Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge
Hewett, D. P., Ockendon, J. R. and Allwright, D. J. (2011) Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge. Wave Motion, 48 (3). pp. 197-213. ISSN 0165-2125
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To link to this article DOI: 10.1016/j.wavemoti.2010.10.005
This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We ﬁrst review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the ﬁeld is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.