THE INNER AND OUTER FLOW-FIELDS DUE TO A PAIR OF SPHERES MOVING UNSTEADILY THROUGH A COMPRESSIBLE FLUID - RECTILINEAR MOTION

Two rigid spheres with equal radii a(0) move with variable speed along their line of centres, through an inviscid compressible fluid. The ac oustic 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 an d the distant sound field is expressed in terms of point sources of mo nopole, dipole and quadrupole type.