STABILITY OF ACOUSTIC PROPAGATION IN 2D DUCT FLOWS: A LOW FREQUENCY APPROACH

2011 ◽  
Vol 21 (05) ◽  
pp. 1121-1151 ◽  
Author(s):  
A.-S. BONNET-BEN DHIA ◽  
M. DURUFLE ◽  
P. JOLY ◽  
L. JOUBERT
Keyword(s):  
Laminar Flow ◽  
Acoustic Waves ◽  
Normal Operator ◽  
Low Frequency ◽  
Acoustic Propagation ◽  
Compressible Fluids ◽  
Well Posedness ◽  
Hydrodynamic Instabilities ◽  
Limit Model

In this paper, we derive a simplified "quasi-1D" limit model for the propagation of low frequency acoustic waves in a laminar flow filling a 2D duct. We analyze the well-posedness of this model in function of the Mach profile of the flow. This can be reduced to the study of the spectrum of a bounded non-normal operator. As a by-product of this analysis, we establish new results for hydrodynamic instabilities of Kelvin–Helmholtz type in compressible fluids.

A Low Frequency Model for Acoustic Propagation in a 2D Flow Duct: Numerical Computation

2012 ◽  
Vol 11 (2) ◽  
pp. 508-524 ◽  
Author(s):  
Lauris Joubert ◽  
Patrick Joly
Keyword(s):  
Numerical Method ◽  
Explicit Expression ◽  
Low Frequency ◽  
Acoustic Propagation ◽  
Asymptotic Model ◽  
Well Posedness ◽  
Frequency Model ◽  
2D Flow ◽  
Profile Flow ◽  
Flow Duct

AbstractIn this paper we study a low frequency model for acoustic propagation in a 2D flow duct. For some Mach profile flow, we are able to give a well-posedness theorem. Its proof relies on a quasi-explicit expression of the solution which provides us an efficient numerical method. We give and comment numerical results for particular linear, tangent and quadratic profiles. Finally, we give a numerical validation of our asymptotic model.

Studies on the interaction of low‐frequency acoustic signals with the ocean bottom

Geophysics ◽  
1979 ◽  
Vol 44 (12) ◽  
pp. 1922-1940 ◽  
Author(s):  
Salvatore R. Santaniello ◽  
Frederick R. DiNapoli ◽  
Robert K. Dullea ◽  
Peter D. Herstein
Keyword(s):  
Acoustic Waves ◽  
Grazing Angle ◽  
Low Frequency ◽  
Propagation Loss ◽  
Ocean Bottom ◽  
Computer Technique ◽  
Quantitative Evidence ◽  
Ocean Sediment ◽  
Wave Models ◽  
Processing Techniques

Understanding the mechanisms by which the ocean sediment redirects impinging sound back into the ocean is necessary in developing propagation models for sonar performance prediction. The Naval Underwater Systems Center (NUSC) has (1) conducted controlled, self‐calibrating acoustic measurements where the ocean bottom interacted signal is isolated in time for analysis, (2) developed deconvolution processing techniques to aid in describing the impulse response of the ocean sediment, and (3) performed modeling to study the interaction of acoustic waves at the ocean bottom. This paper presents a synopsis of studies showing the necessity of considering the refraction of sound by the ocean sediment when predicting low‐frequency propagation loss. Constructive interference between nonplanar wave sediment refracted sound and sound reflected by the ocean‐sediment interface and subbottom layering can cause negative values of bottom loss when using plane‐wave models to interpret measured data. These models cannot account for all possible acoustic arrivals at a receiver. In addition, for a given frequency and constant ocean bottom grazing angle, bottom loss can be dependent upon both processing bandwidth and source/receiver depth. Deconvolution has aided in time resolution of signals that make up the bottom‐interacted signals. Resolution of these signals aids in interpreting results. A modeling effort utilizing the Fast Field Program (a computer technique for evaluating the field integral by the fast Fourier transform) provides quantitative evidence for the necessity of accounting for the refraction of sound by subocean sediments to interpret properly low‐frequency propagation loss measurements.

FLOWS OF VISCOUS COMPRESSIBLE FLUIDS UNDER STRONG STRATIFICATION: INCOMPRESSIBLE LIMITS FOR LONG-RANGE POTENTIAL FORCES

2011 ◽  
Vol 21 (01) ◽  
pp. 7-27 ◽  
Author(s):  
EDUARD FEIREISL
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Stokes System ◽  
Hybrid Methods ◽  
Singular Limit ◽  
Acoustic Energy ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Whole Space ◽  
Rage Theorem

We study the singular limit of the compressible Navier–Stokes system in the whole space ℝ3, where the Mach number and Froude number are proportional to a small parameter ε → 0. The central issue is the local decay of the acoustic energy proved by means of the RAGE theorem. The result is quite general and the proposed approach can be applied to a large variety of problems that concern propagation of acoustic waves in compressible fluids. In particular, the method can be used for showing stability of various numerical schemes based on the so-called hybrid methods.

LOW-FREQUENCY ACOUSTIC SCATTERING BY AN INHOMOGENEOUS MEDIUM

2005 ◽  
Vol 15 (10) ◽  
pp. 1459-1468 ◽  
Author(s):  
GEORGE VENKOV
Keyword(s):  
Refractive Index ◽  
Plane Wave ◽  
Inhomogeneous Medium ◽  
Acoustic Waves ◽  
Spherical Wave ◽  
Low Frequency ◽  
Far Field ◽  
Scattering Medium ◽  
Wave Incidence ◽  
Plane Wave Incidence

This paper deals with the scattering of time-harmonic acoustic waves by inhomogeneous medium. We study the problem to recover the near and the far field using a priori information about the refractive index and the support of inhomogeneity. The incident spherical wave is modified in such a way as to recover the plane wave incidence when the source point approaches infinity. Applying the low-frequency expansions, the scattering medium problem is reduced to a sequence of potential problems for the approximation coefficients in the presence of a monopole singularity located at the source of incidence. Complete expansions for the integral representation formula in the near field as well as for the scattering amplitude in the far field are provided. The method is applied to the case of a spherical region of inhomogeneity and a radial dependent refractive index. As the point singularity tends to infinity, the relative results recover the scattering medium problem for plane wave incidence.

scholarly journals Sub-wavelength focusing of acoustic waves in bubbly media

2017 ◽  
Vol 473 (2208) ◽  
pp. 20170469 ◽  
Author(s):  
Habib Ammari ◽  
Brian Fitzpatrick ◽  
David Gontier ◽  
Hyundae Lee ◽  
Hai Zhang
Keyword(s):  
Acoustic Waves ◽  
Wave Scattering ◽  
Low Frequency ◽  
Scattering Function ◽  
Point Scatterer ◽  
Layer Potential ◽  
Spherical Bubble ◽  
Acoustic Wave Scattering ◽  
Frequency Regime ◽  
Sub Wavelength

The purpose of this paper is to investigate acoustic wave scattering by a large number of bubbles in a liquid at frequencies near the Minnaert resonance frequency. This bubbly media has been exploited in practice to obtain super-focusing of acoustic waves. Using layer potential techniques, we derive the scattering function for a single spherical bubble excited by an incident wave in the low frequency regime. We then propose a point scatterer approximation for N bubbles, and describe several numerical simulations based on this approximation, that demonstrate the possibility of achieving super-focusing using bubbly media.

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