Non-propagating solitary waves with the consideration of surface tension

In this paper, the governing equation for the non-propagating solitary waves, similar to the cubic Schrödinger equation, is derived by the multiple scales with the consideration of surface tension. The non-propagating solitary wave solution is given. It is explained by the capillary-gravity wave theory that the crests are sharpened and the troughs are flattened in the transversal harmonic of the non-propagating solitary waves. On σ～kh plane, two parameter regions are obtained in which the non-propagating solitary wave can occur, but all existing experimental parameters are in region 1 (Fig. 1).     

浅水区海底管道周围海床渗透压力计算研究

我国海上油田开采起步较晚,大部分油田处于浅水区,因此,在设计管道时,应充分考虑由浅水区波浪引起的管道周围海床渗流力。根据浅水波相关假设,考虑自由水面非线性影响,推导出椭圆余弦波的波面方程,在此基础上进一步得到一个关于速度势的表达式,并根据该表达式得出作用于海床表面的波压公式。考虑海床土的压缩性,推导出一阶近似椭圆余弦波作用下浅水区埋置管道周围海床的渗流压力解析解,最后将计算结果与大型水槽试验及以往研究成果作对比。结果表明,在椭圆余弦波的作用下,由一阶椭圆余弦波理论得到的计算结果与试验结果规律基本一致,与相似工况下的现有理论成果数值基本相同,具有一定的可行性和工程价值。     

A meshless numerical wave tank for simulation of nonlinear irregular waves in shallow water

Time domain simulation of the interaction between offshore structures and irregular waves in shallow water becomes a focus due to significant increase of liquefied natural gas (LNG) terminals. To obtain the time series of irregular waves in shallow water, a numerical wave tank is developed by using the meshless method for simulation of 2D nonlinear irregular waves propagating from deep water to shallow water. Using the fundamental solution of Laplace equation as the radial basis function (RBF) and locating the source points outside the computational domain, the problem of water wave propagation is solved by collocation of boundary points. In order to improve the computation stability, both the incident wave elevation and velocity potential are applied to the wave generation. A sponge damping layer combined with the Sommerfeld radiation condition is used on the radiation boundary. The present model is applied to simulate the propagation of regular and irregular waves. The numerical results are validated by analytical solutions and experimental data and good agreements are observed. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling of long nonlinear waves on the interface in a horizontal two-layer viscous channel flow

The dynamics of two-dimensional waves of small but finite amplitude are theoretically studied for the case of a two-layer system bounded by a horizontal top and bottom. It is shown that for relatively large steady-state flow velocities and at certain fluid depth ratios the vertical velocity profile is nonlinear. An evolutionary equation governing the fluid interface disturbances and allowing for the long-wave contributions of the layer inertia and surface tension, the weak nonlinearity of the waves, and the unsteady friction on all the boundaries of the system is derived. Steady-state solutions of the cnoidal and solitary wave type for the disturbed flow are determined without regard for dissipation losses. It is found that the magnitude and the direction of the flow can alter not only the lengths of the waves but also their polarity.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 143–158. Original Russian Text Copyright © 2005 by Arkhipov and Khabakhpashev.     

Two notes on numerical simulation for the properties of solitary waves

In order to suppress the error induced by the modified differential equations, a compensative procedure is designed to desoribe the higher order effect of the non-linear interaction of the solitary waves. The project supported by National Natural Science Foundation of China     

双相介质P波波动方程小波域多尺度模拟

相比于单相介质理论而言,双相介质理论更接近实际地层的真实情况,因此在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用。传统的波动方程数值解法由于本身固有的不足不利于求解诸如双相介质波动方程等复杂的非线性和不规则性问题;而小波方法则由于自身良好的特性可以用来构建解决此类问题的自适应性算法。本文详细推导了双相介质P波波动方程的有限差分矩阵表示形式,利用小波变换将其转移到小波域,设置阈值形成更为稀疏的迭代矩阵以构建自适应算法,从而达到减少计算量,增加地震波场数值模拟灵活性和准确性的目的。地球物理勘探的数值模拟实例验证了方法的有效性。     

对碰波作用下金属圆管材料参数对其运动特征影响的数值模拟

基于两点起爆实验,采用动力学有限元程序,在不考虑圆管破裂的前提下,详细分析了同一炸药爆轰下金属圆管各材料力学参数对其运动的影响规律。计算结果表明:弹性模量越大,泊松比越大,金属圆管的膨胀速度越大,但它们对圆管膨胀的位移和速度影响极小,在工程中可以忽略;屈服应力对金属圆管的运动有一定影响,屈服应力越大,对碰部位的鼓包范围越宽,鼓包峰值越小,但圆管各处的膨胀量均落后于屈服应力较小的情况;密度对圆管运动有较大影响,密度越大,受鼓包影响范围越宽,鼓包峰高越小。     

