Uniform asymptotics for spherical and cylindrical nonlinear acoustic waves generated by a sinusoidal source

1981 ◽  
Vol 375 (1761) ◽  
pp. 211-230 ◽  
Keyword(s):  
Acoustic Waves ◽  
Space Time ◽  
Nonlinear Propagation ◽  
Sound Waves ◽  
Acoustic Beam ◽  
Order Unity ◽  
Spherical Waves ◽  
Leading Term ◽  
Nonlinear Acoustic ◽  
Time Away

This paper is concerned with the nonlinear propagation of sound waves from spherical or cylindrical sinusoidal sources. This problem is governed by the two dimensionless parameters ε and R 0 , and we seek asymptotic expansions valid uniformly in ε , R 0 (as well as in space-time) away from the irreducible domain where both ε and R 0 are of order unity. Various matching asymptotic domains of the parameter plane are defined and in each domain the space-time asymptotic structure is given: in many cases the leading term can actually be solved for analytically. Finally, the application of the results for spherical waves to the important problem of nonlinear acoustic beam spreading are discussed.

A Simple Computational Tool for Studying Acoustic Waves in Nonlinear Medium

2017 ◽  
Author(s):  
Nirmal J. Nair ◽  
Utsav Shah
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Nonlinear Medium ◽  
Numerical Scheme ◽  
Nonlinear Acoustics ◽  
Ultrasonic Waves ◽  
The Self ◽  
Sound Waves ◽  
Computational Tool ◽  
Nonlinear Acoustic

The behaviour of acoustic waves in nonlinear medium is well established in literature. But there is a need of a simple computational tool through which practical problems pertaining to nonlinear acoustics can be treated with minimum effort and expense. Additionally, visualization of nonlinear acoustic waves can be useful towards the applications of acoustic diodes and ultrasonic waves. To address this issue, we have developed a numerical scheme which effectively captures the self-distortion mechanism of acoustic wave in nonlinear medium and the consequential generation of higher harmonics. Additionally, the effects of increasing non-linearity constant of the medium and amplitude of sound waves on distortion of the waveform is studied.

scholarly journals Experimental demonstration of negative refraction with 3D locally resonant acoustic metafluids

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Benoit Tallon ◽  
Artem Kovalenko ◽  
Olivier Poncelet ◽  
Christophe Aristégui ◽  
Olivier Mondain-Monval ◽  
...  
Keyword(s):  
Experimental Data ◽  
Yield Stress ◽  
Multiple Scattering ◽  
Silicone Rubber ◽  
Acoustic Waves ◽  
Scattering Theory ◽  
Negative Refraction ◽  
Volume Fraction ◽  
Experimental Demonstration ◽  
Acoustic Beam

AbstractNegative refraction of acoustic waves is demonstrated through underwater experiments conducted at ultrasonic frequencies on a 3D locally resonant acoustic metafluid made of soft porous silicone-rubber micro-beads suspended in a yield-stress fluid. By measuring the refracted angle of the acoustic beam transmitted through this metafluid shaped as a prism, we determine the acoustic index to water according to Snell’s law. These experimental data are then compared with an excellent agreement to calculations performed in the framework of Multiple Scattering Theory showing that the emergence of negative refraction depends on the volume fraction $$\Phi$$ Φ of the resonant micro-beads. For diluted metafluid ($$\Phi =3\%$$ Φ = 3 % ), only positive refraction occurs whereas negative refraction is demonstrated over a broad frequency band with concentrated metafluid ($$\Phi =17\%$$ Φ = 17 % ).

Propagation of nonlinear acoustic waves in bimodular media with linear dissipation

Wave Motion ◽  
2013 ◽  
Vol 50 (2) ◽  
pp. 191-196 ◽  
Author(s):  
A. Radostin ◽  
V. Nazarov ◽  
S. Kiyashko
Keyword(s):  
Acoustic Waves ◽  
Nonlinear Acoustic ◽  
Bimodular Media

A Linear Acoustic Phased Array for Nonreciprocal Transmission and Reception

2020 ◽  
Author(s):  
R. Adlakha ◽  
M. Moghaddaszadeh ◽  
M. A. Attarzadeh ◽  
A. Aref ◽  
M. Nouh
Keyword(s):  
Phase Modulation ◽  
Frequency Conversion ◽  
Phased Array ◽  
Space Time ◽  
Mathematical Framework ◽  
Sound Waves ◽  
Asymmetric Transmission ◽  
Time Modulation ◽  
Dynamic Phase ◽  
Phase Angles

