方法切实可行,求解精度高,而且迭代次数更少、迭代速度更快。     

Essential properties of Boussinesq equations for internal and surface waves in a two-fluid system

Boussinesq equations describing motions of internal waves in a two-fluid system with the presence of free surface are theoretically derived, and the associated essential properties are examined in this study. Eliminating the dependence on the vertical coordinate from all variables, four equations constitute the Boussinesq model with two flexible parameters, z_u and z_l, which indicate the specific elevations, respectively, in the upper and lower fluids. Similar to the Boussinesq model for a single-layer fluid, z_u and z_l are determined by matching the linear dispersion relation with Lamb's solution. This determines the optimal model. In the analysis stage, this problem is classified into two cases, the thicker-upper-layer case and the thicker-lower-case case, to avoid the possible divergence of wave properties as the thickness ratio grows. Since there exist two modes of motions that may be excited, cases of both modes are separately analyzed. Linear characteristics including the amplitude ratios and normalized particle velocities are analyzed. Second-order harmonic waves are examined to validate nonlinear behaviors of present model. Results of linear and nonlinear investigations show that the present model indeed extends the applicable range of traditional Boussinesq equations.     

Propagation of a solitary wave over rigid porous beds

The unsteady two-dimensional Navier–Stokes equations and Navier–Stokes type model equations for porous flows were solved numerically to simulate the propagation of a solitary wave over porous beds. The free surface boundary conditions and the interfacial boundary conditions between the water region and the porous bed are in complete form. The incoming waves were generated using a piston type wavemaker set up in the computational domain. Accuracy of the numerical model was verified by comparing the numerical results with the theoretical solutions. The main characteristics of the flow fields in both the water region and the porous bed were discussed by specifying the velocity fields. Behaviors of boundary layer flows in both fluid and porous bed regions were also revealed. Effects of different parameters on the wave height attenuation were studied and discussed. The results of this numerical model indicate that for the investigated incident wave as the ratio of the porous bed depth to the fluid depth exceeds 10, any further increase of the porous bed depth has no effect on wave height attenuation.     

Two-dimensional scour simulations based on coupled model of shallow water equations and sediment transport on unstructured meshes

A two-dimensional scour model based on coupled system of shallow water equations (SWEs) and sediment transport on unstructured mesh is developed. The coupled system of hydrodynamic and morphodynamic equations is solved by finite volume method using Godunov scheme. Roe's approximate Riemann solver is used to calculate the inviscid fluxes. The use of unstructured mesh makes the model applicable to complex domains. However, it is difficult to evaluate the eigenvalues and eigenvectors of the Jacobian matrix in the global coordinate. The method proposed herein to deal with this difficulty is to transform the system into the local coordinate with one of the axes in the same direction as the interface outward normal vector. In the local coordinate system, the Jacobian matrix is simplified and the eigenvalues are analyzed using asymptotic method. Regular expansion breaks down when the flow is near critical. Uniformity of the expansion is achieved by changing the scales. Rotational invariance theorem is used to relate the interfacial fluxes in the global and local coordinate systems. Special treatment of the source term on unstructured grid makes the scheme stable and physically balanced (both mass and momentum). The method proposed in this paper for the eigen-system is very efficient comparing to iterative numerical methods. Results from the test cases show good agreement with the experiments.     

A numerical study of swash flows generated by bores

The dynamic processes of bore propagation over a uniform slope are studied numerically using a 2-D Reynolds Averaged Navier–Stokes (RANS) solver, coupled to a non-linear k − ε turbulence closure and a volume of fluid (VOF) method. The dam-break mechanism is used to generate bores in a constant depth region. Present numerical results for the ensemble-averaged flow field are compared with existing experimental data as well as theoretical and numerical results based on non-linear shallow water (NSW) equations. Reasonable agreement between the present numerical solutions and experimental data is observed. Using the numerical results, small-scale bore behaviors and flow features, such as the bore collapse process near the still-water shoreline, the ‘mini-collapse’ during the runup phase and the ‘back-wash bore’ in the down-rush phase, are described. In the case of a strong bore, the evolution of the averaged turbulence kinetic energy (TKE) over the swash zone consists of two phases: in the region near the still-water shoreline, the production and the dissipation of TKE are roughly in balance; in the region farther landwards of the still-water shoreline, the TKE decay rate is very close to that of homogeneous grid turbulence. On the other hand, in the case of a weak bore, the bore collapse generated turbulence is confined near the bottom boundary layer and the TKE decays at a much slower rate.