Three-wave interactions of disturbances in a hypersonic boundary layer on a porous surface

Interactions of disturbances in a hypersonic boundary layer on a porous surface are considered within the framework of the weakly nonlinear stability theory. Acoustic and vortex waves in resonant three-wave systems are found to interact in the weak redistribution mode, which leads to weak decay of the acoustic component and weak amplification of the vortex component. Three-dimensional vortex waves are demonstrated to interact more intensively than two-dimensional waves. The feature responsible for attenuation of nonlinearity is the presence of a porous coating on the surface, which absorbs acoustic disturbances and amplifies vortex disturbances at high Mach numbers. Vanishing of the pumping wave, which corresponds to a plane acoustic wave on a solid surface, is found to assist in increasing the length of the regions of linear growth of disturbances and the laminar flow regime. In this case, the low-frequency spectrum of vortex modes can be filled owing to nonlinear processes that occur in vortex triplets.     

Linear evolution and interaction of disturbances in the boundary layers on impermeable and porous surfaces in the presence of heat transfer

The interaction of disturbances in the compressible boundary layers on both impermeable and porous surfaces is considered in the linear and nonlinear approximations (weakly-nonlinear stability theory) in the presence of surface cooling. The regimes of moderate (Mach number M = 2) and high (M = 5.35) supersonic velocities are considered. It is established that surface cooling leads a considerable change in the linear evolution of the disturbances, namely, the first-mode vortex disturbances are stabilized, whereas the second-mode acoustic disturbances are destabilized, the variation degree being determined by the temperature factor. A porous coating used for controlling flow regimes influences the stability in the opposite fashion. For vortex waves the nonlinear interactions in three-wave systems at M = 2 are considerably attenuated in the presence of cooling. It might be expected that the cooling of the surface can delay the laminar regime for M = 2 and accelerate transition to turbulence for M = 5.35.     

Hysteretic linear and nonlinear acoustic responses from pressed interfaces

An analysis of the linear and nonlinear acoustic responses from an interface between rough surfaces in elastoplastic contact is presented as a model of the ultrasonic wave interactions with imperfect interfaces and closed cracks. A micromechanical elastoplastic contact model predicts the linear and second order interfacial stiffness from the topographic and mechanical properties of the contacting surfaces during a loading–unloading cycle. The effects of those surface properties on the linear and nonlinear reflection/transmission of elastic longitudinal waves are shown. The second order harmonic amplitudes of reflected/transmitted waves decrease by more than an order of magnitude during the transition from the elastic contact mode to the elastoplastic contact mode. It is observed that under specific loading histories the interface between smooth surfaces generates higher elastoplastic hysteresis in the interfacial stiffness and the acoustic nonlinearity than interfaces between rough surfaces. The results show that when plastic flow in the contacting asperities is significant, the acoustic nonlinearity is insensitive to the asperity peak distribution. A comparison with existing experimental data for the acoustic nonlinearity in the transmitted waves is also given with a discussion on its contact mechanical implication.     

Controlling supersonic boundary layer stability by means of distributed mass transfer through a porous wall

The interaction between disturbances in a compressible boundary layer in the presence of distributed mass transfer (injection or suction) through a permeable porous wall is considered in the linear and nonlinear approximations (weakly nonlinear stability theory). The regimes of moderate and high supersonic velocities (Mach numbers M = 2 and 5.35) are studied. The boundary conditions for the disturbances on a permeable wall are derived with account for the gas compressibility in pores and the presence of a suction chamber. Maximum pore dimensions, at which the surface properties have no effect on the disturbance characteristics, which are stabilized upon suction and destabilized upon injection, are determined. When the surface properties are taken into account, intense growth of the first-mode vortex disturbances occurs, which can completely undo the stabilizing effect of the suction. Injection leads to the vortex and acoustic mode destabilization on the linear range and the enhancement of the nonlinear processes on the transitional range.     

