The inner and outer flow fields due to a pair of spheres moving unsteadily through a compressible fluid: rectilinear motion

Abstract

Two rigid spheres with equal radii a 0 move with variable speed along their line of centres, through an inviscid compressible fluid. The acoustic velocity potential is determined asymptotically when a typical speed u 0 of the spheres is small compared with the mean sound speed c 0 and the separation of the two spheres varies on a time scale t 0 = a 0 /u 0 . Inner and outer asymptotic approximations are matched and the distant sound field is expressed in terms of point sources of monopole, dipole and quadrupole type.