Isotropic Wave Dispersion

L. Chee-Seng, S. R. Majumdar, D. R. Westbrook
1976 Proceedings of the Royal Society A  
An isotropic multidimensional medium is propagating dispersive radiation from a suddenly triggered immersed point source. The la tte r's subsequent action is postulated as being transient. A contour integration technique accounts for a p art tim e zero condition plus other supplem entary hypo theses (e.g. th a t of stability), leading via the stationary phase technique to an asym ptotic solution valid for large time. One set of results holds a t com parably far range. In the ensuing dispersion,
more » ... ensuing dispersion, concentrically expanding trains of K elvin approxim ated waves get em itted. These wave train s are generally bounded by spherical advancing frontal and/or rear edges near which A iry-type approxim ations can be made. Several such edges m ay coincide or almost coincide. A nother set of results, involving H ankel or Bessel functions, holds a t any given finite range; it indicates slow wave packets and implies, consistent w ith a transient source, th e ultim ate a tta in m ent of a steady state of silence, possibly w ithin a ' slowest ' spherical edge. Applications are illustrated for elastic plate deflexions and K lein-G ordon governed motions. T*(or) = (2rc)-1J exp r oo+ i y the function T(t)H(t) = T * (o -)ex p (-k rt)d (r. (1.4) J -co+iy f On leave of absence from : D epartm ent of M athem atics, U n iv ersity o f M alaya, K uala Lumpur. [ 205 ] Vol. 349. A. 14-2
doi:10.1098/rspa.1976.0068 fatcat:dqtdrw467jffbnn5pl5lq45wda