Instability of a one-dimensional collapsing cloud

The instability of an one-dimensional collapsing cloud, described by the Zel'dovich solution, with respect to small perturbations is considered. The instability in the case of the one-dimensional contraction is shown to be of kinematic nature. The perturbations at late enough stages represent strongly oblate configurations. The amplitude of perturbations, for which the influence of pressure on their evolution is negligible, is growing with the contraction of the cloud proportionally to its density. The perturbations with the characteristic mass are sound waves. The effective rate of growth of the perturbations with the increasing cloud density in the one-dimensional case will be essentially larger than under spherically symmetrical contraction. The application of the results obtained to the investigation of the one-dimensional collapse of real, weakly-perturbed clouds is discussed