Exact solutions for transient spherical radiation

Abstract

Closed-form, analytic solutions are derived for exterior wave fields generated by the transient, axisymmetric motion of a spherical boundary. These are intended for use as benchmark problems for assessing the accuracy and correctness of transient numerical schemes. Classical Laplace transform methods are used. The derivation of these solutions is presented in sufficient detail to permit their reconstruction by the reader for multipoles of order n where 0 < or = n < or = 25. Composite solutions can also be obtained by superposition. A novel solution of this type is presented for the wave field generated by the transient motion of a spherical piston in a spherical baffle. The transient wave fields obtained in this way are shown to be consistent with steady time-harmonic solutions for large times, and with high-resolution transient numerical solutions at finite times.