Acoustic Vortex Research Articles

Linear phase distribution of acoustical vortices

Linear phase distribution of phase-coded acoustical vortices was theoretically investigated based on the radiation theory of point source, and then confirmed by experimental measurements. With the proposed criterion of positive phase slope, the possibility of constructing linear circular phase distributions is demonstrated to be determined by source parameters. Improved phase linearity can be achieved at larger source number, lower frequency, smaller vortex radius, and/or longer axial distance. Good agreements are observed between numerical simulations and measurement results for circular phase distributions. The favorable results confirm the feasibility of precise phase control for acoustical vortices and suggest potential applications in particle manipulation.

Dynamical behaviors of nonlinear dust acoustic waves: From plane waves to dust acoustic wave turbulence

The dust acoustic wave (DAW), associated with longitudinal dust oscillations in dusty plasmas, can be self-excited from the free energy of ion streaming. It is not only a fundamental plasma wave but also a paradigm to understand the generic dynamical behaviors of self-excited nonlinear longitudinal density waves through optically monitoring particle motion and dust density evolutions over a large area. In this paper, the dynamical behaviors of the wave-particle interaction and wave breaking in ordered self-excited DAW with straight wave fronts, and the defect-mediated wave turbulence with fluctuating defects and chaotic low amplitude hole filaments along defect trajectories in the 2+1D space-time space, are briefly reviewed. The first experimental observation of acoustic vortices with helical waveforms in self-excited acoustic-type defect-mediated wave turbulence, and the dynamics of spontaneous pair generation, propagation, and pair annihilation of acoustic vortices, is demonstrated and discussed.

Nonlinear collapse of vortex

Sound radiation by two vortices with different intensity and sign changes the distribution of vortex field. The acoustic instability and vortices motion may occur in such a system. The linear stage of this process was considered previously the spread of similar vortices (Klyatskin, 1966) and attraction of different vortices (Gryanik, 1983; Kop'ev and leont'ev, 1983). As a result of attraction, the nonlinear effect of collapse of vortices may appear. This process is considered by the method of matched asymptotic expansion of the solution for the point vortices in an incompressible fluid and the solution of nonlinear Burgers equation. The features of cylindrical wave spread and nonlinear distortion both indicated.

Pressure distribution based optimization of phase-coded acoustical vortices

Based on the acoustic radiation of point source, the physical mechanism of phase-coded acoustical vortices is investigated with formulae derivations of acoustic pressure and vibration velocity. Various factors that affect the optimization of acoustical vortices are analyzed. Numerical simulations of the axial, radial, and circular pressure distributions are performed with different source numbers, frequencies, and axial distances. The results prove that the acoustic pressure of acoustical vortices is linearly proportional to the source number, and lower fluctuations of circular pressure distributions can be produced for more sources. With the increase of source frequency, the acoustic pressure of acoustical vortices increases accordingly with decreased vortex radius. Meanwhile, increased vortex radius with reduced acoustic pressure is also achieved for longer axial distance. With the 6-source experimental system, circular and radial pressure distributions at various frequencies and axial distances have been measured, which have good agreements with the results of numerical simulations. The favorable results of acoustic pressure distributions provide theoretical basis for further studies of acoustical vortices.

The effect of Dirac phase on acoustic vortex in media with screw dislocation

We study acoustic vortex in media with screw dislocation using the Katanaev-Volovich theory of defects. It is shown that the screw dislocation affects the beam's orbital angular momentum and changes the acoustic vortex strength. This change is a manifestation of topological Dirac phase and is robust against fluctuations in the system.

Three-dimensional analysis of the acoustic radiation pressure: Application to single-beam acoustical tweezers

Recent studies on the acoustic radiation forces exerted by sound impinging spherical objects suggest the use of structured wavefronts for particle entrapment and controlled manipulation. In the scope of understanding why it is made possible to trap and manipulate small particles with sound, we present a general model for the acoustic radiation forces in three dimensions. A first generalization comes from the extension of well known results for the radiation pressure of plane waves to incident wavefields having arbitrary wavefronts. Second, the elastic spherical target of any dimension is allowed to be arbitrarily located within the wavefield. Introducing a new class of “single-beam” acoustical tweezers, we discuss the capabilities of different acoustical beams to achieve particle trapping and manipulation tasks. In addition, using an efficient experimental setup, we report the propagation of a peculiar beam carrying orbital angular momentum, namely an acoustical vortex, which is our selected candidate to achieve the first three-dimensional acoustic trap for elastic particles.

