非线性抛物型方程反问题的一种新算法

利用反问题新算法—时间域正演反演法研究非线性抛物型方程的逆时反问题。该方法处理反问题的主要思路是先求解相对应的正问题,获得解在特定时间网格处的近似值;然后构造一个合适的全纯映射,在象空间中获得解在时间网格对应点处的近似值;最后利用解析函数的唯一延拓性质实现反问题的逆时间反演。数值模拟例子说明了方法的有效性。     

An approximation to the P-wave reflection coefficient for amplitude variation with long-offset seismic data

近年来,长偏移距排列逐渐被大量应用到海上勘探。传统AVO分析都是小入射角,对于长偏移距数据来说有很大不足。为了探讨拓宽AVO分析的研究范围,本文推导了长偏移距时P波反射系数的一种近似公式,并讨论了其精确性。本文的结果和广泛应用的Shuey公式相类似,Shuey公式可以看作本文结果在小入射角情况的简化。     

Theoretical considerations of meandering winds in simplified conditions

The influence of turbulence on the meandering phenomenon is investigated. The study, based on the three-dimensional Navier–Stokes equations, shows that when the turbulent fluxes can be neglected an asymptotic solution results. This solution reproduces a horizontal wind oscillation with an infinite relaxation time. When there is turbulent forcing, on the other hand, a transition occurs to a new order, characterized by a spatial reorganization, leading to a wind field with a well-defined direction.     

基于AMSS方程的道路影像去噪方法

对道路影像进行去噪处理是道路提取(识别)的重要前提步骤,处理过程中不仅对滤波器的去噪性能有较高的要求,同时对其保持边界的性能要求更高。AMSS(Affine Morphological Scale Space)方程是唯一同时满足对比不变性和仿射不变性的方程。文中从AMSS方程的理论基础着手,从数学角度深入分析了用该方程进行图像处理时能够使图像在去除噪声和保留边缘信息之间达到平衡的内在机理。然后,通过对用于道路提取的遥感影像特征的分析,研究了AMSS方程在遥感影像道路处理中的应用。理论分析与试验表明,文中提出的方法具有良好的效果。     

Interaction between an eddy and a zonal jet : Part II. Two-and-a-half-layer model

In a two-and-a-half-layer quasi-geostrophic model, a process study is conducted on the interaction between a vortex and a zonal jet, both with constant potential vorticity. The vortex is a stable anticyclone, initially located north of the eastward jet. The potential vorticity of the jet is allowed to have various vertical structures, while the vortex is concentrated in only one layer. The flow parameters are set to values characteristic of the Azores region.First, the jet is stable. Weak vortices steadily drift north of the jet without crossing it while strong vortices can cross the jet and tear off a cyclone with which they pair as a heton (baroclinic dipole). This heton often breaks later in the shear exerted by the jet; the two vortices finally drift apart. When crossed by deep anticyclones, the jet develops meanders with 375 km wavelength. These results exhibit a noticeable similarity with the one-and-a-half-layer case studied in Part I.Secondly, the jet is allowed to be linearly unstable. In the absence of the vortex, it develops meanders with 175 km wavelength and 25-day e-folding time on the β-plane. For various vertical structures of the jet, baroclinic instability is shown to barely affect jet–vortex interaction if the linear growth rate of unstable waves is smaller than 1/(14 days). Further simulations with a linearly unstable, nonlinearly equilibrated jet evidence its strong temporal variability when crossed by a deep vortex on the β-plane. In particular, long waves can dominate the spectrum for a few months after jet crossing by the vortex. Again in this process, the deep vortex couples with a surface cyclone and both drift southwestward.     

Direct numerical simulation of bedload transport using a local, dynamic boundary condition

ABSTRACT Temporally and spatially averaged models of bedload transport are inadequate to describe the highly variable nature of particle motion at low transport stages. The primary sources of this variability are the resisting forces to downstream motion resulting from the geometrical relation (pocket friction angle) of a bed grain to the grains that it rests upon, variability of the near‐bed turbulent velocity field and the local modification of this velocity field by upstream, protruding grains. A model of bedload transport is presented that captures these sources of variability by directly integrating the equations of motion of each particle of a simulated mixed grain‐size sediment bed. Experimental data from the velocity field downstream and below the tops of upstream, protruding grains are presented. From these data, an empirical relation for the velocity modification resulting from upstream grains is provided to the bedload model. The temporal variability of near‐bed turbulence is provided by a measured near‐bed time series of velocity over a gravel bed. The distribution of pocket friction angles results as a consequence of directly calculating the initiation and cessation of motion of each particle as a result of the combination of fluid forcing and interaction with other particles. Calculations of bedload flux in a uniform boundary and simulated pocket friction angles agree favourably with previous studies.     

An upscaling method for one‐phase flow in heterogeneous reservoirs. A weighted output least squares (WOLS) approach

In this paper we study the problem of determining the effective permeability on a coarse scale level of problems with strongly varying and discontinuous coefficients defined on a fine scale. The upscaled permeability is defined as the solution of an optimization problem, where the difference between the fine scale and the coarse scale velocity field is minimized. We show that it is not necessary to solve the fine scale pressure equation in order to minimize the associated cost‐functional. Furthermore, we derive a simple technique for computing the derivatives of the cost‐functional needed in the fix‐point iteration used to compute the optimal permeability on the coarse mesh. Finally, the method is illustrated by several analytical examples and numerical experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

An elliptic problem with integral constraints with application to large-scale geophysical flows

We present a weak formulation of a non-standard elliptic equation whose boundary values are determined in part by integral relations. Existence and uniqueness of its solution are proved, and a finite element discretization is described, analyzed, and implemented on a test problem. The equation is a generalization of one that is solved during integration of the three-dimensional Quasigeostrophic equations, which model large-scale rotating stratified flows, where the integral constraints represent conservation of physical properties.