scholarly journals Friedlander–Keller ray expansions and scalar wave reflection at canonically perturbed boundaries

2018 ◽  
Vol 30 (1) ◽  
pp. 1-22 ◽  
Author(s):  
R.H. TEW
Keyword(s):  
High Frequency ◽  
Wave Reflection ◽  
Cylindrical Wave ◽  
Planar Boundary ◽  
Extra Term ◽  
Linear Waves ◽  
Standard Application ◽  
Geometrical Theory Of Diffraction ◽  
Appl Math ◽  
Wave Incidence

This paper concerns the reflection of high-frequency, monochromatic linear waves of wavenumber k(≫ 1) from smooth boundaries which are O(k−1/2) perturbations away from either a specified near-planar boundary or else from a given smooth, two-dimensional curve of general O(1) curvature. For each class of perturbed boundary, we will consider separately plane and cylindrical wave incidence, with general amplitude profiles of each type of incident field. This interfacial perturbation scaling is canonical in the sense that a ray approach requires a modification to the standard WKBJ ‘ray ansatz’ which, in turn, leads to a leading-order amplitude (or ‘transport’) equation which includes an extra term absent in a standard application of the geometrical theory of diffraction. This extra term is unique to this scaling, and the afore-mentioned modification that is required is an application of a generalised type of ray expansion first posed by F. G. Friedlander and J. B. Keller (1955 Commun. Pure Appl. Math.6, 387–394).

NOISE SHIELDING BY SIMPLE BARRIERS: COMPARISON BETWEEN THE PERFORMANCE OF SPHERICAL AND LINE SOUND SOURCES

2000 ◽  
Vol 08 (03) ◽  
pp. 495-502 ◽  
Author(s):  
D. OUIS
Keyword(s):  
Sound Source ◽  
Insertion Loss ◽  
Line Source ◽  
Wave Reflection ◽  
Noise Source ◽  
Sound Level ◽  
Sound Sources ◽  
Noise Shielding ◽  
Noise Barrier ◽  
Wave Incidence

This study is concerned with the theoretical solution to the problem of sound screening by simple hard barriers on the ground with special emphasis given to the type of wave incidence, namely a comparison between the use of either a spherical or a cylindrical sound source. For a receiver at the shadow of the noise source, the field may be assumed to be due to the edge wave and for this, exact solutions are used. Regarding the wave reflection on an impedance ground, exact formulations are also used, and finally, some calculations are made on the performance of a hard noise barrier on a two-impedance ground. As a conclusion, it is found that although the sound level at the receiver may show some small differences depending on the frequency and on the geometry of the problem, the overall insertion loss of the thin hard barrier is almost the same for the spherical and the line source, and the differences are found to amount to less than 1 dB for geometries of practical occurrence.

scholarly journals Evaluation of Cerebrovascular Impedance and Wave Reflection in Mouse by Ultrasound

2015 ◽  
Vol 35 (3) ◽  
pp. 521-526 ◽  
Author(s):  
Christopher K Macgowan ◽  
Sarah Joy Stoops ◽  
Yu-Qing Zhou ◽  
Lindsay S Cahill ◽  
John G Sled
Keyword(s):  
Blood Flow ◽  
Carotid Artery ◽  
High Frequency ◽  
Input Impedance ◽  
Wave Reflection ◽  
Arterial Compliance ◽  
High Frequency Ultrasound ◽  
Microvascular Changes ◽  
Total Arterial Compliance ◽  
Frequency Ultrasound

Genetic and surgical mouse models are commonly used to study cerebrovascular disease, but their size makes invasive hemodynamic testing technically challenging. The purpose of this study was to demonstrate a noninvasive measurement of cerebrovascular impedance and wave reflection in mice using high-frequency ultrasound in the left common carotid artery (LCCA), and to examine whether microvascular changes associated with hypercapnia could be detected with such an approach. Ten mice (C57BL/6J) were studied using a high-frequency ultrasound system (40 MHz). Lumen area and blood flow waveforms were obtained from the LCCA and used to calculate pulse-wave velocity, input impedance, and reflection amplitude and transit time under both normocapnic and hypercapnic (5% CO2) ventilation. With hypercapnia, vascular resistance was observed to decrease by 87%±12%. Although the modulus of input impedance was unchanged with hypercapnia, a phase decrease indicative of increased total arterial compliance was observed at low harmonics together with an increased reflection coefficient in both the time (0.57±0.08 versus 0.68±0.08, P=0.04) and frequency domains (0.62±0.08 versus 0.73±0.06, P=0.02). Interestingly, the majority of LCCA blood flow was found to pass into the internal carotid artery (range=76% to 90%, N=3), suggesting that hemodynamic measurements in this vessel are a good metric for intracerebral reactivity in mouse.

