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.     

Numerical Simulation on Hydraulic Performances of Quarter Circular Breakwater

Quarter circular breakwater （QCB） is a new-type breakwater developed from senti-circular breakwater （SCB）. The superstructure of QCB is composed of a quarter circular front wall, a horizontal base slab and a vertical rear wall. The width of QCB＇ s base slab is about half that of SCB, which makes QCB suitable to be used on relatively finn soil foundation. The numerical wave flume based on the Reynolds averaged Navier-Stokes equations for impressible viscosity fluid is adopted in this paper to simulate the hydraulic performances of QCB. Since the geometry of both breakwaters is similar and SCB has been studied in depth, the hydraulic performances of QCB are given in comparison with those of SCB.     

Two dimensional tensor product B-spline wavelet scaling functions for the solution of two-dimensional unsteady diffusion equations

The fourth-order B spline wavelet scaling functions are used to solve the two-dimensional unsteady diffusion equation. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method.The respective features of 3-spline wavelet scaling functions, 4-spline wavelet scaling functions and quasi-wavelet used to solve the two-dimensional unsteady diffusion equation are compared. The proposed method has potential applications in many fields including marine science.     

Comparison between iterative solution of symmetric and non‐symmetric forms of Biot's FEM equations using the generalized Jacobi preconditioner

Finite element discretization of Biot's consolidation equations can produce a symmetric indefinite system (commonly used in geomechanics) or a non‐symmetric system. While this difference appears to be minor, however, it will require the selection of entirely different Krylov subspace solvers with potentially significant impact on solution efficiency. The former is solved using the symmetric quasi‐minimal residual whereas the latter is solved using the popular bi‐conjugate gradient stabilized. This paper presents an extensive comparison of the symmetric and non‐symmetric forms by varying the time step, size of the spatial domain, choice of physical units, and left versus left–right preconditioning. The generalized Jacobi (GJ) preconditioner is able to handle the non‐symmetric version of Biot's finite element method equation, although there are no practical incentives to do so. The convergence behaviour of GJ‐preconditioned systems and its relation to the spectral condition number or the complete spectrum are studied to clarify the concept of ill‐conditioning within the context of iteration solvers. Copyright © 2007 John Wiley & Sons, Ltd.     

Equilibrium and non-equilibrium of two-arch structures in the solar atmosphere

We have derived a similarity solution in the form of a power series of the nonlinear magnetostatic equilibrium equation and identified the region of convergence in the parameter space. Within this region we have equilibrium configurations, outside it, non-equilibrium configurations. An example of nonlinear equilibrium configuration is shown graphically.

Our results can be used to explain the generation of multi-ribbon flares, the two-arch structures and the structures of the magnetic fields above elongated sunspot groups.     

The maximum mass of neutron stars

Summary. The maximum mass of neutron stars plays an important role in determining the end point of the evolution of massive stars. As the number of stellar mass black holes in binary x-ray sources grows, and as the mass spectrum of the black holes emerges, the value of the maximum mass of neutron stars has acquired great significance. Although it is now more than sixty years since the first attempt by Oppenheimer and Volkoff, no definitive answer can be given. This review will attempt to outline the main difficulties, both conceptual as well as technical, that stand in the way of a reliable estimate of the maximum mass. We shall also highlight how laboratory experiments, as well as astronomical observations, may help to clarify the true nature of the interior of neutron stars. Received 26 November 2001 / Published online 22 April 2002     

基于单位四元数描述的单像空间后方交会

在3维空间里,四元数可以非常方便地表示空间方位、空间向量间的旋转、平移和缩放等关系。将四元数理论引入到摄影测量领域,用单位四元数对坐标旋转矩阵进行描述,提出了一种采用单位四元数描述航摄像片位置与姿态的单张像片空间后方交会新方法。该方法与传统方法相比,在平差时避免了频繁的三角函数运算,不仅收敛速度快,而且精度高。     

A micro-mechanical investigation of the dynamic response and liquefaction of saturated granular soils

A coupled continuum-discrete hydromechanical model was utilized to analyze the meso-scale pore fluid flow and micro-scale solid phase deformation of saturated granular soils. The fluid motion was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid particles. Well established semi-empirical relationships were used to quantify the fluid–particle interactions. Numerical simulations were conducted to investigate the mechanisms of granular deposit liquefaction in the presence of a critical upward pore fluid flow as well as when subjected to a dynamic base excitation. The outcome of these simulations was consistent with experimental observations and revealed valuable information on the micro-mechanical characteristics of soil liquefaction and associated loss of stiffness and strength.     

Refinement of predictive reaeration equations for a typical Indian river

Dissolved oxygen mass balance has been computed for different reaches of River Kali in western Uttar Pradesh (India) to obtain the reaeration coefficient (K₂). A total of 270 field data sets have been collected during the period from March 1999 to February 2000. Eleven most popular predictive equations, used for reaeration prediction and utilizing mean stream velocity, bed slope, flow depth, friction velocity and Froude number, have been tested for their applicability in the River Kali using data generated during field survey. The K₂ values computed from these predictive equations have been compared with the K₂ values observed from dissolved oxygen balance measurements in the field. The performance of predictive equations have been evaluated using error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and correlation statistics. The equations developed by Smoot and by Cadwallader and McDonnell showed comparatively better results. Moreover, a refined predictive equation has been developed using a least‐squares algorithm for the River Kali that minimizes error estimates and improves correlation between observed and computed reaeration coefficients. Copyright © 2001 John Wiley & Sons, Ltd.