On the acoustic modes in a duct containing a parabolic shear flow

The exact solution of the acoustic wave equation in an unidirectional shear flow with a parabolic velocity profile is obtained, representing sound propagation in a plane, parallel walled duct, with two boundary layers over rigid or impedance walls. It is shown that there are four cases, depending on the critical level(s) where the Doppler shifted frequency vanishes: (i) for propagation upstream the critical levels are outside the duct (case II); (ii) for propagation downstream there may be two (case IV), one (case I) or no (case III) critical level inside the duct. The acoustic wave equation is transformed in each of the four cases to particular forms of the extended hypergeometric equation, which has power series solutions, some involving logarithmic singularities. In the cases where critical levels occur, at real or ‘imaginary’ distance, matching of two or three pairs of solutions, valid over regions each overlapping the next, is needed. The particular case of the parabolic velocity profile is used to address general properties of sound in unidirectional shear flows. For example, it is shown that for ducted shear flows, there exist a pair of even and odd eigenfunctions, in the absence of critical levels. It is also proved, in more than one instance, that there is no single set of eigenvalues and eigenfunctions valid across one or two shear layers. This leads to the general conjecture, considering the acoustics of shear flows in ducts, that critical levels separate regions with distinct sets of eigenvalues and eigenfunctions.     

Separation of acoustic waves in isentropic flow perturbations

The present contribution investigates the mechanisms of sound generation and propagation in the case of highly-unsteady flows. Based on the linearisation of the isentropic Navier-Stokes equation around a new pathline-averaged base flow, it is demonstrated for the first time that flow perturbations of a non-uniform flow can be split into acoustic and vorticity modes, with the acoustic modes being independent of the vorticity modes. Therefore, we can propose this acoustic perturbation as a general definition of sound.     

Laminar flame and acoustic waves in two-dimensional flow

The complete system of fluid dynamics equations describing the development of instability of a reaction front in a two-dimensional flow in reversed time are reduced to a closed system of equations of front dynamics by using Lagrangian variables and integrals of motion. The system can be used to analyze processes behind the front without solving the complete system of fluid dynamics and chemical kinetics equations. It is demonstrated how the gas density disturbances induced by the moving front can be described in the adiabatic approximation.     

Energy transport for ion acoustic waves in a spin polarized quantum plasma

The separate spin evolution quantum hydrodynamics(SSE-QHD) model is used to investigate the energy behavior for ion acoustic waves in degenerate quantum plasma. Numerical results show that the energy flow speed decreases with spin polarization parameter. It is also shown that it decreases with the increasing rate up to a certain range of wave number and then it goes to zero asymtotically. It is observed that Bohm potential suppresses the energy flow speed. It is also noticed that the energy flow speed deviates from the group velocity even in the absence of Bohm potential effect. However, the contribution of of Bohm poential effect in spin polarized plasma reduces the extent of deviation.     

Radiation of cylindrical duct acoustic modes with flow mismatch

An analysis is presented for the radiation of spinning acoustic modes from a round duct. The model, based on a plug flow exhaust jet, allows for a flow temperature and velocity mismatch. Solutions to the convected wave equations within and outside the jet are devised, the continuity of acoustic pressure and particle displacement match at the jet interface being used. Formal solution is obtained by applying Fourier transforms, inversion being accomplished by using the Wiener-Hopf technique coupled with the Carrier-Koiter approximations. The analysis also is extended formally to include the inlet problem, but with a plug type inlet flow.The calculations suggest that the influence of the Mach number discontinuity is to offer a conflict between the effects of convection and refraction, the former becoming increasingly more significant at high subsonic Mach numbers by the presence of a strong lobe in the shadow zone. Effects of flight conditions are to weaken such conflicts so that in the limit of uniform Mach number, one recovers Carrier's well-known solution.The effect of a temperature mismatch is rather more dramatic, resulting in a sharp beaming of sound off to the side. This is consistent with the kinematic picture of a plane wave impinging on a temperature discontinuity.     

Investigation of acoustic waves propagation and flow in nanodispersed medium

Propagation of acoustic waves in nanodisperse powders and powder flow under the influence of acoustic vibrations have been investigated in the horizontal tube with the use of visualization and hot-wire anemometer methods.     

Sound intensity measurements for describing acoustic power flow

This paper presents calculated and measured sound intensity data describing power flow in near, reflective and refractive acoustic fields. The data illustrate how the intensity vectors can show sources and sinks in an acoustic system and how near and far fields are linked together to form a continuous power flow. Some problems concerning the measuring technique are discussed.     