scholarly journals High-frequency wavepackets in turbulent jets

2017 ◽  
Vol 830 ◽  
Author(s):  
Kenzo Sasaki ◽  
André V. G. Cavalieri ◽  
Peter Jordan ◽  
Oliver T. Schmidt ◽  
Tim Colonius ◽  
...  
Keyword(s):  
High Frequency ◽  
Turbulent Jets ◽  
Initial Growth ◽  
Mean Flow ◽  
Flow Equations ◽  
Eddy Simulation ◽  
Linear Waves ◽  
Large Eddy ◽  
Homogeneous Linear ◽  
Good Agreement

Wavepackets obtained as solutions of the flow equations linearised around the mean flow have been shown in recent work to yield good agreement, in terms of amplitude and phase, with those educed from turbulent jets. Compelling agreement has been demonstrated, for the axisymmetric and first helical mode, up to Strouhal numbers close to unity. We here extend the range of validity of wavepacket models to Strouhal number $St=4.0$ and azimuthal wavenumber $m=4$ by comparing solutions of the parabolised stability equations with a well-validated large-eddy simulation of a Mach 0.9 turbulent jet. The results show that the near-nozzle dynamics can be correctly described by the homogeneous linear model, the initial growth rates being accurately predicted for the entire range of frequencies and azimuthal wavenumbers considered. Similarly to the lower-frequency wavepackets reported prior to this work, the high-frequency linear waves deviate from the data downstream of their stabilisation locations, which move progressively upstream as the frequency increases.

Cylindrical-wave reflection and antireflection at media interfaces

1994 ◽  
Vol 33 (31) ◽  
pp. 7431 ◽  
Author(s):  
Yuan Jiang ◽  
Jill Hacker
Keyword(s):  
Wave Reflection ◽  
Cylindrical Wave

New structural conditions on decay property with regularity-loss for symmetric hyperbolic systems with non-symmetric relaxation

2018 ◽  
Vol 15 (01) ◽  
pp. 149-174 ◽  
Author(s):  
Yoshihiro Ueda ◽  
Renjun Duan ◽  
Shuichi Kawashima
Keyword(s):  
High Frequency ◽  
Dissipative Structure ◽  
Hyperbolic Systems ◽  
Parabolic Type ◽  
Physical Models ◽  
Fourier Space ◽  
High Frequency Region ◽  
Standard Type ◽  
New Concepts ◽  
Appl Math

This paper is concerned with the weak dissipative structure for linear symmetric hyperbolic systems with relaxation. The authors of this paper had already analyzed the new dissipative structure called the regularity-loss type in [Y. Ueda, R. Duan and S. Kawashima, Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application, Arch. Ration. Mech. Anal. 205 (2012) 239–266]. Compared with the dissipative structure of the standard type in [T. Umeda, S. Kawashima and Y. Shizuta, On the devay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math. 1 (1984) 435–457; Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249–275], the regularity-loss type possesses a weaker structure in the high-frequency region in the Fourier space. Furthermore, there are some physical models which have more complicated structure, which we discussed in [Y. Ueda, R. Duan and S. Kawashima, Decay structure of two hyperbolic relaxation models with regularity loss, Kyoto J. Math. 57(2) (2017) 235–292]. Under this situation, we introduce new concepts and extend our previous results developed in [Y. Ueda, R. Duan and S. Kawashima, Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application, Arch. Ration. Mech. Anal. 205 (2012) 239–266] to cover those complicated models.

SCATTERING NEAR A PLANE INTERFACE USING A GENERALIZED METHOD OF IMAGES APPROACH

2004 ◽  
Vol 12 (02) ◽  
pp. 233-256 ◽  
Author(s):  
ARNAUD COATANHAY ◽  
JEAN-MARC CONOIR
Keyword(s):  
Plane Wave ◽  
Acoustic Field ◽  
High Frequency ◽  
Plane Interface ◽  
Geometrical Theory ◽  
Method Of Images ◽  
Asymptotic Results ◽  
Plane Wave Incident ◽  
Geometrical Theory Of Diffraction ◽  
Long Cylinder

A new method for predicting the scattered acoustic field due to a plane wave incident upon an infinitely long cylinder lying near an penetrable plane interface is presented. The method generalizes the method of images which is restricted to rigid and soft plane interfaces. Validity domains, physical interpretations, simulations and numerical results are described for sedimentary medium-fluid plane interfaces. And, they are well compared with high frequency asymptotic results based on the Geometrical Theory of Diffraction(G.T.D.).

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