A surprising observation on the quarter-plane diffraction problem

Raphael Assier, I David Abrahams

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we revisit Radlow's highly original attempt at a double Wiener-Hopf solution to the canonical problem of wave diffraction by a quarter-plane. Using a constructive approach, we reduce the problem to two equations, one containing his somewhat controversial ansatz, and an additional compatibility equation. We then show that despite Radlow's ansatz being erroneous, it gives surprisingly accurate results in the far-field, in particular for the spherical diffraction coefficient. This unexpectedly good result is established by comparing it to results obtained by the recently established modified Smyshlyaev formulae.
Original languageEnglish
Pages (from-to)60-90
Number of pages31
JournalSIAM Journal of Applied Mathematics
Volume81
Issue number1
Early online date6 Dec 2020
DOIs
Publication statusPublished - Jan 2021

Keywords

  • wave diffraction
  • quarter-plane
  • Wiener--Hopf
  • diffraction coefficient

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