Laminar to Turbulent Buoyant Vortex Ring Regime in Terms of Reynolds Number, Bond Number, and Weber Number

When buoyant vortex rings form, azimuthal disturbances occur on their surface. When the magnitude of the disturbance is sufficiently high, the ring will become turbulent. This paper establishes conditions for categorization of a buoyant vortex ring as laminar, transitional, or turbulent. The transition regime of enclosed-air buoyant vortex rings rising in still water was examined experimentally via two high-speed cameras. Sequences of the recorded pictures were analyzed using matlab. Key observations were summarized as follows: for Reynolds number lower than 14,000, Bond number below 30, and Weber number below 50, the vortex ring could not be produced. A transition regime was observed for Reynolds numbers between 40,000 and 70,000, Bond numbers between 120 and 280, and Weber number between 400 and 800. Below this range, only laminar vortex rings were observed, and above, only turbulent vortex rings.

A balloon bursting underwater

A buoyant vortex ring produced by an underwater bursting balloon was studied experimentally. The effect of dimensionless surface tension on characteristics including rise velocity, rate of expansion, circulation, trajectory, and lifetime of the vortex ring bubble was investigated. Results showed reasonable agreement with the literature on vortex rings produced by conventional approaches. It was observed that as the dimensionless surface tension increased, the rise velocity, the circulation and consequently the stability of the vortex ring bubble increased; however, the rate of expansion tends toward constant values. A semi-analytical model is proposed by modifying the drag-based model presented by Sullivan et al. (J. Fluid Mech., vol. 609, 2008, pp. 319–347) to make it applicable to buoyant vortex rings. The modified model suggests that the vortex ring expansion is essentially due to the buoyancy force. An expression is also derived for the circulation in terms of the initial volume of the balloon and the depth at which the balloon bursts.

A comparison between buoyant vortex rings and vortex pairs

In this paper it is shown how earlier results for buoyant vortex rings may be extended to describe the corresponding two-dimensional case, which arises in the theory of bent-over plumes. It is again assumed that in uniform surroundings the circulation remains constant while the buoyancy acts to increase the momentum of the pair. The behaviour in two dimensions is quite different from that in three, however; a buoyant vortex ring spreads linearly with height, whereas a buoyant pair spreads exponentially with height, or linearly with time (and therefore, in a bent-over plume, linearly with distance downwind).The theory has been extended to describe the rise of buoyant rings and pairs through stably stratified surroundings having a linear density gradient. The behaviour near the maximum height reached is found to depend critically in both cases on the relative rates at which the circulation and the momentum fall to zero. If these reach zero together, the rings or pairs will steadily increase in size and come to rest at a finite height and with a finite radius. If the circulation is non-zero when the momentum vanishes, the radius begins to decrease soon after the buoyancy becomes zero, and the vortices will therefore tend to break up suddenly and mix into their surroundings. There is a considerable increase in the final height which should be attained by vortex rings or bentover plumes if the initial circulation is increased; it is suggested that releasing smoke intermittently, rather than continuously, at high velocity might be a means of increasing the effective height of chimneys in calm conditions. When the circulation reaches zero before the momentum does, the solutions indicate that the radius becomes very large near the level of zero buoyancy.