PIV- and LDV-measurements of baroclinic wave interactions in a thermally driven rotating annulus

Already in the 1950s, an elegant laboratory experiment had been designed to understand how the atmospheric circulation transports heat from equatorial to polar latitudes. It consists of a cooled inner and heated outer cylinder mounted on a rotating platform, mimicking the heated tropical and cooled polar regions of the earth’s atmosphere. Depending on the strength of the heating and the rate of rotation, different flow regimes had been identified: wave-regimes that can be classified by pro-grade propagating waves of different wavenumbers and quasi-chaotic regimes where waves and small-scale vortices coexist. In the present paper, we will use multivariate statistical techniques to understand better the variability of the heated rotating flow (i) in the transition region between regular waves with zonal wave number 3 and 4 and (ii) in the transition region to the quasi-chaotic regime. The former regime is studied by applying the complex empirical orthogonal function (CEOF) method to particle image velocimetry data, the latter by applying the multichannel singular spectrum analysis (M-SSA) to laser Doppler velocimetry (LDV) data. In the annulus, interactions between the dominant mode and the so-called weaker modes, explaining less variance than the dominant mode, can lead to low-frequency amplitude and wave structure vacillations. The CEOF analysis reveals the coexistence of a dominant and a weak mode in the 3-4 wave transition region. This finding confirms earlier ideas on wave dispersion in transition regions between regular waves. Increasing the annulus’ rotation leads to a growth of the weak mode until this mode becomes the dominant one. No coexistence of modes could be found for the regular 4-wave regime but a slight structural vacillation was present. The M-SSA was applied to LDV data corresponding with much faster annulus rotation for which the flow becomes more irregular. The analysis reveals a coexistence of a dominant 4 mode and a much weaker 5 mode for this regime. Our results complement previous observations recovered primarily by thermocouple arrangements.     

波涡相互作用研究的某些进展(Ⅱ)

<正> 5 波涡共振 从第3节的感受性问题再前进一步,自然要问在什么条件下入射波激发起涡中之波的最大响应.这就导致了入射波与层状或轴状涡中受激波之间共振的概念,简称波涡共振.一般说来,在流体内部若有两个或多个波相会,它们将互相穿透而沿原来的方向离去.但若它们的波矢量和频率满足一定的关系(参见Craik 1985),就会在相会点产生新的波.2阶扰动的振幅可达到1阶扰动振幅的量级,而且流场中会出现一些重要的独特性质.这就是流体内部波共振,波涡共振是其一类情形.      

Bispectral analysis of nonlinear processes in the hypersonic boundary layer on a porous cone surface

The results of the experimental investigation of the nonlinear stage of laminar-turbulent transition in the hypersonic boundary layer on porous and impermeable cone surfaces are presented. The bispectral analysis is applied to show that the porous surface suppresses the subharmonic resonance due to second mode disturbances. It is established that on the porous surface nonlinear processes develop more slowly than on the impermeable surface. This behavior indicates that the subharmonic resonance plays the role of a catalyzer in transferring energy from the mean flow to low-frequency disturbances in transition process, in much the same way as it occurs in a subsonic boundary layer.     

Nonlinear Strong Shock Interactions: A Shock-Fitted Approach

This paper addresses nonlinear effects which result from the interaction of shock waves with vortices. A series of experiments are carried out, which involve the interaction of a strong shock wave with a single plane vorticity wave and a randomly distributed wave system. These experiments are first conducted in the linear regime to obtain a mutual verification of theory and computation. They are subsequently extended into the nonlinear regime. A systematic study of the interaction of a plane shock wave and a single vortex is then conducted. Specifically, we investigate the conditions under which nonlinear effects become important, both as a function of shock Mach number, M ₁, and incident vortex strength (characterized by its circulation Γ). The shock Mach number is varied from 2 to 8, while the circulation of the vortex is varied from infinitesimally small values (linear theory) to unity. Budgets of vorticity, dilatation, and pressure are obtained. They indicate that nonlinear effects become more significant as both the shock Mach number and the circulation increase. For Mach numbers equal to 5 and above, the dilatation in the vortex core grows quadratically with circulation. An acoustic wave propagates radially outward from the vortex center. As circulation increases, its upstream-facing front steepens at low Mach numbers, and its downstream-facing front steepens at high Mach numbers. A high Mach number asymptotic expansion of the Rankine--Hugoniot conditions reveals that nonlinear effects dominate both the shock motion and the downstream flow for ΓM ₁ > 1. Received 28 June 1997 and accepted 25 November 1997     

Hydroelastic analysis of gravity wave interaction with submerged horizontal flexible porous plate

