Interactions between pairs of oblique waves in a Bickley jet

We consider the weakly nonlinear spatial evolution of a pair of varicose oblique waves and a pair of sinuous oblique waves superimposed on an inviscid Bickley jet, with each wave being slightly amplified on a linear basis. The two pairs are assumed to both be inclined at the same angle to the plane of the jet. A nonlinear critical layer analysis is employed to derive equations governing the evolution of the instability wave amplitudes, which contain a coupling between the modes. These equations are discussed and solved numerically, and it is shown that, as in related work for other flows, these equations may develop a singularity at a finite distance downstream.     

有限周期微穿孔波纹板吸声体吸声性能研究

为了推动微穿孔吸声体(MPA)在工程中的实际应用,本文采用数值仿真方法,研究了有限尺寸的微穿孔波纹板吸声体的吸声性能.首先,基于微穿孔板阻抗理论,并将平面波谱法和有限元分析方法耦合起来,构造了微穿孔波纹板吸声体(CMPA)的三维仿真模型,给出了在声波垂直入射和斜入射工况下,吸声体声学性能的计算列式;然后,应用有限元软件COMSOL,模拟了有限周期CMPA的吸声性能,分析了波纹深度和波纹间距与吸声性能之间的关系,以及声波入射方向对吸声性能的影响;最后,为改善吸声体对声波方向的敏感性,设计了双向波纹状微穿孔板吸声体.结果表明,在声波垂直入射和斜入射的工况下,相对于传统的平直微穿孔板吸声体,波纹板吸声体具有更好的吸声性能,包括更高的吸声系数和更宽的有效吸声频带;双向波纹板吸声体能显著改善单向波纹板对声波入射方向的敏感性,实现在更大声波入射角范围内的有效吸声,如当入射声波方位角任意且入射角在0°～45°范围内时,双向波纹板吸声体,在500～2500 Hz范围内的吸声系数都大于0.7,表现出了优良的吸声性能.     

Propagation of surface waves in a half-space with vertical,inclined or curved interfaces

The paper reviews the author's theoretical studies on reflection and transmission of surface waves at vertical and near-vertical boundaries. For estimation of reflection and transmission coefficients a new approximate method based on the Green function technique is proposed. The method is valid if a body waves field arised at the boundary is approximately orthogonal to the fields of reflected and transmitted normal modes. It may be used for normal as well as for oblique incidence. A Green function in each quarterspace is assumed to be the same as in a halfspace with the same vertical distribution of elastic parameters. For large angles of incidence when the reflected wave field is strong enough, the Green function may be corrected for the reflected wave. The results of calculation for some models by means of this method are discussed.     

Oblique interactions of weakly nonlinear long waves in dispersive systems

Studies on the oblique interactions of weakly nonlinear long waves in dispersive systems are surveyed. We focus mainly our concentration on the two-dimensional interaction between solitary waves. Two-dimensional Benjamin–Ono (2DBO) equation, modified Kadomtsev–Petviashvili (MKP) equation and extended Kadomtsev–Petviashvili (EKP) equation as well as the Kadomtsev–Petviashvili (KP) equation are treated. It turns out that a large-amplitude wave can be generated due to the oblique interaction of two identical solitary waves in the 2DBO and the MKP equations as well as in the KP-II equation. Recent studies on exact solutions of the KP equation are also surveyed briefly.     

Effect of compression on wave diffraction by a floating elastic plate

In the present paper, the water wave diffraction by a two-dimensional floating elastic plate is analyzed in the presence of compressive force. The solutions in the cases of infinite and finite water depths are derived based on integro-differential equation method in the presence of compressive force under the assumption of small amplitude water wave theory and plate deflection. Further, wave diffraction by the floating elastic plate is analyzed under the assumption of shallow water approximation. The role of compressive force and its limiting values are obtained by using the hydroelastic analysis of the flexural gravity waves. The limiting values of oblique angle of incidence are obtained in different cases and the effect of compressive force on the oblique angle is analyzed. Effect of compressive force and angle of incidence on the hydroelastic behavior of the floating plate are studied by analyzing the reflection coefficients in different cases.     

