Shock wave detection in two-dimensional flow based on the theory of characteristics from CFD data

A method to detect the discontinuity of a shock wave from computational fluid dynamics (CFD) data was developed based on the theory of characteristics and was adopted to replace the inaccurate method that involves observation of the location of steep spatial gradient with respect to the primitive variables, such as pressure. A shock wave is mathematically defined as a convergence of characteristics, in which each type of Riemann invariant is conserved within each characteristic. In the vector field of the characteristics, such convergences are interpreted as critical lines of the streamlines, which are easily identified by calculating the eigenvectors of the vector field of propagation velocity of the Riemann invariant. The use of a triangular cell system enables unique determination of the linearized vector field in each cell and enables analytical identification of the critical line within this field. Shock waves can be successfully extracted using this method. The method can be extended to the detection of moving shock waves by considering the coordinate moving with the shock.     

Multi-taper Spectral Analysis in Gravitational Wave Data Analysis

Spectral estimation plays a significant role in gravitational wave data analysis. We provide a brief introduction to multi-taper methods which use multiple orthogonal tapers (or windows) to provide spectral estimators with excellent bias and variance properties. Multi-taper methods are also extremely powerful for the estimation and removal of sharp spectral peaks in the presence of noise such as arise due to power line harmonics or suspension resonances. We present examples of these methods using the GRASP (Gravitational Radiation Analysis and Simulation Package) software package.     

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebyshev pseudo-spectral method, due to its slow convergence in problems where the solution has steep internal layers. We discuss the effectiveness and conditioning of the proposed discretization, and show that it allows the computation of accurate traveling waves and eigenvalues for small values of the initial water saturation/film precursor, several orders of magnitude smaller than the values considered previously in analogous stability analyses of thin film flows, using just a few hundred grid points.     

Laboratory and modeling study on modulated wave properties

Development of Benjamin?Feir instability is investigated under laboratory conditions and by analytical modeling. Nonlinear properties of the wave train with discrete spectrum are also investigated. The mechanically generated waves are composed of several discrete waves, while the newly generated harmonics are still combined into discrete spectra with the same frequency step. The technique proposed in this study allows us to study accurately the nonlinear variations in main properties of each harmonic with fixed frequency, such as amplitude, phase speed, and wavenumber along the wave tank together with velocities of wave packet crests, especially for the large transient waves. The phase speeds of short waves increase near large transient waves, and the velocities of longer waves are close to the values determined by the linear theory of waves. The relative long wave accompanied by short waves can dramatically change the local kurtosis and skewness of the wave field. They may play an important role for the generation of large transient wave and provide an opportunity for triggering of the freak waves.     

Aerodynamic design of a supersonic three-dimensional inlet

The results of designing and numerical gas-dynamic modeling a supersonic three-dimensional inlet of a new type are considered. A ramp of external compression of this inlet is the V-shaped body forming an initial plane oblique shock wave and a subsequent isentropic compression wave. The inlet incorporates an entrance section of internal compression, where also a plane oblique shock wave and a subsequent isentropic compression wave are formed by a cowl. The designed three-dimensional inlet has small inclination angles of compression surfaces, which ensures its low wave drag. According to the estimates of inlet efficiency in terms of the compression ratio and the total pressure recovery factor, it is close to the optimal two-dimensional shocked inlet of external compression considered by Oswatisch as well as Petrov and Ukhov. The flow in the inlet was computed with the use of the Euler and Navier — Stokes codes provided by the commercial package “FLUENT”. The flow in the inlet throat in the design regime computed under the inviscid flow approximation is uniform. The most substantial effect of the flow viscosity in this regime manifests itself in the interaction of the shock wave from the cowl with the boundary layer on the V-shaped compression body in the inlet internal duct. According to computed data, the boundary layer separation does not occur in this case; however, due to viscosity effects, reflected shock waves are formed here which results in significant deviations of flow structure as compared to the computed inviscid flow.     

