Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries
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 ea...
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| Format: | Article |
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Cambridge University Press
2018
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| Online Access: | https://eprints.nottingham.ac.uk/48432/ |
| _version_ | 1848797761278836736 |
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| author | Tew, R.H. |
| author_facet | Tew, R.H. |
| author_sort | Tew, R.H. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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 ('GTD'). 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 [1]. |
| first_indexed | 2025-11-14T20:09:01Z |
| format | Article |
| id | nottingham-48432 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:09:01Z |
| publishDate | 2018 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-484322020-05-04T19:25:54Z https://eprints.nottingham.ac.uk/48432/ Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries Tew, R.H. 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 ('GTD'). 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 [1]. Cambridge University Press 2018-01-04 Article PeerReviewed Tew, R.H. (2018) Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries. European Journal of Applied Mathematics . ISSN 1469-4425 Geometrical theory of diffraction (GTD); ray theory; WKBJ-method; wave asymptotics; linear waves; asymptotic methods; high-frequency scattering https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/friedlanderkeller-ray-expansions-and-scalar-wave-reflection-at-canonically-perturbed-boundaries/BAD0FA4F8AA5BEEC48F91BFD7CA362E9 doi:10.1017/S0956792517000353 doi:10.1017/S0956792517000353 |
| spellingShingle | Geometrical theory of diffraction (GTD); ray theory; WKBJ-method; wave asymptotics; linear waves; asymptotic methods; high-frequency scattering Tew, R.H. Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries |
| title | Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries |
| title_full | Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries |
| title_fullStr | Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries |
| title_full_unstemmed | Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries |
| title_short | Friedlander-Keller ray expansions and scalar wave reflection at canonically-perturbed boundaries |
| title_sort | friedlander-keller ray expansions and scalar wave reflection at canonically-perturbed boundaries |
| topic | Geometrical theory of diffraction (GTD); ray theory; WKBJ-method; wave asymptotics; linear waves; asymptotic methods; high-frequency scattering |
| url | https://eprints.nottingham.ac.uk/48432/ https://eprints.nottingham.ac.uk/48432/ https://eprints.nottingham.ac.uk/48432/ |