Physical Acoustics and the Method of Matched Asymptotic Expansions

Lesser, Martin; Crighton, D. G.

doi:10.1016/b978-0-12-477911-2.50007-7

Cited by 24 publications

(16 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to this singularity, if not integrable, the Fourier transformation of the pressure in (26) becomes too singular to be interpreted normally and diverges for r → ∞. When we consider the incompressible problem as an inner problem of a larger compressible problem, as in [15,4,16,17], this divergent behaviour disappears as it changes into an outward radiating acoustic wave. The inverse Fourier transform for pressure p is then calculated by splitting off the singular part and interpreting the singular integral in generalised sense [18,19,8].…”

Section: Wiener-hopf Proceduresmentioning

confidence: 99%

Hard wall-soft wall-vorticity scattering in shear flow

Rienstra¹,

Singh²

2014

20th AIAA/CEAS Aeroacoustics Conference

View full text Add to dashboard Cite

An analytically exact solution, for the problem of low Mach number incident vorticity scattering at a hard-soft wall transition, is obtained in the form of Fourier integrals by using the Wiener-Hopf method. Harmonic vortical perturbations of inviscid linear shear flow are scattered at the wall transition. This results in a far field which is qualitatively different for low shear and high shear cases. In particular, for high shear the pressure (apparently driven by the mean flow) does not decay and its Fourier representation involves a diverging integral which is to be interpreted in generalised sense.Then the incompressible hydrodynamic (Wiener-Hopf) "inner" solution is matched asymptotically to an acoustic outer field in order to determine the sound associated to the scattering. The qualitative difference between low and high shear is also apparent here. The low shear case matches successfully. In the high shear case only a partial matching was possible.

show abstract

Section: Wiener-hopf Proceduresmentioning

confidence: 99%

Hard wall-soft wall-vorticity scattering in shear flow

Rienstra¹,

Singh²

2014

20th AIAA/CEAS Aeroacoustics Conference

View full text Add to dashboard Cite

show abstract

“…Note that this equation has a small parameter multiplied by the highest derivative in the X-direction, suggesting a singular perturbation problem [4,18,19,20] with boundary layers in X.…”

Section: The Classical Problemmentioning

confidence: 99%

“…The solution is determined by a source at entrance plane x = 0, and radiation conditions for x → ∞. Other conditions, like a reflecting impedance plane at some exit plane x = L (e.g., modeling a radiating open end [5] or a slit in the wall [4]), are also possible, but they do not essentially alter the present analysis.…”

Section: The Classical Problemmentioning

confidence: 99%

“…The following outer solution analysis will largely follow Lesser and Crighton [4], but we will give it in some detail for two reasons. First, we will have to define the solution for the inner solution at the entrance boundary layer to be discussed later.…”

Section: Asymptotic Analysis: Outer Solutionmentioning

confidence: 99%

“…The structure of the boundary layer was indicated by Lesser and Crighton [4], but they gave explicit examples only for 2D geometries.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Webster's Horn Equation Revisited

Rienstra¹

2005

SIAM J. Appl. Math.

View full text Add to dashboard Cite

Abstract. The problem of low-frequency sound propagation in slowly varying ducts is systematically analyzed as a perturbation problem of slow variation. Webster's horn equation and variants in bent ducts, in ducts with nonuniform soundspeed, and in ducts with irrotational mean flow, with and without lining, are derived, and the entrance/exit plane boundary layer is given. It is shown why a varying lined duct in general does not have an (acoustic) solution. The usual derivation is based on the assumption of a crosswise uniform acoustic pressure field, such that, by averaging over a duct cross section, the spatial dimensions of the problem are reduced from three to one.Although it shows a remarkable evidence of ingenuity and physical insight, this derivation is mathematically unsatisfying. It is not clear (i) what exactly is the small parameter underlying the approximation, (ii) why the pressure may be assumed to be uniform, (iii) what the error is of the approximation, (iv) what the conditions are on the duct geometry and on the frequency of the field, (v) how to generalize to similar problems, (vi) how to generate higher order corrections, and (vii) what happens near the source or duct entrance or exit plane.An asymptotically systematic derivation of the three-dimensional (3D) classic problem was given by Lesser and Crighton [4], extending the derivation of Lesser and Lewis in [5,6]. They also showed for a number of 2D configurations how abrupt changes of the geometry (open end, slit in the wall) can be incorporated as boundary layer regions in a setting of matched asymptotic expansion. Their approach, based on introducing different longitudinal and lateral scales, is a special case of the method of slow variation put forward by Van Dyke [7]. Although only an asymptotically sound derivation is able to indicate the range of validity and the order of the error of the approximation, we found in the literature no variants of this problem (e.g., with mean flow [8,9,10,11,12]) that strictly follow that approach.Particularly interesting would be an investigation of the related problems of lined ducts without and with flow, as this would form a natural long wavelength closure of the multiple scales theory of sound propagation in slowly varying ducts [13,14,15,16].

show abstract

An analytical theory of resonant scattering of SH waves by thin overground structures

Mei

Foda

1979

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

Scattering of SH waves in a half‐space with simple overground structures is studied analytically. For two‐dimensional structures, such as shells, shear walls and a slab‐bridge over a river, the method of matched asymptotics is used for sinusoidal waves long compared to the thickness of the structures. Resonance features are deduced analytically and calculated numerically for various incidences and other parameters.

show abstract

Physical Acoustics and the Method of Matched Asymptotic Expansions

Cited by 24 publications

References 39 publications

Hard wall-soft wall-vorticity scattering in shear flow

Hard wall-soft wall-vorticity scattering in shear flow

Webster's Horn Equation Revisited

An analytical theory of resonant scattering of SH waves by thin overground structures

Contact Info

Product

Resources

About