Vortex ring bubbles
Abstract
Toroidal bubbles with circulation are studied numerically and by means of a physically motivated model equation. Two series of computations are performed by a boundaryintegral method. One set shows the starting motion of an initially spherical bubble as a gravitationally driven liquid jet penetrates through the bubble from below causing a toroidal geometry to develop. The jet becomes broader as surface tension increases and fails to penetrate if surface tension is too large. The dimensionless circulation that develops is not very dependent on the surface tension. The second series of computations starts from a toroidal geometry, with circulation determined from the earlier series, and follows the motion of the rising and spreading vortex ring. Some modifications to the boundaryintegral formulation were devised to handle the multiply connected geometry. The computations uncovered some unexpected rapid oscillations of the ring radius. These oscillations and the spreading of the ring are explained by the model equation which provides a more general description of vortex ring bubbles than previously available.
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 March 1991
 DOI:
 10.1017/S0022112091001702
 Bibcode:
 1991JFM...224..177L
 Keywords:

 Boundary Integral Method;
 Bubbles;
 Computational Fluid Dynamics;
 Vortex Rings;
 Gravitational Effects;
 Interfacial Tension;
 Toroids;
 Fluid Mechanics and Heat Transfer