Evolution of ion–ion acoustic instability in multi-ion plasma sheaths

Nonlinear Dynamics - The generation of ion-acoustic solitary waves is investigated in a nonuniform multicomponent collisional plasma sheath containing cold ions and Boltzmann electrons to probe the...     

Special features of the shock‐wave structure in mixtures of gases with disparate molecular masses

Asymptotic solutions are constructed for the problem of the shockwave structure in mixtures of gases with disparate molecular masses. The effect of emergence of a plateau on the density profile of the light component and nonmonotonicity of the temperature profile of the heavy component is described. Based on a comparison with calculations of the full model, the range of applicability of asymptotic solutions is determined.     

Three-dimensional magnetohydrodynamic description of the process of collision of a solar wind shock wave and the Earth’s bow shock

The propagation of a solar wind shock wave along the surface of the Earth’s bow shock is investigated within the framework of an ideal magnetohydrodynamic model in the three-dimensional non-plane-polarized formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength are considered for the plane front of a solar wind shock wave moving at various velocities along the Sun-Earth radius. The global three-dimensional pattern of the interaction is constructed as a function of the angle of inclination of the surface of the bow shock to the solar wind velocity and the azimuthal angle along the curve of intersection of the fronts of the interacting shock waves. The evolution of the flow developed in the neighborhood of the bow shock is investigated and the parameters of the medium and magnetic field are calculated.     

Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave

The effect of incident shock wave strength on the decay of interface introduced perturbations in the refracted shock wave was studied by performing 20 different simulations with varying incident shock wave Mach numbers (M ~ 1.1? 3.5). The analysis showed that the amplitude decay can be represented as a power law model shown in Eq.7, where A is the average amplitude of perturbations (cm), B is the base constant (cm^?(E?1), S is the distance travelled by the refracted shockwave (cm), and E is the power constant. The proposed model fits the data well for low incident Mach numbers, while at higher mach numbers the presence of large and irregular late time oscillations of the perturbation amplitude makes it hard for the power law to fit as effectively. When the coefficients from the power law decay model are plotted versus Mach number, a distinct transition region can be seen. This region is likely to result from the transition of the post-shock heavy gas velocity from subsonic to supersonic range in the lab frame. This region separates the data into a high and low Mach number region. Correlations for the power law coefficients to the incident shock Mach number are reported for the high and low Mach number regions. It is shown that perturbations in the refracted shock wave persist even at late times for high incident Mach numbers.     

The phenomena of shock wave reflection — a review of unsolved problems and future research needs

Although the phenomenon of shock wave reflection was discovered more than a hundred years ago, active research related to this phenomenon still goes on in many countries in the world (e.g., Australia, Canada, China, Germany, Israel, Japan, Poland, Russia and United States of America). As a matter of fact the research activity increased so drastically in the past decade and a half that a special scientific meeting dedicated to better understanding the reflection phenomena of shock waves, namely The International Mach Reflection Symposium was initiated in 1981 and was held since then in the major research centers actively involved in the research of shock wave reflections. In the present paper the status of the research of the phenomenon of shock wave reflection will be discussed in general, and unresolved problems and future research needs will be pointed out.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Using a hot‐wire anemometer for measurement of characteristics of a random acoustic field in compressible flows

The problem of interpretation of hotwire measurements of acoustic fields in compressible flows is considered. Relations between massflow and totaltemperature fluctuations registered by a hotwire anemometer and pressure and velocity fluctuations are found. The relations obtained are applicable in the general case for measurement of resultant acoustic fluctuations at some point of the flow, which are generated by arbitrary distributed sources of sound with priorunknown properties.     

Plane acoustic wave propagation through a composite of elastic and Kelvin–Voigt viscoelastic material layers

The problem of plane wave propagation through a plane composite layer of thickness h is considered. The composite consists of periodically repeated elastic and Kelvin–Voigt viscoelastic material layers, and all layers are either parallel or perpendicular to the incident wave front. Moreover, it is assumed that the thickness of each separate layer of the composite is much less than the acoustic wave length and the thickness h of the entire composite. We study the problem by using a homogenized model of the composite, which allows us to find the reflection and transmission factors and the variation in the sound intensity level as it propagates though the composite layer of thickness h.     