Wavelet Analysis of the Evolution of a Solitary Wave in a Composite Material

The evolution of a solitary wave propagating through a microstructural material (composite) is studied on the basis of wavelet analysis. A specific feature of the solution technique proposed is the use of Mexican hat (MH) wavelets, which are elastic wavelets, i.e., they are solutions of the basic system of wave equations for an elastic material with a microstructure. The initial wave profile is also chosen in the form of the MH-wavelet. Primary attention is given to the relationship among the profile behavior, wave bottom length, and characteristic microstructure length. A computer analysis conducted demonstrates that the approach proposed allows us to detect the basic wave effects: splitting of the wave into two modes with different phase velocities, simultaneous propagation of both modes in the components of the composite, and strong dependence of the evolution rate on the characteristic lengths of the wave and microstructure     

时域Rankine源法求解有限水深船舶在规则波中的水底压力变化

应用势流理论中的Rankine源面元法和时域步进法,求解了有限水深船舶在规则波中运动的水底压力变化。将速度势分解成基本势、局部势和记忆势,以叠模解作为基本势对自由表面条件和物面条件进行了线性化,通过在水底布置面元来满足水底条件。利用研制的水底压力-水面波浪测量系统,测量了不同入射波船模表面波形与水底压力的时历曲线,理论计算与实验结果符合较好,验证了自编程序的正确性。通过对比二者的等高线图发现,水底压力与表面波形的峰谷有较好的一致性,并且压力较波形更为平滑。     

铝板中激光Lamb波信号的模态分析与缺陷检测研究

激光激励的Lamb波信号具有较宽的频带,且包含多个模态信息。本文采用二维傅里叶变换和时频分析等信号分析技术用于检测信号中的模态成分及缺陷信息识别。首先,对200组激光Lamb波信号进行二维傅里叶变换,得到信号的频率-波数图,可识别出激光Lamb波信号中的低阶A0、S0和高阶模态,并且A0模态能量高,可用于缺陷检测。随后对有、无缺陷状态下Lamb波信号进行连续小波变换,从时频图中识别出缺陷信号的频率成分,进一步提取特定频率下的小波系数幅值信号,实现了缺陷信息的识别。结果表明,二维傅里叶变换能较好地识别激光Lamb波的模态成分,而提取出的连续小波变换系数图,能准确实现缺陷定位。     

复杂气固两相系统的微观结构

流化床中的气固两相流动是一个高度复杂的非线性混沌系统。本文利用激光粒子动态分析仪（ＰＤＡ）得到的循环流化床中颗粒脉动速度信号,采用ＦＦＴ分析了脉动信号的宽频谱特征,在此基础上应用小波法分析了脉动信号的动态特征,得到了颗粒脉动速度的微观结构,指出颗粒脉动速度的非线性特性是流化床具有混沌特性的根源,且在不同的尺度上颗粒脉动速度表现出各向异性的特征。     

Linear and nonlinear rheology of micellar solutions in the isotropic,cubic and hexagonal phase probed by rheo-small-angle light scattering

Aqueous solutions of a branched nonionic surfactant were studied in the isotropic, cubic and hexagonal phase by means of rheological and small-angle light scattering (SALS) experiments. The isotropic phase behaved like a Newtonian liquid. An increase of activation energy of viscous flow was found near the overlap concentration of spherical micelles, but no shear thinning was observed. The viscosity of low concentrated samples increased slightly when the lower critical solution temperature was approached. This increase of viscosity was much smaller compared to common nonionic surfactants. The cubic phases behaved as elastic solids with a high plateau modulus, and shear melting occurred at high shear stresses. The hexagonal phase showed complex behavior. Shear orientation could be achieved by large amplitude oscillatory shear and was proved by rheo-small-angle light scattering. Two orientations were observed, at first perpendicular to the flow direction, i.e., log-rolling state and, secondly, an in-shear-plane orientation parallel to the flow direction. The linear viscoelastic region of the hexagonal phase was extremely small and was detected by simultaneous rheo-small angle light scattering. Shear alignment lead to a decrease of the moduli.     

地震作用下水库坝体与水体相互作用数值模拟

地震作用下水库坝体受迫振动,推动坝后水体波动,造成水体动压作用于坝体,形成坝-水耦合作用,影响坝体安全.为了评估坝体振动引起的水面波动及坝体所受动水荷载作用,建立坝体动边界条件下的不可压水体运动数学模型,模拟了地震波作用下的坝后水体波动和动力荷载.结果 表明,在忽略坝体自身弹性变形的条件下,地震作用下坝体激发的水体表面...     