Measured scattering of a first-order vortex beam by a sphere: Cross-helicity and helicity-neutral near-forward scattering and helicity modulation

The wavefield of a traveling wave acoustic vortex beam has an axial null and an angular phase ramp. An appropriately phased four-element transducer array can be used to generate a first order vortex beam [Hefner and Marston, J. Acoust. Soc. Am. 106, 3313–3316 (1999)]. The direction of the phase ramp determines the helicity of the beam. Superposition of signals from an appropriately positioned four-element receiver array gives a helicity selective detector and commutation of diagonal source elements can be used to reverse the source helicity [Marston and Marston, J. Acoust. Soc. Am. 127, 1856 (2010)]. These techniques were used to investigate the near forward scattering by a small sphere placed on or near a beam’s axis. The forward scattering vanishes in the on-axis case [Marston, J. Acoust. Soc. Am. 124, 2905–2910 (2008)]. As the sphere is moved off axis the scattering to a helicity neutral receiver is found to increase linearly in the displacement with a first order phase swirl as a function of the sphere coordinates. For cross-helicity detection (detection opposite the beam’s helicity) as required by symmetry, the signal is approximately quadratic in the displacement with a second-order phase swirl. [Work supported by ONR.]

Phase-coded approach for controllable generation of acoustical vortices

Based on the acoustic radiation of point source, a phase-coded approach is proposed as a general technology to generate controllable acoustical vortices. For N sources, acoustical vortices can be generated with the phase difference of 2πm/N for the source topological charge m. It is proved that more circular pressure distributions of acoustical vortices with higher pressure peak amplitude can be generated for more sources. The number and spiral direction of phase twists are demonstrated to be determined by m and the maximum topological charge of acoustical vortices is |L|=Fix[(N−1)/2], where Fix(x) rounds the element x toward zero. To produce acoustical vortices with a maximum topological charge L, the minimum source number of Nmin=max(2|L|+1,4) should be employed with the phase difference of 2πL/Nmin and the phase difference resolution is also demonstrated to be π. The phase-coded approach has been verified by a 6-source experiment. The measured distributions of pressure and phase as well as the topological charge of acoustical vortices agree well with theoretical results, which suggest the feasibility of the phase-coded approach for controllable generation of acoustical vortices.

Three-dimensional acoustic radiation force on an arbitrarily located elastic sphere

This work aims to model the acoustic radiation forces acting on an elastic sphere placed in an inviscid fluid. An expression of the axial and transverse forces exerted on the sphere is derived. The analysis is based on the scattering of an arbitrary acoustic field expanded in the spherical coordinate system centered on the spherical scatterer. The sphere is allowed to be arbitrarily located. The special case of high order Bessel beams, acoustical vortices, are considered. These types of beams have a helicoidal wave front, i.e., a screw-type phase singularity and hence, the beam has a central dark core of zero amplitude surrounded by an intense ring. Depending on the sphere's radius, different radial equilibrium positions may exist and the sphere can be set in rotation around the beam axis by an azimuthal force. This confirms the pseudo-angular moment transfer from the beam to the sphere. Cases where the axial force is directed opposite to the direction of the beam propagation are investigated and the potential use of Bessel beams as tractor beams is demonstrated. Numerical results provide an impetus for further designing acoustical tweezers for potential applications in particle entrapment and remote controlled manipulation.

709 流れ方向に密な千鳥配列管群における気柱共鳴現象と渦放出(流体力学6)

709 流れ方向に密な千鳥配列管群における気柱共鳴現象と渦放出(流体力学6)

Acoustic gravity tornadoes in the atmosphere

It is shown that three-dimensional (3D) acoustic gravity waves (AGWs) in the atmosphere can appear in the form of acoustic gravity tornadoes (AGTs) characterized by twisted density structures or density ropes carrying orbital angular momentum. For our purposes, we use a previously obtained 3D wave equation for AGWs, and show that this equation in the paraxial approximation admits solutions in the form of Laguerre–Gauss acoustic gravity vortex beams or AGTs/AG whirls with twisted density structures supporting the dynamics of the AGTs.

