具有任意阶非线性薛定谔方程的新行波解

对具有任意阶非线性薛定谔方程的行波解进行了研究。给出具有任意阶非线性薛定谔方程的精确解。利用行波变换和辅助函数法把具有任意阶非线性薛定谔方程最终转化为一个非线性常微分方程的解,通过对这个微分方程的研究可以得到具有任意阶非线性薛定谔方程的行波解。具有任意阶非线性薛定谔方程存在的孤立波解、三角孤立波解、扭孤立波解、Jacobi椭圆函数解。得到了具有任意阶非线性薛定谔方程新的Jacobi椭圆函数解。     

热源强迫的非线性惯性重力内波及其应用

利用动力学分析中的相平面方法,由z坐标系下的非绝热大气运动方程组导出了与非线性惯性重力内波有关的KdV方程,然后利用直接积分法得到两类有天气意义的孤立波解.初步建立了孤立波解与高原低涡的联系,进一步从理论上论证了高原低涡具有与热带气旋类低涡类似的涡眼和暖心结构的特征.     

振荡型Rossby孤立波与大气阻塞

从正压涡度方程出发,在弱非线性和弱基流切变条件下,导得了描述非线性大气长波活动的推广的Ｋｄｖ方程,并得到了方程的孤立波解及其色散关系。取近似于实际大气运动的物理参数作数值计算,得到了振荡型Ｒｏｓｂｙ孤立波的水平结构和移动特征,其结果较之寻常的Ｋｄｖ孤立波更接近于实际大气中的阻塞流型。     

大气扰动中的非线性波及其相互作用

1895年,Korteweg和de Vries在研究洪水波演进(evolution)问题题中推导出了著名的半线性方程,即目前,一般所称作的KdV-方程。它是近代物理学中三个著名的半线性方程之一。此方程中含有非线性项及色散项,尤其是方程的解含有非线性波的孤立波或称孤立子(soliton)而受到广泛的重视。本文是针对小尺度运动略去Coriolis力,引入ρ=ρ_0(?)常数(均匀大气)的假定,将x(或)y方向的水平运动方程及垂直运动方程的未知函数视为解析幽数,故可在ζ=0附近怍Taylor级数展开,以迭套消元的方     

斜压大气中非线性ROSSBY波

本文利用位涡守恒方程,导出了斜压大气中非线性Rossby波满足KDV方程和MKDV方程,求得了斜压大气中非线性Rossby波足椭园余弦波和孤立波,并对它们的性质进行了讨论,着重用斜压Rossby立波的性质解释了大气中的一些重要天气现象如极涡、阻塞高压和切断低压。     

基于非静压模型类海啸波作用下海堤越浪特性

【目的】研究海啸波在斜坡海堤上越浪的水动力特性。【方法】基于非静压模型NHWAVE建立高精度二维数值波浪水槽,通过对日本2011年实测真实海啸进行参数化形成类海啸波形,并设置系列计算工况,深入分析入射波高、水深、岸滩坡度及海堤坡度对类海啸波作用下海堤越浪特性的影响,并将计算结果与孤立波进行对比。【结果与结论】相同工况下,类海啸波的单宽越浪量大于孤立波,波浪经海堤消能后,能量衰减,孤立波能量损耗率大于类海啸波;随波高和水深增加,越浪量均增大;海堤坡度对越浪量的影响不大;岸滩坡度减缓,波浪速度将在堤前聚集,类海啸波在1∶20的岸滩坡度下越浪量达到最大。研究结果可为近岸水利防护工程的建设提供参考。     

动态时间归整算法抑制前向散射直达波干扰

基于衍射CT成像技术,在弱散射条件下根据收发分置目标散射强度的指向分布特性,可以重建目标形状、以及周围介质的声学参数。在目标的正前方,前向散射波和直达波同时到达接收阵,特别是当目标为密度和声速接近于水的弱散射目标时,散射回波完全淹没在直达波中,抑制直达波干扰才能实现目标的识别、方位估计以及声学特性解释。基于语音识别的动态时间归整(Dynamic Time Warping,DTW)算法,是利用归整路径距离的动态规划来求解发音长短不一的孤立词模板匹配的问题。固定入射波方向,以浸没水中的无限长圆柱体目标为例获取实验数据,将DTW算法用于直达波和散射波的分离,并将消除直达波影响后的目标散射远场的强度与严格的解析结果进行了对比,结果表明DTW算法可以有效地在强直达波干扰背景中有效提取目标散射信息。     

