Negatively buoyant projectiles – from weak fountains to heavy vortices

Abstract

An experimental investigation to establish the maximum rise height zm attained by a finite volume of fluid forced impulsively vertically upwards against its buoyancy into quiescent surroundings of uniform density is described. In the absence of a density contrast, the release propagates as a vortex ring and the vertical trajectory is limited by viscous effects. On increasing the source density of the release, gravitational effects limit the trajectory and a maximum rise height zm is reached. For these negatively buoyant releases, the dependence of zm on the length L of the column of ejected fluid, nozzle diameter D (= 2r0), dispensing time and source reduced gravity is determined by injecting saline solution into a fresh-water environment. For 3.4 ≲ L/D ≲ 9.0, zm/r0 is shown to scale on the source parameter η = Fr(L/D), a product of the source Froude number Fr and the aspect ratio L/D for the finite-volume release. Our results show that the morphology of the cap that develops above the source and the vortical motion induced within are sensitively dependent on the source conditions. Moreover, three rise-height regimes are identified: ‘weak-fountain-transition’, ‘vorticity-development’ and ‘forced-release’ regimes, each with a distinct morphology and dependence of dimensionless rise height on η.