On the origin of solar wind. Alfvén waves induced jump of coronal temperature

Absorption of Alfvén waves is considered to be the main mechanism of heating in the solar corona. It is concluded that the sharp increase of the plasma temperature by two orders of magnitude is related to a self-induced opacity with respect to Alfvén waves. The maximal frequency for propagation of Alfvén waves is determined by the strongly temperature dependent kinematic viscosity. In such a way the temperature jump is due to absorption of high frequency Alfvén waves in a narrow layer above the solar surface. It is calculated the power per unit area dissipated in this layer due to damping of Alfvén waves that blows up the plasma and gives birth to the solar wind. A model short wave-length (WKB) evaluation takes into account the 1/f² frequency dependence of the transversal magnetic field and velocity spectral densities. Such spectral densities agree with old magnetometric data taken by Voyager 1 and recent theoretical calculations in the framework of Langevin-Burgers MHD. The presented theory predicts existence of intensive high frequency MHD Alfvén waves in the cold layer beneath the corona. It is briefly discussed how this statement can be checked experimentally. It is demonstrated that the magnitude of the Alfvén waves generating random noise and the solar wind velocity can be expressed only in terms of satellite experimental data. It is advocated that investigation of properties of the solar surface as a random driver by optical methods is an important task for future solar physics.     

Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.     

等离子体光栅靶的表面粗糙度对高次谐波产生的影响

极紫外光和软X射线由于其波长和脉冲持续时间极短,可用于超快物理过程和物质微观结构的探测.最近几年,研究人员发现激光和等离子体相互作用可以产生持续时间极短(阿秒)且相干性较好的高次谐波辐射,其波长可接近甚至达到水窗波段.然而,实验研究指出,理论上应出现的一些谐波在实验中并没有出现.本文针对超短超强激光与非理想条件下的等离子体光栅靶相互作用产生高次谐波的物理过程进行了理论分析和粒子模拟.研究结果表明,等离子体光栅的周期性结构对于高次谐波的频谱和辐射角分布存在显著调制效果.光栅靶表面粗糙度直接影响光栅的光学调制效果,改变高次谐波的频谱分布和辐射角分布.理想光栅条件下,满足光栅匹配条件的特定阶数谐波明显获得增强,且辐射张角集中在平行靶面的方向.靶表面粗糙度的出现,导致光栅匹配条件失效,高次谐波能量向各阶分散且辐射张角逐渐偏离靶表面方向.研究结果较好地解释了实验中观测到的谐波频谱分布,为进一步的研究提供了一定参考.     

Nonlinear noise waves in soft biological tissues

The study of intense waves in soft biological tissues is necessary both for diagnostics and therapeutic aims. Tissue represents an inherited medium with frequency-dependent dissipative properties, in which waves are described by nonlinear integro-differential equations. The equations for such waves are well known. Their group analysis has been performed, and a number of exact solutions have been found. However, statistical problems for nonlinear waves in tissues have hardly been studied. As well, for medical applications, both intense noise waves and waves with fluctuating parameters can be used. In addition, statistical solutions are simpler in structure than regular solutions; they are useful for understanding the physics of processes. Below a general approach is described for solving nonlinear statistical problems applied to the considered mathematical models of biological tissues. We have calculated the dependences of the intensities of the narrowband noise harmonics on distance. For wideband noise, we have calculated the dependence of the spectral integral intensity on distance. In all cases, wave attenuation is determined both by the specific dissipative properties of the tissue and the nonlinearity of the medium.     

Laboratory study of nonlinear trapping of magnetized Langmuir waves inside a density depletion

The formation of a small-scale plasma density depletion region extended along the ambient magnetic field and caused by the nonlinear interaction of the upper-hybrid plasma waves with a magnetoplasma has been observed under laboratory conditions modeling the ionospheric heating experiments. Plasma waves are trapped inside the depletion due to their specific dispersion properties. The threshold of the nonlinear wave trapping significantly increases in the vicinity of the harmonics of the electron gyrofrequency.     