Effect of shock–wave loading on the properties of cryogenic TiNi — a shape–memory alloy

Results of an experimental study of the shock–wave deformation of TiNi and its effect on the crystallographic structure and temperature of austenite–martensite transformations are given. It is found that, for pressures of up to 2 GPa, shock–wave loading changes the defect structure and parameters of the lattice; however, this does not lead to a noticeable change in the temperature of the austenite–martensite transformation and the manifestation of the shapeNdash;memory effect.     

Generation of the tollmien–schlichting wave in a supersonic boundary layer by two sinusoidal acoustic waves

The problem is solved using parabolized equations of stability for threedimensional perturbations of a compressible boundary layer on a flat plate. Nonlinearity is taken into account by quadratic terms that are most significant in estimates of the viscous critical layer of the stability theory. These terms are determined by the total field of two acoustic perturbations, and the equations become linear and inhomogeneous. The calculations are performed for one acoustic wave being stationary in the reference system fitted to the plate for Mach numbers M=2 and 5. Solutions are presented, which are identified very accurately with Tollmien–Schlichting waves at a rather large distance from the plate edge.     

Oblique collision of a plane-polarized Alfvén discontinuity and a slow shock wave propagating in opposite directions in magnetohydrodynamics

Collision of plane fronts of a plane-polarized Alfvén discontinuity and a slow shock wave propagating in opposite directions at a certain angle is considered within the framework of an ideal magnetohydrodynamic model. The initial state of an infinitely conducting medium at rest with a frozen-in magnetic field is assumed to be given. Calculations are carried out for various values of the shock wave Mach number and the magnetic field strength using a special software which makes it possible to find an exact solution of the Riemann problem of breakdown of a discontinuity between the states downstream of the interacting waves by means of a computer. The wave flow structure is investigated and a bifurcation map of flow restructuring is constructed. Domains of the initial parameters for which the interaction differs qualitatively are distinguished. The parameters of the medium and magnetic field are found as functions of the angle between the colliding discontinuities and the inclination of the magnetic field. The results obtained may be used in investigations of magnetic reconnection.     

High accuracy wave simulation – Revised derivation,numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic wave equation

The nearly analytic integration discrete (NAID) method for solving the two-dimensional acoustic wave equation has been fully mathematically revised, analyzed and tested. The NAID method is an alternative numerical modeling method for generating synthetic seismograms. The acoustic wave equation is first transformed into a system of first-order ordinary differential equations (ODEs) with respect to time variable t, and then directly integrated at a small time interval of [t_n, t_n+1] to obtain semi-discrete ordinary differential equations. The integral kernel is expanded into a truncated Taylor series, to which the integration operator is explicitly applied. The high-order temporal derivatives involved in the integral kernel are replaced by high-order spatial derivatives, which then are approximately calculated as a weighted linear combination of the displacement, the particle-velocity, and their spatial gradients. In this article, we investigate the theoretical properties of the revised NAID method, including the discrete error and the stability criteria. Numerical results for constant and layered velocity models show that, comparing to the Lax–Wendroff correction (LWC) scheme and the staggered-grid finite difference method, the NAID method can effectively suppress the numerical dispersion and source-noises caused by the discretization of the acoustic wave equation with too-coarse spatial grids or when models have strong velocity contrasts between adjacent layers. The proposed NAID method has been applied in computing the acoustic wavefields for two heterogeneous models – the corner edge model and the Marmousi model. Promising numerical results illustrate that the NAID method provides an encouraging tool for large-scale and complex wave simulation and inversion problems based on the acoustic equation.     

Asymptotic analysis of the structure of long‐wave Görtler vortices in a hypersonic boundary layer

An asymptotic (at high Reynolds and Görtler numbers) model of nonlinear longwave Görtler vortices localized inside the boundary layer near a concave surface located in a hypersonic viscous gas flow in the regime of weak viscidinviscid interaction is constructed. The maximum wavelength is evaluated. Numerical solutions are obtained for an inviscid local limit in the linear approximation. It is shown that an increase in the freestream Mach number exerts a stabilizing effect on the vortices, and a change in the Prandtl number has no significant effect on them. For the case where the vortices form a threelayered disturbed flow structure, it is shown analytically for the first time that surface heating exerts a stabilizing action on the vortices.     

