  A general formulation is presented for studying the motion of buoyant
vortices in a homogeneous ambient fluid. It extends the well-known Hamiltonian
framework for interacting homogeneous point vortices to include buoyancy
effects acting on the vortices. This is then used to systematically examine the
buoyant 1-, 2-, and 3-vortex problems. In doing so we find that 2 buoyant
vortices may either evolve as a pair in bounded circular orbits, or as two
independent unbounded vortices that drift apart, and a criteria is found to
distinguish these cases. Special attention is given to the buoyant vortex
couple, consisting of two vortices of equal and opposite circulation, and equal
buoyancy anomaly. We show that a theoretical maximum height is generally
possible for the rise (or fall) of such couples against buoyancy forces.
Finally, the possibility and onset of chaotic motions in the buoyant 3-vortex
problem is addressed. In contrast to the homogeneous 3-vortex problem, the
buoyant vortex system shows evidence that chaos is present. We also demonstrate
the chaotic advection of tracer parcels arising from the flow field induced by
just 2 buoyant vortices.
