The region of nonlinear effects for intensive sound pulses in the ocean

The formation of a stationary shock wave is studied in media with an arbitrary power dependence of the damping coefficient on the frequency. The conditions for existence of a stationary shock wave are defined and it is shown that when acoustic signals propagate in the ocean the region of nonlinear effects is limited. For acoustic waves generated by explosive sources a calculation is given of the location of the transition point of the nonlinear wave into a linear one, and the dependence of this point on the charge weight is defined.     

Dust entrainment by means of a planar shock induced vortex over loose dust layers

Conclusions The recent study of Ben-Dor and Rayevsky (1994) regarding the interaction of planar shock waves with high density layers was reconsidered in order to demonstrate a possible dust entrainment mechanism which has not received appropriate attention so far. It was shown that, as a result of the interaction, a large vortex is generated. This vortex could in fact contribute to the entrainment of dust when planar shock waves interact with loose dusty layers.In addition, the effect of viscosity on the proposed dust entrainment mechanism was also considered.     

Solution of Riemann problem for dusty gas flow

A direct approach is used to solve the Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady planar flow of an isentropic, inviscid compressible fluid in the presence of dust particles. The elementary wave solutions of the Riemann problem, that is, shock waves, rarefaction waves and contact discontinuities are derived and their properties are discussed for a dusty gas. The generalised Riemann invariants are used to find the solution between rarefaction wave and the contact discontinuity and also inside rarefaction fan. Unlike the ordinary gasdynamic case, the solution inside the rarefaction waves in dusty gas cannot be obtained directly and explicitly; indeed, it requires an extra iteration procedure. Although the case of dusty gas is more complex than the ordinary gas dynamics case, all the parallel results for compressive waves remain identical. We also compare/contrast the nature of the solution in an ordinary gasdynamics and the dusty gas flow case.     

Multiple scales analysis of wave�Cwave interactions in?a?cubically nonlinear monoatomic chain

The interaction of waves in nonlinear media is of practical interest in the design of acoustic devices such as waveguides and filters. This investigation of the monoatomic mass?Cspring chain with a cubic nonlinearity demonstrates that the interaction of two waves results in different amplitude and frequency dependent dispersion branches for each wave, as opposed to a single amplitude-dependent branch when only a single wave is present. A theoretical development utilizing multiple time scales results in a set of evolution equations which are validated by numerical simulation. For the specific case where the wavenumber and frequency ratios are both close to 1:3 as in the long wavelength limit, the evolution equations suggest that small amplitude and frequency modulations may be present. Predictable dispersion behavior for weakly nonlinear materials provides additional latitude in tunable metamaterial design. The general results developed herein may be extended to three or more wave?Cwave interaction problems.     

Dust acoustic shock waves in coupled dusty plasmas with nonthermal ions

Dust acoustic shock waves of the Korteweg-de Vries–Burgers (KdV–Burgers) equation and the modified Korteweg-de Vries–Burgers (MKdV–Burgers) equation are studied in strongly coupled dusty plasmas containing nonthermal ions and Boltzmann-distributed electrons. The effects of important parameters, such as nonthermal parameter, relative temperature, relative density and dust particles viscosity, on the properties of shock waves are discussed.     

Design and analysis of nonlinear-transformation-based broadband cloaking for acoustic wave propagation

A coordinate-transformation method can be used to design invisibility cloaks for many types of waves, including acoustic waves. The traditional method for designing a cloak depends on a transformation from a virtual space to a physical space. Previous acoustic cloaks that are mainly designed with linear-transformation-based acoustics have drawbacks that acoustic wave trajectories in the cloaks cannot be controlled and tuned. This work uses a nonlinear mapping from a ray trajectory perspective to construct acoustic cloaks with tunable non-singular material properties. Use of a ray trajectory equation is a straightforward and alternate way to study propagation characteristics of different types of waves, which allows more flexibility in controlling the waves. A broadband cylindrical cloak for acoustic waves in an inviscid fluid is realized with layered non-singular, homogeneous, and isotropic materials based on a nonlinear transformation. Some advantages and improvements of the invisibility nonlinear-transformation cloak over a traditional linear-transformation cloak are analyzed. The invisibility capability of the nonlinear-transformation cloak can be tuned by adjusting a design parameter that is shown to have influence on the acoustic wave energy flowing into the region inside the cloak. Numerical examples show that the nonlinear-transformation cloak is more effective for making a domain undetectable by acoustic waves in an inviscid fluid and shielding acoustic waves from outside the cloak than the linear-transformation cloak in a broad frequency range. The methodology developed here can be used to design nonlinear-transformation cloaks for other types of waves.     

