On the velocity structure in clumpy planetary nebulae

Hydrodynamical, axisymmetric simulations and analytic calculations are presented for the interaction of a fast tenuous stellar wind with a spherical distribution of high-density clouds or clumps embedded in a stationary intercloud medium with an approximately inverse square density fall-off. Two distinct cases are studied. In the first case, clumps are formed by dynamic and thermal instabilities in the shocked wind. In the second case clumps, are assumed to have been formed by inhomogeneities in the AGB wind, prior to the onset of the fast wind. We find that the velocity distribution of these two cases is very different. However, in both cases the ensemble of clumps develops a positive velocity gradient with distance, and the kinematics might provide information on the evolutionary stage of the nebula.