一个非均匀破裂圆盘模式的远场位移解

本文给出了一个非均匀破裂圆盘模式P波远场位移解的解析算式,并计算了包括介质与仪器影响在内的空间幅射特征。据此,指出了在利用P波初动资料测定介质和震源参数以及在震源机制求解中值得注意的几个问题。     

动脉内壁剪切应力动态分布数值模拟研究

针对人体动脉系统,利用心动周期内血管血液流量波建立了血管壁面切应力动态分布的求解体系,在一定的假设条件下,推导了不同Womersley数下该体系的分析解;最后采用该求解体系和分析解,利用血流动力学数据计算了猪颈动脉的管壁切应力动态分布,结果是本文的数值模拟求解计算量少,而且考虑了血管壁的弹性特性,得到更趋于合理的管壁切应力分布。     

基于震源机制和剪切波分裂分析鄂尔多斯地块内部一次显著性地震:2022-07-12盐池M_(L)4.0地震北大核心CSCD

结合宁夏区域地震台网和预警台网资料,通过Hash方法计算2022-07-12盐池M_(L)4.0地震震源机制,采用gCAP方法得到该地震震源机制、矩张量解及矩心深度,确定震源机制中心解,计算中心解两个节面上的相对剪应力与正应力,最后对符合剪切波分裂窗口的台站进行快波偏振方向和慢波时间延迟分析。结果表明,盐池地震是一起天然走滑型地震事件,不同方法确定的震源机制中心解为节面Ⅰ走向99°、倾角71°、滑动角8°,节面Ⅱ走向6°、倾角83°、滑动角161°,P轴方位54°;应力张量在震源机制中心解节面Ⅰ及节面Ⅱ上产生的相对剪应力分别为0.982和0.942。近台剪切波分裂显示,快波偏振方向为55°,慢波时间延迟为1.7 ms/km。分析发现,盐池M_(L)4.0地震震源机制P轴方位及其快波偏振方向均受到区域构造应力场控制,且震源机制两个节面的滑动角均与剪应力的滑动角基本一致。结合已有研究认为,本次地震发震断层可能与鄂尔多斯地块内部EW向基底断裂附近的平行伴生构造有关,并在主压应力轴为NE-SW向的区域构造应力场作用下,经过长时间应力积累,在剪应力的最优释放节面发生破裂。     

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean, and are parts of a large-scale system in fluid. The theory and observation show that, they satisfy quasi-geostrophic and quasi-static equilibrium approximations. In this paper, solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied. In order to simplify the problem, the topography is taken as a linear function of latitude variable y, then employing a weakly nonlinear method and a perturbation method, a KdV （Korteweg-de Vries） equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived. The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow, and extend the classical geophysical theory of fluid dynamics.     

A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea

A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow. One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained. The model simulations describe the generation and propagation of internal waves well. When the strength of imposed barotropic tides and the water stratification stay unchanged, the steepness of the sill slope can control both (a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves, and (b) the amplitude of the internal solitary waves generated. If the steepness of the sill is asymmetric, the nonlinear internal solitary waves may be induced on the steeper side of the sill. These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.     

