Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse transverse to the axis

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis and directed transverse to the axis is studied on the basis of the linearized Navier-Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. The flow behaviour differs qualitatively from that for a point impulse in the direction of the axis in that there is no coupling to a diffusive sound mode. As a consequence, the transverse velocity autocorrelation function of a suspended Brownian particle decays at long times faster than t(-3/2).