水下连续脉冲冲击波的声学特性

为探求金属爆炸索在水下爆炸声源研究领域的应用前景,设计了一种可以连续产生若干个脉冲冲击波的装置,称之为水下连续脉冲冲击波发生装置。利用小波分析对该装置产生的连续脉冲冲击波信号进行分解与重构,考察其频谱特性,并进一步分析了信号的声压级特性。结果表明:该装置产生的信号声压级较高,具有很强的声功率;信号包含频率十分丰富,雷管和金属爆炸索由于装药结构及传爆方式的不同,爆炸所产生的冲击波频谱特性也有所差异。雷管爆炸产生的冲击波主要分布在15.6 kHz以下的频带内,金属爆炸索爆炸产生的脉冲冲击波信号则主要分布在62.5 kHz以下的频带内;脉冲冲击波的个数和声持续时间可由爆炸索的排列方式和长度控制,脉冲冲击波间的时间间隔可调,发生装置稳定易控     

Modelling of dust lifting using the Lagrangian approach

The subject of this paper is dust lifting behind shock waves, a process that is important for the formation of explosive dust clouds in air. While Eulerian–Eulerian has been the standard numerical technique for such simulations, the Eulerian–Lagrangian technique has been used in this paper, making it possible to take into account more physical phenomena, such as particle–particle and particle–wall collisions. The results of the simulations are shown mainly graphically, as snapshots of particle positions at given times after the passing of the shock wave. The results show that the collisions, and the coefficient of restitution assumed for them, is important in determining the mobility and lifting of dust behind shock waves. The results also show that the idea of a horizontally travelling shock wave is an oversimplification: the strong pressure gradient at the surface results in a series of reflected waves generated at the surface and travelling into the gas phase.     

Rarefaction waves in dusty gases

The propagation of normal rarefaction waves in dusty gases has been investigated numerically, using the modified random choice method with operator splitting technique. The effects of the dust parameters on the flow properties inside and behind the rarefaction wave are studied. The results are compared with those appropriate to a dust-free gas.     

Three-wave interactions between disturbances in the hypersonic boundary layer on impermeable and porous surfaces

The interaction between disturbances in the hypersonic boundary layer on impermeable and porous surfaces is considered within the framework of weakly-nonlinear stability theory. It is established that on the impermeable surface nonlinear interactions between different waves (acoustic and vortex) occur in the parametric resonance regime. The role of pumping wave is played by a plane acoustic wave. The nonlinear interactions take place over a wide frequency range and can lead to the packet growth of Tollmien-Schlichting waves. On the porous surface the analogous interactions are fairly weak and result in a slight decay of the acoustic mode and a slight amplification of the vortex mode. This leads to the dragging out of the laminar flow regime and the regions of linear disturbance growth. In this situation the low-frequency spectrum of the vortex modes may be filled on account of the nonlinear processes occurring in the three-wave systems between the vortex components.     

结构中微裂纹与超声波的混频非线性作用数值仿真研究

针对结构中微裂纹检测难题,本文对结构中微裂纹与超声波的混频非线性作用进行了数值仿真研究。基于经典非线性理论,得到了两列超声纵波相互作用产生混频效应的理论条件。通过有限元仿真,研究了两列纵波与微裂纹相互作用产生混频的条件,并分析了界面处静应力、摩擦系数和裂纹方向对混频效应的影响。研究发现,超声波与微裂纹相互作用产生混频非线性效应的发生条件仍符合经典非线性理论下的混频产生条件。裂纹界面处施加的静应力对差频横波幅值有明显影响;当施加静应力与无裂纹模型得到的最大应力值接近时,混频非线性效应最强;裂纹界面的摩擦系数对超声波的混频非线性效应影响较小;透射差频横波传播方向与经典非线性理论预测的理论差频分量方向基本一致,且几乎不受裂纹方向变化的影响,而反射差频横波的传播方向随裂纹方向的改变而有所不同。本文研究工作为微裂纹检出及方向识别做了有益探索。     

