Numerical study of the non-linear stage of thermal instability in cooling flows - II. The non-linear perturbation in the case of a spherically symmetric background flow

Abstract

Two-dimensional numerical hydrodynamical calculations of thermal instability in cooling flows have been performed in a spherical coordinate system, in order to investigate the evolution of the nonlinear axisymmetric perturbation. If the relative density contrast is smaller than the critical value the perturbation decays, due to the formation of the vortex ring before the perturbation cools. One-dimensional spherically symmetric calculations are carried out, and it is shown that even if the density contrast is smaller than the critical value, in the case of the spherically symmetric perturbation it can cool. The numerical results show that the non-radial motion is very important for the evolution of the nonlinear perturbation.