非线性弹性介质中冲击波斜反射的研究

本文讨论了各向同性非线性超弹性介质在平面小应变下的冲击波斜反射问题。给出了本构关系、简单波解和冲击波解,并作为例子求解了入射冲击波在自由面的斜反射问题。     

成层饱和介质平面波斜入射问题的一维化时域方法

地震波斜入射下自由场的输入是大型结构抗震分析中亟待解决的问题之一,尤其是成层饱和多孔介质自由场问题,由于问题的复杂性,目前研究甚少. 本文基于Biot提出的饱和多孔介质动力方程,建立了一种新的求解平面波斜入射下基岩上覆饱和多孔介质成层场地自由场分析的一维化时域计算方法. 该方法首先根据Snell定律将饱和多孔介质二维空间问题转化为一维时域问题,通过对深度方向的有限元离散,得到饱和多孔介质波动问题的一维化有限元方程,然后采用单相弹性介质精确人工边界条件模拟基岩半空间的波动辐射和输入特征,通过考虑基岩与饱和多孔介质间透水或不透水边界条件以及不同饱和多孔介质交界面边界条件,形成基岩上覆成层饱和介质系统的整体有限元方程,最后采用中心差分法与Newmark平均加速度近似格式相结合的方法对时间进行离散,得到节点的动力时程的显式表达. 典型场地的地震反应分析表明,本文方法的计算结果与传递矩阵法结合傅里叶变换的计算结果完全吻合,证明了其有效性.      

Reflection and Refraction of Anti-Plane Shear Waves from a Moving Phase Boundary

The reflection and refraction of anti-plane shear waves from an interface separating half-spaces with different moduli is well understood in the linear theory of elasticity. Namely, an oblique incident wave gives rise to a reflected wave that departs at the same angle and to a refracted wave that, after transmission through the interface, departs at a possibly different angle. Here we study similar issues for a material that admits mobile elastic phase boundaries in anti-plane shear. We consider an energy minimal equilibrium state in anti-plane shear involving a planar phase boundary that is perturbed due to an incident wave of small magnitude. The phase boundary is allowed to move under this perturbation. As in the linear theory, the perturbation gives rise to a reflected and a refracted wave. The orientation of these waves is independent of the phase boundary motion and determined as in the linear theory. However, the phase boundary motion affects the amplitudes of the departing waves. Perturbation analysis gives these amplitudes for general small phase boundary motion, and also permits the specification of the phase boundary motion on the basis of additional criteria such as a kinetic relation. A standard kinetic relation is studied to quantify the subsequent energy partitioning and dissipation on the basis of the properties of the incident wave.     

驻定斜爆轰波并行数值模拟

采用多组分化学反应Euler方程组对驻定在高速飞行弹丸上的斜爆轰波流场进行了数值模拟。计算中分别采用TVD格式和基元反应模型,并基于并行编程模型MPI（message passing interface）实现了非结构网格上的并行计算,对流项和化学反应项用时间分裂法进行处理。计算结果表明并行计算能有效地提高计算速度,扩展计算规模,为进一步研究超驱爆轰推进技术奠定基础。     

Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

Nonlinear interactions of the two-dimensional(2D) second mode with oblique modes are studied numerically in a Mach 6.0 flat-plate boundary layer, focusing on its selective enhancement effect on amplification of different oblique waves. Evolution of oblique modes with various frequencies and spanwise wavenumbers in the presence of 2D second mode is simulated successively, using a modified parabolized stability equation(PSE) method, which is able to simulate interaction of two modes with different frequencies efficiently. Numerical results show that oblique modes in a broad band of frequencies and spanwise wavenumbers can be enhanced by the finite amplitude 2D second mode instability wave. The enhancement effect is accomplished by interaction of the 2D second mode, the oblique mode, and a forced mode with difference frequency. Two types of oblique modes are found to be more amplified, i.e., oblique modes with frequency close to that of the 2D second mode and low-frequency first mode oblique waves. Each of them may correspond to one type of transition routes found in transition experiments. The spanwise wavenumber of the oblique wave preferred by the nonlinear interaction is also determined by numerical simulations.     