The present study deals with the surface gravity wave interaction with submerged horizontal flexible porous plate under the assumption of small amplitude water wave theory and structural response. The flexible porous plate is modeled using the thin plate theory and wave past porous structure is based on the generalized porous wavemaker theory. The wave characteristics due to the interaction of gravity waves with submerged flexible porous structure are studied by analyzing the complex dispersion relation using contour plots. Three different problems such as (i) wave scattering by a submerged flexible porous plate, (ii) wave trapping by submerged flexible porous plate placed at a finite distance from a rigid wall and (iii) wave reflection by a rigid wall in the presence of a submerged flexible porous plate are analyzed. The role of flexible porous plate in attenuating wave height and creating a tranquility zone is studied by analyzing the reflection, transmission and dissipation coefficients for various wave and structural parameters such as angle of incidence, depth of submergence, plate length, compression force and structural flexibility. In the case of wave trapping, the optimum distance between the porous plate and rigid wall for wave reflection is analyzed in different cases. In addition, effects of various physical parameters on free surface elevation, plate deflection, wave load on the plate and rigid wall are studied. The present approach can be extended to deal with acoustic wave interaction with flexible porous plates.     

The role of dust charging frequency in the linear and nonlinear propagation of dust acoustic waves

The effect of dust charge fluctuation on the existence and propagation of dust acoustic waves in unmagnetized dusty plasma is studied. Dispersion relation for the dust acoustic waves with temporal dust charge fluctuations is calculated based on the reductive perturbation technique. By considering two different limiting cases of the dust charging frequency, it is shown that the dusty plasma system gives rise to linear or nonlinear dust acoustic waves. The well-known collisionless damping of two existing normal modes and one purely damped mode are recovered when the dust charging frequency is comparable to the dust acoustic wave frequency. On the other hand, when the dust charging frequency is considerably higher than the wave frequency, it is then possible to derive a nonlinear Schrödinger type equation with envelope soliton as solution.     

The shock–vortex interaction patterns affected by vortex flow regime and vortex models

We have used a third-order essentially non-oscillatory method to obtain numerical shadowgraphs for investigation of shock–vortex interaction patterns. To search different interaction patterns, we have tested two vortex models (the composite vortex model and the Taylor vortex model) and as many as 47 parametric data sets. By shock–vortex interaction, the impinging shock is deformed to a S-shape with leading and lagging parts of the shock. The vortex flow is locally accelerated by the leading shock and locally decelerated by the lagging shock, having a severely elongated vortex core with two vertices. When the leading shock escapes the vortex, implosion effect creates a high pressure in the vertex area where the flow had been most expanded. This compressed region spreads in time with two frontal waves, an induced expansion wave and an induced compression wave. They are subsonic waves when the shock–vortex interaction is weak but become supersonic waves for strong interactions. Under a intermediate interaction, however, an induced shock wave is first developed where flow speed is supersonic but is dissipated where the incoming flow is subsonic. We have identified three different interaction patterns that depend on the vortex flow regime characterized by the shock–vortex interaction.      

孤立波与多孔介质结构物的非线性相互作用

基于精确至Ｏ（εμ＾２,μ＾４）的多孔介质无压渗流模型方程和均匀流体质波动的Ｂｏｕｓｓｉｎｅｓｑ方程,本文对孤立波与多孔介质结构物的相互作用了较系统的数值实验。控制方程采用基于有限差分方程离散,在时域上采用了预估－校正方法进行了时间积分。在求解演化方程的过程中,引入“内迭代”过程实现流体域和多孔介质交界面的连接条件。结果表明孤立波在多孔介质上的反射与在不可渗透的界面上的反射类似,形成反向的孤立波但     

Impingement of a supersonic underexpanded jet onto obstacles with different permeabilities

Results of an experimental study of the flow structure and characteristics of flow oscillations induced by impinging of a supersonic underexpanded jet onto obstacles made of permeable and impermeable materials are presented. Spectral characteristics of the acoustic field in the regime of unsteady interaction between the jet and the obstacle are determined. The influence of permeability of porous obstacles on these characteristics is identified.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

