Seismic Responses of a Hemispherical Alluvial Valley to SV Waves: A Three-Dimensional Analytical Approximation

An analytical solution to the three-dimensional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expansion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot's dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn: (1) there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; (2) the normalized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; (3) with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

Effect of weak Brownian motion on gravitational coagulation

The effect of a small amount of Brownian diffusion on gravitational coagulation is numerically calculated by incorporating gravitational and interparticle forces (both attractive and repulsive), as well as hydrodynamic interactions. It is found that weak Brownian diffusion, the effect of which is nonlinearly coupled with gravity, can act to decrease the coagulation rate.

Effective Stress and Liquefaction of Seabed Under the Action of Standing Waves

波浪作用下海床的稳定性与液化分析是海底管线、防波堤和海洋平台设计中必须仔细考虑的问题。推荐了一个循环载荷作用下土体的弹塑性实用本构模型,并给出了一种粉土的模型参数,该模型直接根据初始应力状态和循环应力的大小与作用时间计算土体的塑性应变增量,在有限元计算中不需要引入弹塑性矩阵。采用Biot理论和有限单元法,对海床有效应力的变化过程分析表明,波腹点下海床存在较大的液化可能性。波浪作用对海床存在一定的压密作用。

The Interaction Between Shock Waves and Solid Spheres Arrays in a Shock Tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in. the wave propagation process. The wave interactions with vortices behind each sphere's wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

The investigation on dynamic fracture behavour of materials under compressive-shear combined stress waves

In this paper, an improved plate impact experimental technique is presented for studying dynamic fracture mechanism of materials, under the conditions that the impacting loading is provided by a single pulse and the loading time is in the sub-microsecond range. The impacting tests are carried out on the pressure-shear gas gun. The loading rate achieved is dK/dt similar to 10(8) MPa m(1/2) s(-1). With the elimination of influence of the specimen boundary, the plane strain state of a semi-infinite crack in an infinite elastic plate is used to simulate the deformation fields of crack tip. The single pulses are obtained by using the "momentum trap" technique. Therefore, the one-time actions of the single pulse are achieved by eradicating the stress waves reflected from the specimen boundary or diffracted from the crack surfaces. In the current study, some important phenomena have been observed. The special loading of the single pulse can bring about material damage around crack tip, and affect the material behavior, such as kinking and branching of the crack propagation. Failure mode transitions from mode I to mode II crack are observed under asymmetrical impact conditions. The mechanisms of the dynamic crack propagation are consistent with the damage failure model.

用高速阴影技术研究K9玻璃中的失效波=Investigations of Failure Waves in K9 Glass Using Shadowgraph

用高速阴影摄影技术研究了爆轰加载下K9 玻璃样品中波的传播和压缩区内损伤破坏的物理图象 和规律。实验中观测到冲击波阵面后有一个移动速度为2. 1～2. 2 mm/μs 的黑色阴影区边界,即失效波(Failure wave) ;实验发现只有当冲击载荷接近材料的HEL 时,在冲击波和失效波之间的区域才有少量的微裂纹成 核和长大,而在冲击载荷较低时却没有观察到;同时实验中观测到失效波萌生于被撞击面,并在两块玻璃的交 界面上观测到失效波的再生。这些结果表明失效波的产生基本与冲击相变无关,主要与玻璃样品表面的初始 损伤有关,换言之,失效波是玻璃样品表面微裂纹在冲击波作用下失稳扩展造成的。

How important are shock waves to single-bubble sonoluminescence?

By solving numerically the full set of hydrodynamic equations governing the pulsation of a bubble,we show that shock waves are often absent in a stable sonoluminescing bubble. Nevertheless, for a wide range of physical parameters, a continuous compressional wave emerges and heats up the bubble, and the resulting black-body radiations have pulse heights and widths that agree with experimental data. Shock waves, being much less robust, are not essential for stable single-bubble sonoluminescence.

Receptivity To Free-Stream Disturbance Waves For Hypersonic Flow Over A Blunt Cone

A high-order shock-fitting finite difference scheme is studied and used to do direction numerical simulation (DNS) of hypersonic unsteady flow over a blunt cone with fast acoustic waves in the free stream, and the receptivity problem in the blunt cone hypersonic boundary layers is studied. The results show that the acoustic waves are the strongest disturbance in the blunt cone hypersonic boundary layers. The wave modes of disturbance in the blunt cone boundary layers are first, second, and third modes which are generated and propagated downstream along the wall. The results also show that as the frequency decreases, the amplitudes of wave modes of disturbance increase, but there is a critical value. When frequency is over the critial value, the amplitudes decrease. Because of the discontinuity of curvature along the blunt cone body, the maximum amplitudes as a function of frequencies are not monotone.

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.

An Efficient Front-Tracking Method For Fully Nonlinear Interfacial Waves

A fully nonlinear and dispersive model within the framework of potential theory is developed for interfacial (2-layer) waves. To circumvent the difficulties arisen from the moving boundary problem a viable technique based on the mixed Eulerian and Lagrangian concept is proposed: the computing area is partitioned by a moving mesh system which adjusts its location vertically to conform to the shape of the moving boundaries but keeps frozen in the horizontal direction. Accordingly, a modified dynamic condition is required to properly compute the boundary potentials. To demonstrate the effectiveness of the current method, two important problems for the interfacial wave dynamics, the generation and evolution processes, are investigated. Firstly, analytical solutions for the interfacial wave generations by the interaction between the barotropic tide and topography are derived and compared favorably with the numerical results. Furthermore simulations are performed for the nonlinear interfacial wave evolutions at various water depth ratios and satisfactory agreement is achieved with the existing asymptotical theories. (c) 2008 Elsevier Inc. All rights reserved.

Hydrodynamic interaction between two vertical cylinders in water waves

The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Transition waves and nonlinear interactions in the near wake of a circular cylinder

Transition waves and interactions between two kinds of instability-vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000-10 000 are studied by a domain decomposition hybrid numerical method. Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency, i.e. f(t)/f(s) similar to Re-0.87 are obtained. The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza's prediction and some early experimental results f(t)/f(s) similar to Re-0.5 given by Bloor et nl. The multi-interactions between two kinds of vortex are clearly visualized numerically. The strong nonlinear interactions between the two independent frequencies (f(t), f(s)) leading to spectra broadening to form the coupling mf(s) +/- nf(t) are predicted and analyzed numerically, and the characteristics of the transition are described. Longitudinal variations of the transition wave and its coupling are reported. Detailed mechanism of the flow transition in the near wake before occurrence of the three-dimensional evolution is provided.