  An evolution of a spherical region, subjected to uniform buoyancy force, is
investigated. Incompressibility and axial symmetry are assumed, together with a
buoyancy discontinuity at the boundary. The boundary turns into a vortex sheet
and the system evolves into a ring. Contrary to the case of mechanically
generated rings, buoyancy-driven rings are unstable. This is due to the
generation of negative vorticity at the bottom. Furthermore, a sequence of
Kelvin-Helmholtz instabilities arises along the buoyancy anomaly boundary. This
sequence transfers the energy toward large scales with $\kappa^{-3}$
distribution. The vortex blob method has been used to simulate the system
numerically. An optimization algorithm, used previously in two dimensions, has
been extended to the axisymmetric case. It reduces computational complexity
from $N^2$ to $N \log N$, where N is the number of nodes. Additionally, a new
algorithm has been developed as a remedy for the exponential growth of the
number of nodes required. It exploits a tendency of the vortex sheet to form
many parallel stripes, by merging them together.