Drift and ion acoustic wave driven vortices with superthermal electrons

Linear and nonlinear analysis of coupled drift and acoustic mode is presented in an inhomogeneous electron-ion plasma with κ-distributed electrons. A linear dispersion relation is found which shows that the phase speed of both the drift wave and the ion acoustic wave decreases in the presence of superthermal electrons. Several limiting cases are also discussed. In the nonlinear regime, stationary solutions in the form of dipolar and monopolar vortices are obtained. It is shown that the condition for the boundedness of the solution implies that the speed of drift wave driven vortices reduces with increase in superthermality effect. Ignoring density inhomogeniety, it is investigated that the lower and upper limits on the speed of the ion acoustic driven vortices spread with the inclusion of high energy electrons. The importance of results with reference to space plasmas is also pointed out.

Mechanical Evidence of the Orbital Angular Momentum to Energy Ratio of Vortex Beams

We measure, in a single experiment, both the radiation pressure and the torque due to a wide variety of propagating acoustic vortex beams. The results validate, for the first time directly, the theoretically predicted ratio of the orbital angular momentum to linear momentum in a propagating beam. We experimentally determine this ratio using simultaneous measurements of both the levitation force and the torque on an acoustic absorber exerted by a broad range of helical ultrasonic beams produced by a 1000-element matrix transducer array. In general, beams with helical phase fronts have been shown to contain orbital angular momentum as the result of the azimuthal component of the Poynting vector around the propagation axis. Theory predicts that for both optical and acoustic helical beams the ratio of the angular momentum current of the beam to the power should be given by the ratio of the beam's topological charge to its angular frequency. This direct experimental observation that the ratio of the torque to power does convincingly match the expected value (given by the topological charge to angular frequency ratio of the beam) is a fundamental result.

Axial acoustic radiation torque of a Bessel vortex beam on spherical shells

The present paper investigates the interaction of an acoustic Bessel vortex beam centered on a viscoelastic polyethylene sphere and spherical shells filled with air or water immersed in nonviscous water and mercury, and the induced axial acoustic radiation torque (ART) resulting from the transfer of angular momentum. Closed-form series expansions for the axial ART are derived for the case of progressive, standing, and quasistanding waves. The ART is shown to be the result of acoustic absorption inside the particle's material. Numerical predictions shown in the form of two-dimensional (2D) plots illustrate the theory, and reveal new properties related to the ART of Bessel vortex beams. Potential applications are in particle rotation and manipulation. Other applications, such as the characterization of fluids from induced angular accelerations (produced by the ART) and containerless processing, may benefit from the analysis developed here.

216 気柱共鳴現象発生前後における格子配列管群からの渦放出に関する研究(流体工学(騒音・音響・渦2))

216 気柱共鳴現象発生前後における格子配列管群からの渦放出に関する研究(流体工学(騒音・音響・渦2))

Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects

An acoustic vortex in an inviscid fluid and its radiation torque on an axisymmetric absorbing object are analyzed beyond the paraxial approximation to clarify an analogy with an optical vortex. The angular momentum flux density tensor from the conservation of angular momentum is used as an efficient description of the transport of angular momentum. Analysis of a monochromatic nonparaxial acoustic vortex beam indicates that the local ratio of the axial (or radial) flux density of axial angular momentum to the axial (or radial) flux density of energy is exactly equal to the ratio of the beam's topological charge l to the acoustic frequency ω. The axial radiation torque exerted by the beam on an axisymmetric object centered on the beam's axis due to the transfer of angular momentum is proportional to the power absorbed by the object with a factor l/ω, which can be understood as a result of phonon absorption from the beam. Depending on the vortex's helicity, the torque is parallel or antiparallel to the beam's axis.