A numerical study on the generation of a distinct type of nonlinear internal wave packet in the South China Sea

A distinct type of nonlinear internal-wave packet, with the largest internal solitary wave in the middle of the packet, was regularly observed in the South China Sea during the Asian Seas International Acoustics Experiment in 2001. Data analysis shows that the occurrence of the distinct internal wave packet is closely related with the occurrence of lower-high internal tides; the internal tides are mixed in the experimental area and, thus, there is diurnal inequality between the heights of two neighboring internal tides. Modeling of internal tides and internal solitary waves in a shoaling situation suggests that this type of wave packet can be generated in the South China Sea by the large shoaling of internal solitary waves and internal tides. Both the internal solitary waves and the internal tides come from the direction of Luzon Strait. The initial large internal solitary waves contribute to the occurrence of the largest internal solitary wave in the middle of the packet and the waves behind the largest internal solitary wave, while the shoaling internal tides bring about the nonlinear internal waves in front of the largest internal solitary wave via interaction with the local shelf topography.     

PROGRESS OF STUDIES ON THE INTERNAL TIDE GENERATED BY THE PASSAGE OF BAROTROPIC TIDE OVER CONTINENTAL SHELF/SLOPE

Various aspects of studies on internal tides are reviewed .Both beam-like structure and modal structure of internal tides may exist in the ocean . Bottom intensifications are caused by many factors .e.g. upstream blocking , which is the result of nonlinear interaction among waves . The energy may decay very fast so that internal tides are mostly locally generated .Internal tides may have considerable residual currents.In a 3-D frame, numerical study revealed that internal waves may interfere with each other to cause strong motions fer from the generation sources.The mechanism that determines how the lee waves break to form various nonlinear waves such as solitary waves, hydraulic jumps and internal surges or bores remains unclear. Analytic study is difficult , so numerical method may be effective . A radiation condition on the open boundary must be employed. A complete 3-D model may gain interesting result.Study on internal tides in China is limited to field observations and data analysis .     

INTERNAL TIDES, SOLITARY WAVES AND BORES IN SHALLOW SEAS

Remote sensing and in situ observations of internal tides, solitary waves and bores in shallow water are briefly reviewed in this paper. The emphasis is laid on interpreting SAR images based on oceanographic measurements, and analyzing characteristics of internal waves in the China Seas. Direc-tions for future research are discussed.     

Laboratory Experiments on an Internal Solitary Wave over a Triangular Barrier

Laboratory experiments were conducted to investigate the evolution of interfacial internal solitary waves(ISWs) incident on a triangular barrier. ISWs with different amplitudes were generated by gravitational collapse. The ISW energy dissipation and turbulence processes were calculated as waves passed over the triangular barrier. Experimental results showed that ISWs were reflecting back off the triangular barrier, and shoaling ISWs led to wave breaking and mixing when waves propagated over the obstacle. Wave instability created the dissipation of energy as it was transmitted from waves to turbulence. The rate of ISW energy dissipation, the maximum turbulent dissipation, and the buoyancy diffusivity linearly increased with the increase in the incident wave energy.     

Study on the propagation velocity of internal solitary waves in the Andaman Sea using Terra/Aqua-MODIS remote sensing images

Journal of Oceanology and Limnology - The Andaman Sea has been a classic study region for internal solitary waves (ISWs) for several decades, and extraordinarily large ISWs are characteristic of...     

Distribution of vertical turbulent mixing parameter caused by internal tidal waves and solitary waves in the South Yellow Sea

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.     

Multi-Waves,Breathers, Periodic and Cross-Kink Solutions to the(2+1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

The present article deals with multi-waves and breathers solution of the(2+1)-dimensional variable-coefficient CaudreyDodd-Gibbon-Kotera-Sawada equation under the Hirota bilinear operator method.The obtained solutions for solving the current equation represent some localized waves including soliton,solitary wave solutions,periodic and cross-kink solutions in which have been investigated by the approach of the bilinear method.Mainly,by choosing specific parameter constraints in the multi-waves and breathers,all cases the periodic and cross-kink solutions can be captured from the 1-and 2-soliton.The obtained solutions are extended with numerical simulation to analyze graphically,which results in 1-and 2-soliton solutions and also periodic and cross-kink solutions profiles.That will be extensively used to report many attractive physical phenomena in the fields of acoustics,heat transfer,fluid dynamics,classical mechanics,and so on.We have shown that the assigned method is further general,efficient,straightforward,and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and engineering.We have depicted the figures of the evaluated solutions in order to interpret the physical phenomena.