TY - JOUR

T1 - Anomalies of Acoustic Wave Scattering Near the Cut-off Points of Continuous Spectrum (A Review)

AU - Nazarov, S. A.

N1 - Funding Information: This work was supported by the Russian Scientific Foundation (project no. 17-11-01003). Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - Several anomalies of wave scattering that occur in acoustic waveguides with cylindrical or corrugated rigid walls at frequencies close to the cut-off points (thresholds) of continuous spectrum are considered. The notion of threshold resonances generated by "almost standing waves", which cause no energy transfer to infinity, is introduced. For corrugated waveguides, examples are presented to illustrate the opening of spectral gaps (wave stopping zones) and eigenvalues near their edges and common or degenerate thresholds. Weinstein's and Wood's anomalies are described, which occur above and below the thresholds and manifest themselves in "almost complete" reflection and transmission of waves, and in disproportionally fast variation of the diffraction pattern, respectively. Examples of complete wave transmission ("invisibility of obstacle") are discussed along with the procedures of sharpening and smoothing of Wood's anomalies, specifically, formation of eigenvalues embedded into the continuous spectrum and corresponding trapped waves. The Sommerfeld, Umov-Mandelshtam, and limiting absorption principles are compared along with the specific features of their application at thresholds.

AB - Several anomalies of wave scattering that occur in acoustic waveguides with cylindrical or corrugated rigid walls at frequencies close to the cut-off points (thresholds) of continuous spectrum are considered. The notion of threshold resonances generated by "almost standing waves", which cause no energy transfer to infinity, is introduced. For corrugated waveguides, examples are presented to illustrate the opening of spectral gaps (wave stopping zones) and eigenvalues near their edges and common or degenerate thresholds. Weinstein's and Wood's anomalies are described, which occur above and below the thresholds and manifest themselves in "almost complete" reflection and transmission of waves, and in disproportionally fast variation of the diffraction pattern, respectively. Examples of complete wave transmission ("invisibility of obstacle") are discussed along with the procedures of sharpening and smoothing of Wood's anomalies, specifically, formation of eigenvalues embedded into the continuous spectrum and corresponding trapped waves. The Sommerfeld, Umov-Mandelshtam, and limiting absorption principles are compared along with the specific features of their application at thresholds.

KW - cut-off points of continuous spectrum

KW - cylindrical and corrugated acoustic waveguides

KW - eigenfrequencies and trapped waves

KW - radiation conditions

KW - spectral gaps (stopping zones)

KW - threshold and augmented scattering matrices

KW - threshold resonances

KW - Wood’s and Weinstein’s anomalies

KW - QUANTUM

KW - SURFACE-WAVES

KW - GUIDE

KW - TRAPPED MODES

KW - ASYMPTOTIC EXPANSIONS

KW - PERIODIC BOUNDARY

KW - DIFFRACTION

KW - MEDIA

KW - Wood's and Weinstein's anomalies

KW - GAPS

KW - WOODS ANOMALIES

UR - http://www.scopus.com/inward/record.url?scp=85090377140&partnerID=8YFLogxK

U2 - 10.1134/S1063771020050115

DO - 10.1134/S1063771020050115

M3 - Review article

AN - SCOPUS:85090377140

VL - 66

SP - 477

EP - 494

JO - Acoustical Physics

JF - Acoustical Physics

SN - 1063-7710

IS - 5

ER -