Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries

Radjen, Anthony; Gradoni, Gabriele; Tew, Richard

Abstract

Reflection and transmission phenomena associated with high-frequency linear wave incidence on irregular boundaries between adjacent acoustic or electromagnetic media, or upon the irregular free surface of a semi-infinite elastic solid, are studied in two dimensions. Here, an ‘irregular’ boundary is one for which small-scale undulations of an arbitrary profile are superimposed upon an underlying, smooth curve (which also has an arbitrary profile), with the length scale of the perturbation being prescribed in terms of a certain inverse power of the large wave-number of the incoming wave field. Whether or not the incident field has planar or cylindrical wave-fronts, the associated phase in both cases is linear in the wave-number, but the presence of the boundary irregularity implies the necessity of extra terms, involving fractional powers of the wave-number in the phase of the reflected and transmitted fields. It turns out that there is a unique perturbation scaling for which precisely one extra term in the phase is needed and hence for which a description in terms of a Friedlander–Keller ray expansion in the form as originally presented is appropriate, and these define a ‘distinguished’ class of perturbed boundaries and are the subject of the current paper.

Citation

Radjen, A., Gradoni, G., & Tew, R. (2019). Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries. IMA Journal of Applied Mathematics, 84(6), 1203-1219. https://doi.org/10.1093/imamat/hxz029

• Journal Article Type: Article
• Acceptance Date: Oct 3, 2019
• Online Publication Date: Dec 23, 2019
• Publication Date: Dec 23, 2019
• Deposit Date: Jan 3, 2020
• Publicly Available Date: Dec 24, 2020
• Journal: IMA Journal of Applied Mathematics
• Print ISSN: 0272-4960
• Electronic ISSN: 1464-3634
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 84
• Issue: 6
• Pages: 1203-1219
• DOI: https://doi.org/10.1093/imamat/hxz029
• Keywords: Applied Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/3659510
• Publisher URL: https://academic.oup.com/imamat/advance-article/doi/10.1093/imamat/hxz029/5681665
• Additional Information: This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record Anthony Radjen, Gabriele Gradoni, Richard Tew, Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries, IMA Journal of Applied Mathematics, hxz029, https://doi.org/10.1093/imamat/hxz029 is available online at: https://doi.org/10.1093/imamat/hxz029