Non-linear acoustic radiation by an underwater vibrating spherical shell

I.IntroductionMostofthepublishedstudiesontheacousticwaveradiationfromelasticbodyconcen-tratedon1ineartheory.However,iftheamplitudeislargeandthefrequencyishigh,theresultingsoundwavepropagatinginthemediumwillgenerateconsiderablenonlineardistor-tion.Sothest.di.s[1]inthisfieldarelimited.Inthispaperwetreatedasphericalshell.Itconsistsoftwoaspects:oneisthestructuralresponseofasphericalshellinacousticfield.Becausethenonlineareffectofacousticwavecumulateswithpropagatingdistance,itisnegligibleonthesph…     

Rayleigh mechanism of local elevation of energy in propagation of a shock wave in an active medium

A mechanism of action of a shock wave on an active medium, which leads to an additional energy release source, is considered. This source moves together with the shock wave front and depends on the magnitude and direction of the electric field applied to the plasma and on the current density in the plasma. The study is a continuation of an earlier publication devoted to the propagation of weak shock waves. Here, we consider shock waves of an arbitrary intensity with an arbitrary mechanism of formation of an additional energy contribution due to variation of the parameters of the medium as a result of passage of the shock wave. Special cases of this effect are the propagation of a shock wave in a plasma and detonation burning.     

Nanodomain shock wave in near-field laser–material interaction

In this work, molecular dynamics simulation is conducted to explore the shock wave phenomena in a nanodomain in near-field laser–material interaction. A large system consisting of over 800,000 atoms is studied. The work focuses on the kinetic and physical properties of the disturbed gas compression driven by the high speed movement of the molten particulates ejected from the solid target in a nanodomain. The quick interaction between solid and gas atoms compresses the gas and forms a steep shock wave front, which moves at a supersonic speed. The fast compression of gas also induces a steep interface of density, temperature and pressure distribution, which is viewed as typical characteristics of nanoscale shock waves. Evolutions of shock wave front position, velocity and Mach number are also explored and show quick decay during wave propagation.     

Modeling the propagation of ultrasonic waves in the interface region between two bonded elements

An important task in nondestructive materials evaluation is the development of techniques to characterize the bond quality of adherent joints. Binding forces are nonlinear and cause a nonlinear modulation of transmitted and reflected ultrasonic waves. As a consequence, the higher harmonics generated by an insonified monochromatic wave give information about the adhesive bonds. The local binding forces in thin bonded interfaces can be obtained by the amplitudes of the ultrasonic waves of the insonified frequency and its higher harmonics as transmitted through the interface. Additional phase measurements may enable one to obtain the evaluation of the full hysteretic cycle of the interaction force. In order to gain a deeper understanding of the interface region and to improve the technique, numerical simulations of the ultrasonic wave propagation through specimens of two bonded elements can be used. A simple model based on the local interaction simulation approach (LISA) is described in this contribution, and a comparison between the results of the simulations and the experimental data is presented. Besides its intrinsic relevance for NDE, the problem considered in this paper may be very useful to analyze and test models for the simulation of ultrasonic wave propagation in nonclassical nonlinear mesoscopic elastic materials.     

化学反应和球面聚心爆轰波的相互作用

考察球面爆轰波聚心传播过程中,波阵面附近压力和温度不断升高引起化学反应进程的改变;对比氢氧可燃气体与氮气的数值模拟结果,分析化学反应对波面温度和压力的影响,从而考察Zeldovich理论预测聚心爆轰波后参数的精确性.数值结果表明,爆轰波聚心传播初期,放热的燃烧反应对波后热力学参数起主导作用;传播后期,波阵面趋近于对称中心时,吸热的气体解离反应变得非常活跃,解离反应对后期的汇聚压力影响不大,但会在很大程度上限制汇聚温度的升高.     