Effect of flow on quasi-one-dimensional acoustic wave propagation in a variable area duct of finite length

The general equation for the velocity potential of quasi-one-dimensional acoustic wave motion in a variable area, finite duct with one-dimensional flow is derived by using a perturbation technique. The non-linear second-order partial differential equation is linearized and then solved, by either a power series expansion method or the Runge-Kutta fourth-order method, for harmonic time dependence. The boundary condition taken at the duct mouth is that of matching the impedance of the duct sound field to that of the radiation field at the duct opening. Three axial Mach number variations along the duct axis are considered and the results obtained are compared with those for the case of constant Mach number, to determine the influence of the axial velocity gradient on sound propagation. The effect of flow on the radiation impedance is also considered.     

Backward ion‐acoustic waves in plasma with unidirectional ion flow

This paper considers ion‐acoustic waves in a plasma in which the ions move unidirectionally. The dispersion equation is considered and analysed as a two‐dimensional problem. It is shown that the ion‐acoustic waves can be in the form of backward waves (BWs ). The area boundaries in the plane {k _x , k _y } where the BW exists are found.     

Ion acoustic solitary waves in a two-electron-temperature plasma

Due to the presence of a relatively cold electron component in a plasma, the ion acoustic solitary wave of a given width has a larger amplitude. When the temperature difference between the two electron components is sufficiently large, the strength of dispersion is reduced to an extent that a solitary solution is no longer possible.     

Dust acoustic waves in a nonequilibrium dusty plasma

With the use of the method of moments applicable for any values of the parameter of the nonideality of a dusty plasma and the hydrodynamic approach applicable only for small nonideality parameters, the theory of waves and oscillations of a complex plasma has been generalized to the case of a two-exponential interaction potential. It has been shown that the hydrodynamic approach and method of moments give the same dispersion relation for small nonideality parameters. It has been demonstrated that the velocity of dust acoustic waves in the long- and short-wavelength regions is determined by the small and large screening constants, respectively. It has been shown that the velocity of dust acoustic waves in nonequilibrium plasma is much higher than that obtained in the Debye screening theory for equilibrium plasma. In the hydrodynamic approach, the importance of the inclusion of the self-consistent mutual effect of the dust, electron, and ion components, and sinks of electrons and ions on dust particles, which lead to a noticeable change in the parameters of the interaction potential of dust particles, has been demonstrated.     

Surface acoustic waves in interaction with a dislocation

A surface acoustic wave can interact with dislocations that are close to the surface. We characterize this interaction and its manifestations as scattered surface acoustic waves for different orientations with respect to the surface of an edge dislocation. For dislocations that are parallel or perpendicular to the free surface, we present an analytical result for short dislocations with respect to the wave-length that reproduce qualitatively the main features observed for dislocations of various sizes.     

Extended acoustic waves in a one-dimensional aperiodic system

We numerically study the propagation of acoustic waves in a one-dimensional system with an aperiodic pseudo-random elasticity distribution. The elasticity distribution was generated by using a sinusoidal function whose phase varies as a power-law, f μ nⁿphi propto n^{nu}, where n labels the positions along the media. By considering a discrete one-dimensional version of the wave equation and a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicates the presence of extended acoustic waves with non-zero frequency for sufficient degree of aperiodicity.     

Dust acoustic waves in a dc glow-discharge plasma

The spontaneous excitation of low-frequency oscillations of the macroparticle density in ordered dust structures levitating in standing striations of a dc glow discharge is discovered. It is concluded on the basis of a simplified linear model of an ideal collisionless plasma that the observed instability is caused by the drift motion of ions relative to the dust, which leads to the excitation of dust acoustic oscillations of the plasma. Zh. éksp. Teor. Fiz. 116, 902–907 (September 1999)     

Surface acoustic waves at a free-metallized interface

Light scattering was used to study surface acoustic waves at a free-metalized interface on piezoelectric lithium niobate. An interaction region of several acoustic wavelengths was observed in which a reflected surface wave and a continuous spectrum of bulk waves are generated.     

Ion acoustic shock waves in a relativistic electron-positron-ion plasmas

The Korteweg-de Vries-Burger (KdVB) equation is derived for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma. Electrons, positrons are considered isothermal and ions are relativistic. The travelling wave solution has been acquired by employing the tangent hyperbolic method. The vivid display of the graphical results is presented and analyzed. It is observed that amplitude and steepness of the shock wave decrease with increase of the relativistic streaming factor, the positron concentration and they increase with the increase of the coefficient of kinematic viscosity and vice versa. It is determined that at low temperature the shock wave propagates, whereas at very high temperature the solitary wave propagates in the system. The results may have relevance in astrophysical plasmas as well as in inertial confinement fusion plasmas.