Abstract Acoustic phased arrays are capable of steering and focusing a beam of sound via selective coordination of the spatial distribution of phase angles between multiple sound emitters. Here, we propose a controllable acoustic phased array with space-time modulation that breaks time-reversal symmetry, and enables phononic transition in both momentum and energy spaces. By leveraging the dynamic phase modulation, the proposed linear phased array is no longer bound by the reciprocity principle, and supports asymmetric transmission and reception patterns that can be tuned independently. Through theoretical and numerical investigations, we develop and verify a mathematical framework to characterize the nonreciprocal phenomena, and analyze the frequency conversion between the wave fields. The space-time acoustic phased array facilitates unprecedented control over sound waves in a variety of applications including underwater telecommunication.

Photoacoustic Nanotracers for Subsurface Applications: Opportunities and Challenges

2021 ◽  
Author(s):  
Jesus Manuel Felix Servin ◽  
Hala A. Al-Sadeg ◽  
Amr Abdel-Fattah
Keyword(s):  
Acoustic Waves ◽  
Oil And Gas ◽  
Continuous Wave ◽  
Tracer Tests ◽  
Oil And Gas Industry ◽  
Oil Reservoirs ◽  
Medical Community ◽  
Sound Waves ◽  
Time Data ◽  
Gas Industry

Abstract Tracers are practical tools to gather information about the subsurface fluid flow in hydrocarbon reservoirs. Typical interwell tracer tests involve injecting and producing tracers from multiple wells to evaluate important parameters such as connectivity, flow paths, fluid-fluid and fluid-rock interactions, and reservoir heterogeneity, among others. The upcoming of nanotechnology enables the development of novel nanoparticle-based tracers to overcome many of the challenges faced by conventional tracers. Among the advantages of nanoparticle-based tracers is the capability to functionalize their surface to yield stability and transportability through the subsurface. In addition, nanoparticles can be engineered to respond to a wide variety of stimuli, including light. The photoacoustic effect is the formation of sound waves following light absorption in a material sample. The medical community has successfully employed photoacoustic nanotracers as contrast agents for photoacoustic tomography imaging. We propose that properly engineered photoacoustic nanoparticles can be used as tracers in oil reservoirs. Our analysis begins by investigating the parameters controlling the conversion of light to acoustic waves, and strategies to optimize such parameters. Next, we analyze different kind of nanoparticles that we deem potential candidates for our subsurface operations. Then, we briefly discuss the excitation sources and make a comparison between continuous wave and pulsed sources. We finish by discussing the research gaps and challenges that must be addressed to incorporate these agents into our operations. At the time of this writing, no other study investigating the feasibility of using photoacoustic nanoparticles for tracer applications was found. Our work paves the way for a new class of passive tracers for oil reservoirs. Photoacoustic nanotracers are easy to detect and quantify and are therefore suitable for continuous in-line monitoring, contributing to the ongoing real-time data efforts in the oil and gas industry.

A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow

2008 ◽  
Vol 601 ◽  
pp. 365-379 ◽  
Author(s):  
DALE R. DURRAN
Keyword(s):  
Acoustic Waves ◽  
Large Scale ◽  
Mass Conservation ◽  
Simple Expression ◽  
Reference State ◽  
Small Scale ◽  
Sound Waves ◽  
State Equations ◽  
Planetary Scale ◽  
Atmospheric Motions

An incompressibility approximation is formulated for isentropic motions in a compressible stratified fluid by defining a pseudo-density ρ* and enforcing mass conservation with respect to ρ* instead of the true density. Using this approach, sound waves will be eliminated from the governing equations provided ρ* is an explicit function of the space and time coordinates and of entropy. By construction, isentropic pressure perturbations have no influence on the pseudo-density.A simple expression for ρ* is available for perfect gases that allows the approximate mass conservation relation to be combined with the unapproximated momentum and thermodynamic equations to yield a closed system with attractive energy conservation properties. The influence of pressure on the pseudo-density, along with the explicit (x,t) dependence of ρ* is determined entirely by the hydrostatically balanced reference state.Scale analysis shows that the pseudo-incompressible approximation is applicable to motions for which ${\cal M})$2 ≪ min(1,${\cal R})$2, where ${\cal M})$ is the Mach number and ${\cal R}$ the Rossby number. This assumption is easy to satisfy for small-scale atmospheric motions in which the Earth's rotation may be neglected and is also satisfied for quasi-geostrophic synoptic-scale motions, but not planetary-scale waves. This scaling assumption can, however, be relaxed to allow the accurate representation of planetary-scale motions if the pressure in the time-evolving reference state is computed with sufficient accuracy that the large-scale components of the pseudo-incompressible pressure represent small corrections to the total pressure, in which case the full solution to both the pseudo-incompressible and reference-state equations has the potential to accurately model all non-acoustic atmospheric motions.