A parametric study of the head-on collision of normal shock waves in dusty gases

The effect of the various flow parameters, namely: the diameter of the solid particles, the material density of the solid particles, and the loading ratio of the solid particles on the flow field which is obtained when two normal shock waves collide head-on in a two phase dust-gas suspension has been investigated numerically, using the modified random choice method (RCM). The results were compared with those appropriate to the dust physical parameters used recently by Elperin, Ben-Dor and Igra in their study of the head-on collision of normal shock waves in dusty gases.     

Self-switching of a transverse plane wave propagating through a two-component elastic composite

The paper discusses the results of theoretical and numerical analysis of the interaction of nonlinear elastic plane harmonic waves in a composite material whose nonlinear properties are described by modeling it with a two-phase mixture. The interaction of two transverse vertically polarized harmonic waves is studied using the method of slowly varying amplitudes. The truncated and evolutionary equations as well as the Manley-Rowe relations are derived. The mechanism of energy pumping from a strong pumping wave with frequency ω to a weak signal wave with frequency 3ω is analyzed. The switching mechanism for hypersonic waves in a nonlinear elastic composite is similar to the switching mechanism observed in transistors __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 35–46, July 2007.     

Analytical extension of Finite Element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack

Nonlinear scattering of ultrasonic waves by closed cracks subject to contact acoustic nonlinearity (CAN) is determined using a 2D Finite Element (FE) coupled with an analytical approach. The FE model, which includes unilateral contact with Coulomb friction to account for contact between crack faces, provides the near-field solution for the interaction between in-plane elastic waves and a crack of different orientations. The numerical solution is then analytically extended in the far-field based on a frequency domain near-to-far field transformation technique, yielding directivity patterns for all linear and nonlinear components of the scattered waves. The proposed method is demonstrated by application to two nonlinear acoustic problems in the case of tone-burst excitations: first, the scattering of higher harmonics resulting from the interaction with a closed crack of various orientations, and second, the scattering of the longitudinal wave resulting from the nonlinear interaction between two shear waves and a closed crack. The analysis of the directivity patterns enables us to identify the characteristics of the nonlinear scattering from a closed crack, which provides essential understanding in order to optimize and apply nonlinear acoustic NDT methods.     

Bilinear Bäcklund transformation,Lax pair and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics/fluid mechanics/plasma physics

In this paper, outcomes of the study on the Bäcklund transformation, Lax pair, and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics, fluid mechanics, and plasma physics are presented. Via the Hirota bilinear method, a bilinear Bäcklund transformation is obtained, based on which a Lax pair is constructed. Via the symbolic computation, mixed rogue–solitary and rogue–periodic wave solutions are derived. Interactions between the rogue waves and solitary waves, and interactions between the rogue waves and periodic waves, are studied. It is found that (1) the one rogue wave appears between the two solitary waves and then merges with the two solitary waves; (2) the interaction between the one rogue wave and one periodic wave is periodic; and (3) the periodic lump waves with the amplitudes invariant are depicted. Furthermore, effects of the noise perturbations on the obtained solutions will be investigated.

     

Chemical properties and origin of dust aerosols in Beijing during springtime

Ground observation of dust aerosols was conducted in Beijing in the spring of 2005 in order to investigate the element composition and origin of mineral dust. Mass concentrations of most mineral elements of particles increased during dust events. Mineral elements were predominant in the sums of total element loadings in both dusty and non-dusty days. Mg, Si, Fe, Al or Ti can be used as an indicator of dust outflow; Cl can be viewed as an evidence of dust particles mixing with anthropogenic emissions. Mineral and pollutant elements showed a bimodal mass particle-size distribution (MSD) in non-dusty days, and a trimodal distribution in dusty days, but their peak concentrations fell in different size stages. Zn and S were mainly enriched in fine particles, whereas Cl was enriched in medium particles, but most mineral elements and Cu were enriched in coarse particles. Mineral elements were dominated by crustal material in dusty even non-dusty days, but pollutant elements were from non-crustal material including local and remote sources. Back trajectory analysis indicated that dust particles in Beijing mainly originated from the Gobi and desert regions of Mongolian and northern China.     