On Small-Displacement Waves in Prestressed Bodies with Isotropic Incremental Elasticity Tensor

We consider a body at rest in a prestressed configurationwhich responds elastically to small incremental displacements fromthe incremental elasticity tensor is supposed isotropic. On the basis of the paper [1] we characterize the conditions for the propagation of longitudinal, transverse, and oblique small-displacement waves superimposed toFormulae for the propagation speeds of these waves are written in terms of the prestress components and Lamparameters. The amplitudes of longitudinal and transverse waves are eigenvectors for the prestress.     

Diffraction of surface waves on an inhomogeneous elastic plate

The oblique incidence of small-amplitude waves on an elastic semi-infinite composite plate floating on the free surface of finite-depth water is studied. The front part of a constant-width plate is highed to the basic part and has characteristics different from those of the basic part. The reflection and transmission coefficients of the waves and the vertical displacements of the plate are determined. It is shown that the heterogeneity of the plate material exerts a strong effect on surface-wave diffraction. Methods for decreasing the elastic deformations of the basic part of the plate are proposed. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 42–48, July–August, 2000.     

An experimental study of oblique transition in a Blasius boundary layer flow

Transition initiated by a pair of oblique waves was investigated experimentally in a Blasius boundary layer flow by using hot-wire measurements and flow visualisation. The oblique waves were generated by periodic blowing and suction through an array of pipes connecting to the flow through a transverse slit in the flat plate model. The structure of the flow field is described and the amplitude of individual frequency-spanwise wave number modes was determined from Fourier transforms of the disturbance velocity. In contrast to results from investigations of oblique transition at subcritical flow conditions, the transition process at the present conditions suggests the combined effect of non-modal growth of streaks and a second stage with exponential growth of oblique waves to initiate the final breakdown stage.     

Experimental evidence of transversal oscillations in a sea-connected rectangular basin

The response of a rectangular basin along a straight, perfectly reflecting coastline, subject to monochromatic waves coming either normally or obliquely from the sea, was investigated theoretically and experimentally.While the theoretical analysis allowed recognition of various kinds of longitudinal and transversal oscillations and their properties as a function of the geometrical dimensions of the basin, wave length and wave incidence, the experimental investigation confirmed, both for normal and oblique incidence, the validity of the theoretical results and particularly the importance of the transversal oscillations.     

Bilinear form and soliton interactions for the modified Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics

In this paper, we investigate the modified Kadomtsev–Petviashvili (mKP) equation for the nonlinear waves in fluid dynamics and plasma physics. By virtue of the rational transformation and auxiliary function, new bilinear form for the mKP equation is constructed, which is different from those in previous literatures. Based on the bilinear form, one- and two-soliton solutions are obtained with the Hirota method and symbolic computation. Propagation and interactions of shock and solitary waves are investigated analytically and graphically. Parametric conditions for the existence of the shock, elevation solitary, and depression solitary waves are given. From the two-soliton solutions, we find that the (i) parallel elastic interactions can exist between the (a) shock and solitary waves, and (b) two elevation/depression solitary waves; (ii) oblique elastic interactions can exist between the (a) shock and solitary waves, and (b) two solitary waves; (iii) oblique inelastic interactions can exist between the (a) two shock waves, (b) two elevation/depression solitary waves, and (c) shock and solitary waves.     

斜爆轰发动机的推力性能理论分析

爆轰燃烧具有释热快、循环热效率高的特点. 斜爆轰发动机利用斜爆轰波进行燃烧组织, 在高超声速吸气式推进系统中具有重要地位. 以往研究主要关注斜爆轰波的起爆、驻定以及波系结构等, 缺少从整体层面出发对斜爆轰发动机开展推力性能分析. 本文将斜爆轰发动机内的流动和燃烧过程分解成进气压缩、燃料掺混、燃烧释热和排气膨胀4个基本模块并分别进行理论求解, 建立了斜爆轰发动机推力性能的理论分析模型. 在斜爆轰波系研究成果的基础上, 选取了过驱动斜爆轰、Chapman?Jouguet斜爆轰、过驱动正爆轰和斜激波诱导等容燃烧等4种燃烧模式来描述燃烧室内的燃烧释热过程, 并对比分析了不同燃烧模式对发动机比冲性能的影响. 此外, 还获得了不同来流参数、燃烧室参数和进排气参数等对发动机推力的影响规律, 发现来流马赫数和尾喷管的膨胀面积比是发动机理论燃料比冲的主要影响因素. 最后, 结合以往关于受限空间内斜爆轰波驻定特性等方面的研究成果, 提出了斜爆轰发动机燃烧室的设计方向.      

