Buoyant vortex rings

Abstract

It is pointed out that there is a fundamental difference in the behaviour of vortex rings projected upwards, according as they do or do not contain fluid which is lighter than the surroundings. A theory based on the perfect fluid approximation is developed to describe the motion of buoyant rings in a uniform fluid. The essential assumption is that the circulation remains constant with time while the buoyancy force acts to increase the impulse of a ring. This leads to the prediction that increasing the buoyancy will give a greater rate of expansion and a lower velocity of rise. The theory is extended to the case of a ring rising through a stably stratified fluid having a constant density gradient; in this case increasing the buoyancy should lead to a lower final height. The predictions of the theory have been verified by carrying out experiments in the laboratory with small vortex rings formed in water, using methylated spirits and salt to produce the density differences. The observations suggest that substantially the same analysis may be applicable to phenomena on a larger scale in the atmosphere; the velocity and final height of an explosion cloud should be determined by the buoyancy and circulation generated near the ground and the stability conditions of the atmosphere.