A Multi-Field Space-Time Finite Element Method for Structural Acoustics

1995 ◽  
Author(s):  
Lonny L. Thompson
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Acoustic Waves ◽  
Space Time ◽  
High Order ◽  
Elastic Structure ◽  
Structural Acoustics ◽  
Field Representation ◽  
Element Discretization ◽  
Acoustic Fluid

Abstract A Computational Structural Acoustics (CSA) capability for solving scattering, radiation, and other problems related to the acoustics of submerged structures has been developed by employing some of the recent algorithmic trends in Computational Fluid Dynamics (CFD), namely time-discontinuous Galerkin Least-Squares finite element methods. Traditional computational methods toward simulation of acoustic radiation and scattering from submerged elastic bodies have been primarily based on frequency domain formulations. These classical time-harmonic approaches (including boundary element, finite element, and finite difference methods) have been successful for problems involving a limited range of frequencies (narrow band response) and scales (wavelengths) that are large compared to the characteristic dimensions of the elastic structure. Attempts at solving large-scale structural acoustic systems with dimensions that are much larger than the operating wavelengths and which are complex, consisting of many different components with different scales and broadband frequencies, has revealed limitations of many of the classical methods. As a result, there has been renewed interest in new innovative approaches, including time-domain approaches. This paper describes recent advances in the development of a new class of high-order accurate and unconditionally stable space-time methods for structural acoustics which employ finite element discretization of the time domain as well as the usual discretization of the spatial domain. The formulation is based on a space-time variational equation for both the acoustic fluid and elastic structure together with their interaction. Topics to be discussed include the development and implementation of higher-order accurate non-reflecting boundary conditions based on the exact impedance relation through the. Dirichlet-to-Neumann (DtN) map, and a multi-field representation for the acoustic fluid based on independent pressure and velocity potential variables. Numerical examples involving radiation and scattering of acoustic waves are presented to illustrate the high-order accuracy achieved by the new methodology for CSA.

scholarly journals Sound-wave instabilities in dilute plasmas with cosmic rays: implications for cosmic ray confinement and the Perseus X-ray ripples

2020 ◽  
Vol 493 (4) ◽  
pp. 5323-5335 ◽  
Author(s):  
Philipp Kempski ◽  
Eliot Quataert ◽  
Jonathan Squire
Keyword(s):  
Cosmic Rays ◽  
Thermal Plasma ◽  
Acoustic Waves ◽  
Cosmic Ray ◽  
High Energy ◽  
Density Fluctuations ◽  
Sound Waves ◽  
X Ray ◽  
Acoustic Instability ◽  
Anisotropic Viscosity

ABSTRACT Weakly collisional, magnetized plasmas characterized by anisotropic viscosity and conduction are ubiquitous in galaxies, haloes, and the intracluster medium (ICM). Cosmic rays (CRs) play an important role in these environments as well, by providing additional pressure and heating to the thermal plasma. We carry out a linear stability analysis of weakly collisional plasmas with CRs using Braginskii MHD for the thermal gas. We assume that the CRs stream at the Alfvén speed, which in a weakly collisional plasma depends on the pressure anisotropy (Δp) of the thermal plasma. We find that this Δp dependence introduces a phase shift between the CR-pressure and gas-density fluctuations. This drives a fast-growing acoustic instability: CRs offset the damping of acoustic waves by anisotropic viscosity and give rise to wave growth when the ratio of CR pressure to gas pressure is ≳αβ−1/2, where β is the ratio of thermal to magnetic pressure, and α, typically ≲1, depends on other dimensionless parameters. In high-β environments like the ICM, this condition is satisfied for small CR pressures. We speculate that the instability studied here may contribute to the scattering of high-energy CRs and to the excitation of sound waves in galaxy-halo, group and cluster plasmas, including the long-wavelength X-ray fluctuations in Chandra observations of the Perseus cluster. It may also be important in the vicinity of shocks in dilute plasmas (e.g. cluster virial shocks or galactic wind termination shocks), where the CR pressure is locally enhanced.

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