Acoustic radiation torque of arbitrary shaped waves

In this work, a general expression of the acoustic radiation torque produced over an object by an arbitrary shaped beam is presented. The object is immersed in an inviscid fluid. To obtain the expression, the stress tensor of the angular momentum is integrated over a farfield virtual sphere, which encloses the object. The incident and scattered acoustic fields are represented through the partial wave expansion in the spherical coordinates. After performing the integration, the radiation torque is given in terms of the beam-shape and the scattering coefficients, which come from the incident and scattered partial wave series, respectively. The method is applied to compute the torque upon a fluid sphere by a vortex (first-order) Bessel beam in both on- and off-axis configurations. It is shown that the torque only arises on absorbing spheres. In this case, the angular acceleration and velocity are obtained from the torque. It is found that the angular acceleration may reverse its direction depending on the wave frequency. In conclusion, the presented theory might be useful for describing the particle dynamics of a sphere subjected to acoustic vortex beams.

The Elastoplast Discontinuous Galerkin (EDG) method for the Navier–Stokes equations

The present work details the Elastoplast (this name is a translation from the French “sparadrap”, a concept first applied by Yves Morchoisne for Spectral methods [1]) Discontinuous Galerkin (EDG) method to solve the compressible Navier–Stokes equations. This method was first presented in 2009 at the ICOSAHOM congress with some Cartesian grid applications. We focus here on unstructured grid applications for which the EDG method seems very attractive. As in the Recovery method presented by van Leer and Nomura in 2005 for diffusion, jumps across element boundaries are locally eliminated by recovering the solution on an overlapping cell. In the case of Recovery, this cell is the union of the two neighboring cells and the Galerkin basis is twice as large as the basis used for one element. In our proposed method the solution is rebuilt through an L 2 projection of the discontinuous interface solution on a small rectangular overlapping interface element, named Elastoplast, with an orthogonal basis of the same order as the one in the neighboring cells. Comparisons on 1D and 2D scalar diffusion problems in terms of accuracy and stability with other viscous DG schemes are first given. Then, 2D results on acoustic problems, vortex problems and boundary layer problems both on Cartesian or unstructured triangular grids illustrate stability, precision and versatility of this method.

Radiation torque on solid spheres and drops centered on an acoustic helicoidal Bessel beam.

Somewhat analogous to circularly polarized electromagnetic waves carrying axial angular momentum and generating a corresponding torque, a helicoidal acoustic (vortex) beam also carries axial angular momentum and absorption of such a beam should also produce an axial radiation torque [B. T. Hefner and P. L. Marston, J. Acoust Soc. Am. 106, 3313–3316 (1999)]. Here the acoustic radiation torque on solid spheres and spherical liquid drops centered on acoustic helicoidal Bessel beams is analyzed. Using a relation between the scattering and the partial wave coefficients for a sphere in a helicoidal Bessel beam, the torque is predicted to be proportional to the ratio of the absorbed power to the acoustic frequency. Calculations suggest that beams with a low topological charge tend to be more efficient for generating torques on solid spheres for all frequencies and on liquid drops in the low frequency regime. Balanced by drag torque, a steady rotation is generated. Calculations of the steady‐state angular velocit...

Arbitrary acoustic scattering of a high‐order Bessel vortex beam by a sphere.

The arbitrary acoustic scattering of a high‐order Bessel vortex beam by a sphere is investigated. It is shown here that shifting the sphere off of the axis of wave propagation induces a dependence of the scattering on the azimuthal angle. Theoretical expressions for the incident and scattered fields from a rigid immovable sphere are derived. The near‐ and far‐field acoustic scattering fields are expressed using partial wave series involving the mth‐order spherical harmonics, the scattering coefficients of the sphere, the half‐conical angle of the wave number components of the beam, its order, and the beam‐shape coefficients. The scattering coefficients of the sphere and the three‐dimensional (3‐D) scattering directivity plots in the near‐ and far‐field regions are evaluated using a numerical integration procedure. The calculations indicate that the scattering directivity patterns near the sphere and in the far‐field are strongly dependent on the position of the sphere facing the incident high‐order Bessel vortex beam. In addition to providing physical insight into the off‐axial scattering of acoustic Bessel vortex beams, this investigation would potentially assist in the development of the transverse acoustic radiation force and could provide a useful test of finite element codes for the evaluation of the scattering.