Electron acceleration and type II radio emission at quasi-parallel shock waves

Solar type II radio bursts are interpreted as the radio signature of shock waves travelling through the solar corona. Some of these shock waves are able to enter into the interplanetary medium and are observed as interplanetary type II bursts. The nonthermal radio emission of these bursts indicates that electrons are accelerated up to superthermal and/or relativistic velocities at the corresponding shocks. Plasma wave measurements at interplanetary shock waves support the assumption that the fundamental type II radio emission is generated by wave-wave interactions of electron plasma waves and ion acoustic waves and that the source region is located near the transition region of the shock. Therefore, the instantaneous bandwidth of type II bursts should reflect the density jump across the shock. Comparing the theoretically predicted density jump of coronal shock waves (Rankine-Hugoniot relations) and the measured instantaneous bandwidth of solar type II radio bursts it is appropriate to assume that these bursts are generated by weak supercritical quasi-parallel shock waves. Two different mechanisms for the accelaration of electrons at this kind of shock waves are investigated in the form of test particle calculations in given magnetic and electric fields. These fields have been extracted from in-situ measurements at the quasi-parallel region at Earth’s bow shock, which showed large amplitude magnetic field fluctuations (so-called SLAMS: Short Large Amplitude Magnetic Field Structures) as constituent parts. The first mechanism treats these structures as strong magnetic mirrors, at which charged particles are reflected and accelerated. Thus, thermal electrons gain energy due to multiple reflections between two approaching SLAMS. The second mechanism shows that it is possible to accelerate electrons inside a single SLAMS due to a noncoplanar component of the magnetic field in these structures. Both mechanism are described in the form of test particle calculations, which are supplemented by calculations according to adiabatic theory. The results are discussed for circumstances in the solar corona and in interplanetary space.     

Physical investigation of acoustic waves induced by the oscillation and collapse of the single bubble

The objective of this paper is to apply both experimental and numerical methods to investigate acoustic waves induced by the oscillation and collapse of a single bubble. In the experiments, the schlieren technique is used to capture the temporal evolution of the bubble shapes, and the corresponding acoustic waves. The results are presented for the single bubble generated by a low-voltage bubble generator in the free field of water. During the numerical simulations, a three-dimensional (3D) weakly compressible model is introduced to investigate the single bubble dynamics, including the generation and propagation of acoustic waves. The results show that (1) Compression wave, rarefaction wave and shock wave are generated during expansion stage, collapse stage and rebound stage of the bubble respectively. (2) Compression waves are induced by the rapid expansion of the bubble and eventually steepen into one shock wave propagating outward in the liquid, then another strong shock wave is emitted at the final collapse stage. The velocity and pressure of the liquid field increases after the shock wave. (3) Rarefaction waves are generated during the collapse stage due to the contraction of the bubble. The rarefaction wave reduces the liquid pressure and its spatial distribution is dispersive. The pressure of these acoustic waves and their effect on the liquid velocity attenuate with the increase of propagation distance.     

Background Oriented Schlieren Method as an Optical Method to Study Shock Waves

Background oriented schlieren method is applied in diagnostics of shock waves in air. The method can be used for visualization of shock waves that are generated after explosion or due to motion at ultrasonic speeds. Experimental data make it possible to observe propagation of a shock wave in space, estimate the asymmetry of energy liberation in explosion, and determine parameters of shock wave.     

Contribution of steep irregularities to the radio-brightness temperature of the ocean

We propose a new mechanism of a change in the brightness temperature of the ocean due to the contribution from steep mesoscale waves and estimate the contribution of such waves to the brightness temperature of the ocean. A steep wave is simulated by an inclined surface. The estimates show that variations in the radio-brightness temperature due to steep irregularities can reach several kelvins at low grazing angles. For short observation distances and low grazing angles, the brightness temperature has bursts similar to those observed in the case of backscattering. These bursts occur when breaking waves hit the observation area. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 3, pp. 217–223, March, 2000     

The Self-Similarity Index of the Convergence of Strong Cylindrical Shock Waves in a Gas with a Uniform Density

A model of the convergence of cylindrical shock waves (SWs) in a gas with a uniform density has been considered. The partial differential equations of this model have been reduced to ordinary differential equations, from which the law of convergence of such shock waves and the dependence α = f(γ, γ_eff) of their self-similarity index α on the heat-capacity ratio in front of the shock wave (γ) and behind the shock wave front (γ_eff) of the gas have been found. This dependence for cylindrical shock waves has been shown to agree with the experimental data within the measurement error.