The generalized Boussinesq equations and obliquely interacting solitary waves in a stratified fluid

In this paper, on the basis of Boussinesq’s shallow water theory, we establish the basic equations governing the motion of a stratified fluid, a kind of the generalized Boussinesq equations. And then by way of them, we study the weak interaction of two pairs of obliquely colliding solitary waves, give the second-order approximate solutions for wave profiles and maximum amplitudes, as well as conclude that when the included angle between the directions of propagation of impinging solitary waves is less than 120°, the effect of oblique interaction is stronger than that of the head-on one, but when the angle concerned is greater than 120°, the former is slightly weaker than the latter.     

Reflection and refraction of plane waves on the interface of two anisotropic media

We use generalized functionally invariant solutions [1] of the equations of motion to obtain and analytically study solutions of the plane problem of reflection and refraction of plane waves on the interface of two anisotropic media with four elastic constants depending on the angles of incidence of primary waves for various relations between the elastic constants of the contacting media. For the primary waves, we find the ranges of incidence angles for which real and complex secondary waves are excited. We study all possible combinations of the distribution of phase velocities and reflection and refraction angles in detail and obtain conditions characterizing the directions of the energy flux vectors for the primary and secondary waves depending on the incidence angles of the primary waves for different relations between the elastic constants of the contacting media, which satisfy the necessary and sufficient conditions for the elastic energy form to be positive definite.     

Over forty years of continuous research at UTIAS on nonstationary flows and shock waves

Analytical and experimental research on non-stationary shock waves, rarefaction waves and contact surfaces has been conducted continuously at UTIAS since its inception in 1948. Some unique facilities were used to study the properties of planar, cylindrical and spherical shock waves and their interactions. Investigations were also performed on shock-wave structure and boundary layers in ionizing argon, water-vapour condensation in rarefaction waves, magnetogasdynamic flows, and the regions of regular and various types of Mach reflections of oblique shock waves. Explosively-driven implosions have been employed as drivers for projectile launchers and shock tubes, and as a means of producing industrial-type diamonds from graphite, and fusion plasmas in deuterium. The effects of sonic-boom on humans, animals and structures have also formed an important part of the investigations. More recently, interest has focussed on shock waves in dusty gases, the viscous and vibrational structure of weak spherical blast waves in air, and oblique shock-wave reflections. In all of these studies instrumentation and computational methods have played a very important role. A brief survey of this work is given herein and in more detail in the relevant references.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

一维与二维爆轰传播的时空关联特性数值研究

一维爆轰传播的理论完备、计算准确, 二维斜爆轰传播由于壁面与黏性效应, 大尺度、高精度预测还有一定难度. 利用Euler方程和H₂-Air基元反应模型, 对二维有限长楔面诱导的斜爆轰和活塞驱动一维非定常正爆轰进行计算比较研究, 从时空两个维度方面, 分析了两者在起爆过程、稀疏波传播、爆轰波面演化中的关联特性. 研究结果表明: 在过驱动度相同的条件下, 经过时空变换的活塞驱动一维爆轰传播与二维驻定斜爆轰在起爆区波系结构、波面演化特征和主要参数分布规律方面无论定性或者定量对比均符合较好, 所以, 一维非定常爆轰和二维驻定斜爆轰具有时空相关性. 两者的差异主要体现在过驱动斜爆轰受稀疏波影响过渡到近Chapman-Jouguet (C-J)爆轰状态所需的弛豫时间不同, 原因可能是起源于活塞和壁面稀疏波强度的差异. 本文提出的一维与二维爆轰传播的时空关联方法不仅有助于认知斜爆轰起爆、过驱爆轰产生、胞格爆轰演化的三阶段规律, 还可以对比揭示壁面、边界层和黏性效应的影响, 应用在斜爆轰发动机燃烧室设计中能够有效节约计算时间和成本, 并降低复杂度.