Pressure Wave Evolution in a Fluid with a Bubble Zone

The specific features of pressure wave dynamics in a fluid containing a bubble zone are considered. It is found that for nonlinear waves the shielding effect of the bubble zone, typical of acoustic waves, is less pronounced. In some cases, due to the nonlinear effects and the radial inertia of the bubbly fluid [1], the bubble zone may result in a certain increase in the original-signal amplitude. It is shown that when a bubble screen is located near a solid surface, by choosing an appropriate bubble radius and volume fraction, it is possible to achieve (i) the absence of a reflected signal and (ii) substantial damping of the wave action on the wall.     

Theory of nonlinear waves in a plasma

Stationary nonlinear waves propagating in a cold rarefied plasma composed of electrons and two types of ions are considered. The structure of isolated waves and shock waves is found. In recent years an intensive study has been made of finite-amplitude waves and collisionless shock waves in a rarefied plasma, in connection with laboratory experiments [1] and astrophysical applications (the problem of the interaction of the solar wind with the Earth's magnetosphere [2]). When allowance is made for dispersion effects associated with the departure of the dispersion law =(k) from the linear, and for the compensating nonlinear twisting of the wave profile, we are able to obtain the profile of stationary nonlinear waves of finite amplitude, and when allowance is made for damping we can also obtain the structure of a collisionless shock wave [3]. Such waves have been studied fairly fully for the case of a two-component plasma. The present paper examines stationary nonlinear waves propagating across a magnetic field in a cold rarefied quasi-neutral plasma composed of electrons and two types of ions.     

Self-demodulation acoustic signatures for nonlinear propagation in glass beadsSignatures acoustiques de l'auto-démodulation basse fréquence lors de la propagation non linéaire dans des billes de verres

The present Note describes some experimental work related to the nonlinear propagation of acoustic waves in granular media such as unconsolidated glass beads. The studied nonlinear effect is a self-demodulation process performed with the operation of the so-called parametric transmitting antenna. The pump (or carrier) wave is generated by a high power ultrasonic broad-band transducer (100 kHz central frequency) which is LF (low frequency, i.e., a few kHz) amplitude modulated. As the attenuation of acoustic waves increases with frequency, only the LF demodulated wave can be transmitted. A parametric study is performed where the HF central frequency is monitored between 60 and 300 kHz. The LF demodulation profile versus the HF frequency is modified, its shape being temporally derived almost twice. A numerical analysis of the order of temporal derivation is done in the Fourier domain, its value varying from 1.25 to 2.7. Qualitative agreement with current theoretical models is described, and an advanced theoretical analysis by the same authors [Phys. Rev. E 66 (2002) 041303], taking into account absorption, nonlinearity, dispersion and scattering, is briefly discussed. To cite this article: V. Tournat et al., C. R. Mecanique 331 (2003).     

Measurement of the acoustic velocity field of nonlinear standing waves using the synchronized PIV technique

The motion of gas within an air-filled rigid-walled square channel subjected to acoustic standing waves is experimentally investigated. The synchronized particle image velocimetry (PIV) technique has been used to measure the acoustic velocity fields at different phases over the excitation signal period. The acoustic velocity measurements have been conducted for two different acoustic intensities in the quasi-nonlinear range (in which the nonlinear effects can be neglected in comparison with the dissipation effects), and one acoustic intensity in the finite-amplitude nonlinear range (in which both the nonlinear term and the dissipative term play a role in the wave equation). The experimental velocity fields for the quasi-nonlinear cases are compared with the analytical results obtained from the time-harmonic solution of the wave equation. Good agreement between the experimental and analytical velocity fields proves the ability of the synchronized PIV technique to accurately measure both temporal and spatial variations of the acoustic velocity fields. The verified technique is then used to measure the acoustic velocity fields of the finite-amplitude nonlinear case at different phases.