On the interaction of cubically nonlinear transverse plane waves in an elastic material

The paper presents theoretical results on the interaction of cubically nonlinear harmonic elastic plane waves in a nonlinear material described by the Murnaghan potential. The interaction of two harmonic transverse waves is studied using the method of slowly varying amplitude. Reduced and evolution equations and the Manley-Rowe relations are derived. An analysis is made of the mechanism of energy transfer from the strong pumping wave, which has frequency ω, to the weak signal wave, which has frequency 3ω because of this interaction. A switching mechanism for hypersonic waves in a nonlinear elastic material is described, which is similar to the switching mechanism observed in transistors __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 61–70, June 2006.     

Weighted average flux method and flux limiters for the numerical simulation of shock waves in rigid porous media

The one‐dimensional flow field generated by the passage of a shock wave in a rigid, thermoelastic porous foam has been simulated using a two‐phase mathematical model. The work presented here makes use of the weighted average flux method to solve the system of six equations that govern the problem. Spurious oscillations are eliminated through the application of total variation diminishing limiting methods. Four different limiters were tested: van Leer, SuperA, MinA and van Albada. Numerical tests were carried out to verify the performance of each flux limiter in terms of accuracy. The results were compared to analytical and previously obtained data to assess the performance of the mathematical model. Excellent agreement was obtained. Copyright © 2002 John Wiley & Sons, Ltd.     

浅层水中爆炸冲击波对混凝土墩斜碰撞作用试验研究

通过含铝炸药JHL-3的实爆试验,得到混凝土墩在单个装药浅层水中爆炸、两个装药浅层水中对称及不对称设置同步起爆爆炸作用下、混凝土墩迎爆面上的冲击波压力响应数据;获得了迎爆面中心反射压力峰值计算模型;分析了两个装药浅层水中爆炸冲击波对混凝土墩绕射及透射作用效应。     

水中爆炸激波对水泥试样作用的数值模拟分析

通过对水中爆炸激波在水泥净浆试样中传播的数值模拟,再现了爆炸激波的传播过程,采用对典型单元受到的激波作用和应力进行分析的方法,得出了水泥试样各个区域损伤破坏的成因,数值模拟结果和实验现象吻合。     

覆水饱和双相介质圆弧场地P波激励下散射问题的理论解

采用波函数展开法对平面P波入射复杂水域地形的空间变异性地震动场进行研究,该水域地形具有覆水层、饱和双相介质、场地非平坦以及第二类分层(场地跨越分层界面)等属性.首先,依据地震波反射和透射特性推导直角坐标系下的自由波场分布;然后,根据场地属性并引入大圆弧法分析极坐标系下的含有待定系数的散射波场;进而,结合土-水分界面和饱和土层分界面边界条件,求解散射波场中的待定系数;最后,通过自由波场和散射波场得到覆水饱和双相介质圆弧场地波函数理论解.基于理论解,通过算例验证了理论推导的合理性及可靠性,分析了地表位移在不同入射条件下的差异性.结果 表明,相对于均匀介质,饱和双相介质会显著影响地表位移分布.此外,入射波频率和角度对地震地面运动特性也有较大的影响.     

Dispersion and stability analyses of the linearized two‐dimensional shallow water equations in boundary‐fitted co‐ordinates

In the present investigation, a Fourier analysis is used to study the phase and group speeds of a linearized, two‐dimensional shallow water equations, in a non‐orthogonal boundary‐fitted co‐ordinate system. The phase and group speeds for the spatially discretized equations, using the second‐order scheme in an Arakawa C grid, are calculated for grids with varying degrees of non‐orthogonality and compared with those obtained from the continuous case. The spatially discrete system is seen to be slightly dispersive, with the degree of dispersivity increasing with an decrease in the grid non‐orthogonality angle or decrease in grid resolution and this is in agreement with the conclusions reached by Sankaranarayanan and Spaulding (J. Comput. Phys., 2003; 184 : 299–320). The stability condition for the non‐orthogonal case is satisfied even when the grid non‐orthogonality angle, is as low as 30° for the Crank Nicolson and three‐time level schemes. A two‐dimensional wave deformation analysis, based on complex propagation factor developed by Leendertse (Report RM‐5294‐PR, The Rand Corp., Santa Monica, CA, 1967), is used to estimate the amplitude and phase errors of the two‐time level Crank–Nicolson scheme. There is no dissipation in the amplitude of the solution. However, the phase error is found to increase, as the grid angle decreases for a constant Courant number, and increases as Courant number increases. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis of a second‐order upwind method for the simulation of solute transport in 2D shallow water flow

A two‐dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first‐order upwind technique, a second order in space and time and an extended first‐order method are applied to solve the non‐diffusive terms in both the flow and solute equations and a centred implicit discretization is applied to the diffusion terms. The stability constraints are studied and the form to avoid oscillatory results in the solute concentration in the presence of complex flow situations is detailed. Some comparisons are carried out in order to show the performance in terms of accuracy of the different options. Copyright © 2007 John Wiley & Sons, Ltd.