Collision of an interplanetary shock wave with the Earth’s bow shock. Hydrodynamic parameters and magnetic field

Hydrodynamic parameters and magnetic field generated in each of the waves in neighborhood of the Earth’s bow shock when an interplanetary shock wave impinges on it and propagates along its surface are found in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model. The interaction pattern is constructed in the quasi-steady-state formulation as a mosaic of exact solutions, obtained by means of a computer, to the Riemann problem of breakdown of a discontinuity between the states downstream of the impinging wave and the bow shock on the traveling line of intersection of their fronts. The calculations are carried out for typical parameters of the quiescent solar wind and the interplanetary magnetic field in the Earth’s orbit when the plane front of a shock wave moves along the Sun-Earth radius with various given velocities. The solutions obtained can be used to interpret measurements carried out by spacecraft in the solar wind and in neighborhood of the Earth’s magnetosphere.     

Oscillations of the plastic wave front under high‐rate loading

Two models of elastoplastic wave propagation in metals under uniaxial deformation are considered. The first model treats plastic deformation as being due to dislocation motion during heterogeneous formation of dislocations. The second model assumes that plastic deformation occurs by motion of dipoles of partial disclinations. It is shown that in both cases, certain conditions can give rise to damped oscillations of the plastic wave front, which were detected in shock loading experiments with flat specimens made of 28Kh3SNMFA steel.     

Interaction between a submerged evacuated cylindrical shell and a shock wave—Part I: Diffraction–radiation analysis

The interaction between a submerged elastic circular cylindrical shell and an external shock wave is addressed. A linear, two-dimensional formulation of the problem is considered. A semi-analytical solution is obtained using a combination of the classical analytical approach based on the use of the Laplace transform and separation of variables, and finite difference methodology. The study consists of two parts. Part I focuses on the simulation and analysis of the acoustic fields induced during the interaction. Both the diffraction (absolutely rigid cylinder) and complete diffraction–radiation (elastic shell) are considered. Special attention is paid to the lower-magnitude shell-induced waves representing radiation by the elastic waves circumnavigating the shell. The focus of Part II is on the numerical analysis of the solution. The convergence of the series solution and finite-difference scheme is analysed. The computation of the response functions of the problem is discussed as well, as is the effect of the bending stiffness on the acoustic field. The membrane model of the shell is considered to analyse such an effect, which, in combination with the models addressed in Part I, allows for the analysis of the evolution of the acoustic field around the structure as its elastic properties change from an absolutely rigid cylinder to a membrane. The results of the numerical simulations are compared to available experimental data, and a good agreement is observed.     

Correlation study in shock wave�Cturbulent boundary layer interaction

Shock wave–turbulent boundary layer interaction is a critical problem in aircraft design. Therefore, a thorough understanding of the processes occurring in such flows is necessary. The most important task is to study the unsteady phenomena, in particular, the low-frequency ones, for this interaction. An experimental study of separated flow has been performed in the zone of interaction of the incident oblique shock wave with a turbulent boundary layer at Mach 2. Two-point correlation data in the separation zone and the upstream flow were obtained and showed that low-frequency oscillations of the reflected shock waves are related to pulsations in the inflow turbulent boundary layer.     

Stiffness problem in modeling wave flows of heterogeneous media with a three‐temperature scheme of interphase heat and mass transfer

The numerical modeling of wave flows of heterogeneous media with a threetemperature scheme of interphase heat and mass transfer involves the problem of equation stiffness. A discrete model of improved stability was developed to describe these processes. Test calculations of the interaction of a shock wave with a bounded layer of a mixture of a gas and droplets assuming a discrete model over a wide range of initial data showed that the stability conditions do not depend on the rate of interphase interaction (Cstability).     

Resonance Waves in a Model of a Two‐Layered Liquid

With allowance for surface interaction between phases, the behavior of longwave perturbations at the interface between two layers of dissimilar liquids, which form resonance triplets described by a pseudodifferential equation, is studied.