Dynamic photoelasticity as an aid in developing new ultrasonic-test methods

A prerequisite for the development of quantitative ultrasonic-inspection techniques for surface flaws is a thorough understanding of the ways in which elastic waves interact with defects. Analytical and numerical approaches are presently inadequate. Experimental methods are needed for a better understanding of wave interactions with real geometries. This paper describes how dynamic photoelasticity was used to study the interaction between Rayleigh waves and slots. To fully interpret the interactions between an incident Rayleigh wave and a surface slot, the problem was subdivided as follows: first, the reflections and mode conversions of a Rayleigh wave at a corner were studied. This simulated the Rayleigh-wave interaction with a slot opening. Then, the interaction when a Rayleigh wave ran off the tip of a slot was observed, and, finally, the total interaction with slots perpendicular to the surface was studied. The results for these three cases are presented. It is suggested that the most important property of a Rayleigh wave that can be used to size surface and near-surface defects is the subsurface particle motions. These motions persist up to a depth of the order of a wavelength. The shape (that is, the frequency spectrum of the transmitted wave) should, therefore, be affected by the depth of the slot. Spectroscopic analysis is applied to the photoelastic data to develop a simple method for sizing slots. Results from ultrasonic tests on slots in steel confirm the validity of the suggested method. By applying contemporary concepts of signal processing to photoelastic data, a powerful new area of experimental investigation is introduced. It promises to overcome the current inability of scatter theories to predict the interactions between real-life defects and acoustic waves as used in ultrasonic testing. Applications of this approach will improve the quantitative ability of ultrasonic-inspection methods.     

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave, also known as surface acoustic wave(SAW), solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.     

Nonreflecting boundary conditions based on nonlinear multidimensional characteristics

Nonlinear characteristic boundary conditions based on nonlinear multidimensional characteristics are proposed for 2‐ and 3‐D compressible Navier–Stokes equations with/without scalar transport equations. This approach is consistent with the flow physics and transport properties. Based on the theory of characteristics, which is a rigorous mathematical technique, multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. Nonreflecting boundary conditions are derived by setting corresponding characteristic variables of incoming waves to zero and by partially damping the source terms of the incoming acoustic waves. In order to obtain the resulting optimal damping coefficient, analysis is performed for problems of pure acoustic plane wave propagation and arbitrary flows. The proposed boundary conditions are tested on two benchmark problems: cylindrical acoustic wave propagation and the wake flow behind a cylinder with strong periodic vortex convected out of the computational domain. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The numerical simulations yield accurate results, confirm the optimal damping coefficient obtained from analysis, and verify that the method substantially improves the 1‐D characteristics‐based nonreflecting boundary conditions for complex multidimensional flows. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear Lamb waves in plate/shell structures

鉴于常规超声检测技术对分布式材料细微损伤和接触类结构损伤的检测效果不佳,近年来非线性超声技术逐渐引起广泛关注.超声波在板壳结构中通常以兰姆波的形式进行传播,然而由于兰姆波的频散及多模特性,使得非线性兰姆波的理论和实验研究进展缓慢.本文从经典非线性理论出发,总结了源于材料固有非线性诱发的非线性兰姆波的理论和实验两个方面的研究进展,并综述了兰姆波的二次谐波发生效应在材料损伤评价方面的若干应用;从接触声非线性理论出发,讨论了目前由于接触类结构损伤诱发的非线性兰姆波的研究现状.最后展望了非线性兰姆波的未来研究重点及发展趋势.     

On diffraction of acoustic and electric waves in piezoelectric medium by an absorbent half-plane electrode

Diffraction of incident acoustic and incident electric waves in a transversally isotropic piezoelectric medium at the boundary of a half-plane absorbent electrode is systematically investigated using the quasi-hyperbolic approximation. The electrode is assumed to be very thin so that its thickness and stiffness can be neglected. By exact inversion, the explicit expressions for the scattering waves are obtained. A closed form solution is obtained by applying Laplace transformations and the Wiener–Hopf technique. By means of the Cagniard–de Hoop method a detailed investigation of the structure of the electro-acoustic wave is conducted. The mode conversion between electric and acoustic waves, the effect of electro-acoustic head wave, the Bleustein–Gulyaev surface wave and the structure of the wave in terms of the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in detail. It is shown that in piezoelectric materials, absorbent electrodes are neither completely opaque nor completely transparent to electric and acoustic waves. The dynamic field intensity factors at the tip of the electrode are functions of the angle of incidence and time; they are derived explicitly and discussed through a detailed numerical analysis.