An application of Boussinesq equations to Bragg reflection of irregular waves

A numerical model based on the second-order fully nonlinear Boussinesq equations of Wei et al. [1995. Journal of Waterway, Port, Coastal and Ocean Engineering 121 (5), 251-263] is developed to simulate the Bragg reflection of both regular and irregular surface waves scattered by submerged bars. Particularly for incident regular waves, the computed results are observed to agree very well with the existing experimental data as presented by Davies and Heathershaw [1984. Journal of Fluid Mechanics 144, 419-446] and Kirby and Anton [1990. Proceedings of the 22nd International Conference on Coastal Engineering, ASCE, New York, pp. 757–768). In the case of incident irregular waves, the simulated results reveal that the distribution of Bragg reflection from irregular waves becomes more flat than that of regular waves. Due to lack of experimental data, the numerical results for incident irregular waves are compared with those of the evolution equation of the mild-slope equation [Hsu et al., 2002 Proceedings of the 24th Ocean Engineering Conference in Taiwan, pp. 70–77 (in Chinese)]. In addition, several parameters such as the number of bars, the relative height of bars and the spacing of bars affecting Bragg reflection are also discussed.     

Computational improvement of gravitational mode calculation of basins discretised by orthogonal curvilinear grids

The present note illustrates a criterion to improve the computational capability of the approaches proposed by Beltrami et al. [Beltrami, G.M., Bargagli, A., Briganti, R., 2003. Gravitational mode calculation of basins discretised by orthogonal curvilinear grids. Ocean Engineering 30, 833–853] for the direct numerical solution of the eigenvalue problem associated to the linear shallow-water equations when adiabatic boundary conditions apply. It is shown that—given the nature of its spatial differential operator—the problem can be solved by the singular value decomposition (SVD) of the real bidiagonal matrix resulting from a previous ad hoc Householder reduction of the operator matrix image. This procedure actually requires 1/8 of the random-access memory (RAM) needed by a standard library routine to compute all the eigenvalues and eigenvectors of the matrix image of the above-mentioned differential operator. Given the intrinsic limitation of a computing-machine RAM, this procedure dramatically improves the computational capability of both the proposed approaches.     

Bragg reflection of sinusoidal waves due to trapezoidal submerged breakwaters

Numerical and laboratory experiments are performed to investigate characteristics of the Bragg reflection due to multi-arrayed trapezoidal submerged breakwaters. The numerical model is based on the Reynolds averaged Navier–Stokes equations with the VOF method and the k–ε turbulence closure model. As expected, the reflection coefficients increase as the array of submerged breakwaters increases in both laboratory measurements and numerical results. The resonant periods provide similar relative wave numbers regardless of the permeability and the number of arrays. The reflection coefficients due to porous breakwaters are smaller than those due to non-porous breakwaters. The velocity contours for two and three arrays are also described.     

Assimilation of simulated float data in Lagrangian coordinates

We implement an approach for the accurate assimilation of Lagrangian data into regional general ocean circulation models. The forward model is expressed in Lagrangian coordinates and simulated float data are incorporated into the model via four-dimensional variational data assimilation. We show that forward solutions computed in Lagrangian coordinates are reliable for time periods of up to 100 days with phase speeds of 1 m/s and deformation radius of 35 km. The position and depth of simulated floats are assimilated into the viscous, Lagrangian shallow water equations. The weights for the errors in the model and data are varied and the assimilation results react appropriately. We show the effect of different spatial and temporal samplings of float data on all Lagrangian trajectories in the computational domain. At the end of the assimilation period, results from the Lagrangian shallow water equations could be interpolated and used as initial and boundary conditions in an Eulerian general ocean circulation model.     

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.